SMART: spatial multi-omic aggregation using graph neural networks and metric learning

Domain: biology
Published: 2026-03-27
Editorial outcome: major_revision

Abstract
Spatial multi-omics enables the exploration of tissue microenvironments and heterogeneity from the perspective of different omics modalities across distinct spatial domains within tissues. To jointly analyze the spatial multi-omics data, computational methods are desired to integrate multiple omics with spatial information into a unified space. Here, we present SMART (Spatial Multi-omic Aggregation using gRaph neural networks and meTric learning), a computational framework for spatial multi-omic integration. SMART leverages a modality-independent modular and stacking framework with spatial coordinates and adjusts the aggregation using triplet relationships. SMART excels at accurately identifying spatial regions of anatomical structures, compatible with spatial datasets of any type and number of omics layers, while demonstrating exceptional computational efficiency and scalability on large datasets. Moreover, a variant of SMART, SMART-MS, expands its capabilities to integrate spatial multi-omics data across multiple tissue sections. In summary, SMART provides a versatile, efficient, and scalable solution for integrating spatial multi-omics data.

Introduction
In recent years, spatial single-omics technologies, such as spatial transcriptomics, epigenomics, and metabolomics have established a vital role and are regarded as next generation techniques in biological and medical research. The emergence of spatial multi-omics enables simultaneous detection of different modal omics within the same tissue section, which offers valuable perspectives for in-depth analysis and understanding of gene regulation and microenvironment. Currently, the predominant spatial multi-omics technologies encompass simultaneous detection of spatial transcriptomics and epigenomics, such as CUT&Tag-RNA-seq1 and MISAR-seq2, as well as the concurrent detection of spatial transcriptomics and proteomics including SM-Omics3, SPOTS4, GeoMX DSP5, Stereo-CITE-seq6 and 10x Genomics Visium CytAssist. Different omics can provide complementary information of the tissues, but also pose an urgent demand for computational methods capable of integrating multi-omics data and accurately identifying distinct spatial domains, such as anatomical structures or cell types, within tissues.

The main challenge in integrating spatial multi-omics data lies in the inherent biological heterogeneity across different omics, which often exhibit distinct data dimensionalities and distributions. Moreover, the incorporation of spatial coordinate information complicates the integration of these diverse omic data into a unified representation. Graph neural network-based approaches have demonstrated promising performance in modeling spatial information within spatial transcriptomics, such as SpaGCN7, CCST8, STAGATE9, GraphST10, conST11, DeepST12, and SpaceFlow13, but these approaches were originally developed for spatial transcriptomics data and have not yet been applied to spatial multi-omics data integration. Recently, multimodal machine learning methods have been proposed such as contrastive learning-based methods14–17, dynamically learning modality gap18, and hierarchical multimodal metric learning19. Although numerous computational methods have been proposed for multi-omic integration, such as MOFA+20, StabMap21, scMM22, SeuratWNN23, CiteFuse24, totalVI25, SNF26, MEFISTO27, and multiVI28, they do not incorporate the spatial coordinates and are therefore not demonstrated the capability to identify spatial domains within tissue samples. Recently, SpatialGlue29, CellCharter30, MISO31, COSMOS32, SpaMultiVAE33, and PRESENT34 were proposed to integrate multi-omics data with spatial information. However, MISO, CellCharter, and SpaMultiVAE integrate multi-omics features merely through simple concatenation or basic operations, failing to effectively capture and utilize the complementary characteristics among different omics layers, which results in suboptimal integration performance. Although COSMOS constructs graph models based on spatial adjacency, such approaches primarily capture local spatial information and may overlook functionally similar regions that are spatially distant. SpatialGlue constructs separate graphs for spatial coordinates and omics features rather than generating a unified graph representation that jointly models both types of information. Moreover, its dual-attention mechanism leads to increased computational complexity with the number of omics modalities and has not demonstrated to support multi-section analysis. PRESENT mainly models specific omics modalities, and its applicability and scalability to emerging omics technologies remain to be further evaluated. In addition, its computationally intensive statistical parameter estimation process further limits its performance. Therefore, there is an urgent need for a computation method that can construct a unified spatial omics graph representation and efficiently process the spatial multi-omics data from both single and multiple tissue sections.

In this work, we propose SMART (Spatial Multi-omic Aggregation method using gRaph neural networks and meTric learning), an unsupervised deep learning framework that leverages graph sampling, aggregation and metric learning for spatial multi-omic integration. SMART constructs a unified graph by incorporating spatial coordinates and omic features. It learns the graph representations using graph neural networks and refines the aggregation process based on the relationships among omic spots through metric learning, thereby integrating multi-omics data with spatial context into a unified latent space. Furthermore, SMART is applicable to datasets at different spatial resolutions and across multiple tissue sections. To validate the effectiveness of SMART, we first conducted experiments on simulated tri-omics data, which demonstrated that SMART theoretically outperforms other methods in both qualitative and quantitative assessments. Subsequently, we applied SMART to jointly detected spatial transcriptomics and proteomics data from human lymph nodes, as well as jointly detected spatial transcriptomics and epigenomics data from mouse brains. These datasets were generated using a variety of spatial multi-omics technologies, encompassing methods such as 10x Genomics Visium CytAssist, MISAR-seq2, SPOTS4, Stereo-CITE-seq6. SMART demonstrated superior quantitative performance and more accurate spatial domain identification on real-world datasets. Finally, we applied the SMART-MS model, a variant of SMART for Multi-Section analysis, to integrate spatial transcriptomics and proteomics data from mouse spleen and thymus across multiple tissue sections. This approach enabled more precise identification of cell types and anatomical structures within the tissues. These experimental results underscore the advantages of SMART in analyzing spatial multi-omics data.

Results
Overall structure of SMART
SMART is a computational method using graph neural networks combined with metric learning to integrate multiple omics modalities and spatial tissue distribution into a unified latent representation (Fig. 1a). It constructs a graph using spatial coordinates and omic-derived principal components to capture spatial correlations across tissue spots. Some spots may belong to the same cell type or anatomical structure but be spatially distant. To account for this, we applied metric learning with triplet loss to adaptively adjust the latent representation. The input of SMART includes omic matrices from transcriptomics, proteomics, or epigenomics, along with corresponding spatial coordinates indicating locations. SMART aims to derive an integrated representation that can provide a more comprehensive understanding of spatial domains within tissue samples and is applicable to datasets collected by diverse platforms, including 10x Genomics Visium CytAssist, MISAR-seq2, SPOTS4 and Stereo-CITE-seq6. Instead of analyzing raw or highly variable omic features, we applied principal components, which reflect omic variation and synergy for further analysis, aligning with the biological premise that genes function cooperatively. Moreover, spatial omics data are typically sparse due to limitations of current sequencing technologies. Directly similarity calculations based on raw omic features can be misleading, as zero expression from different spots may be incorrectly interpreted as similar. Therefore, we applied principal component analysis (PCA) to each omics, reducing high-dimensional expression data to lower-dimensional representations that retain biologically meaningful patterns. Its variant, SMART-MS, designed for multi-section multi-omics integration, utilizes PCA and Harmony to remove batch effects, and uses the processed data as input to the model (Fig. 1b).

As cells communicate with their neighbors, each cell within a tissue is influenced by its surrounding environment35,36. To model this spatial context, SMART constructs spatial neighbor graphs based on the spatial coordinates of tissue sections through k-nearest-neighbor algorithm (KNN). To integrate omic features with spatial information, we applied graph sampling and aggregation (GraphSAGE37)-based encoders to embed both the spatial neighbor graph and the low-dimensional features obtained through PCA. A fully connected network then integrates the embeddings from different omics to generate unified representations, which can reconstruct omic-specific features through GraphSAGE-based decoders.

However, the spatial neighbor graph only captures local spatial context and neglects spots that are of the same type but located distally within the tissue. Therefore, our model assesses the similarity of principal component between spots to identify similar groups. A mutual nearest neighbor algorithm (MNN) is employed to detect pairs of spots that in each other’s similar group. These spot pairs are then designated as anchor-positive pairs for metric learning. For single-section data, positive samples are selected from within the same section, whereas for multi-section data, positive samples are drawn from different sections. In both cases, negative samples are consistently selected from within the same section as anchors (Fig. 1c). A triplet loss is constructed to guide the spatial graph by adjusting the representation between spots based on their mutual similarity in principal component space, even when they are spatially distant within the tissue.

SMART is designed to preserve the original omics-specific features in the latent space while maintaining similarity between spots and incorporating spatial context. Despite its simplicity, SMART is effective for integrating datasets containing two or three omics layers and is theoretically scalable to both single-omics and more complex multi-omics scenarios. Moreover, SMART supports the integration of spatial multi-omics data across different technologies, resolutions, and tissue sections (Fig. 1d). To validate the design of SMART, we conducted a series of ablation studies, evaluating different graph neural network encoders (e.g., GCN38, GAT39, GraphConv40), strategies for selecting anchor and positive pairs in metric learning, alternative loss functions and other architectural components (Supplementary Table 1 and Supplementary Figs. 1–4).

Moreover, SMART allows for tuning the number of neighbors K in the spatial graph construction and the weight of the triplet loss to bias the embedding toward either cell type or spatial domain preferences (Supplementary Fig. 5). SMART also supports multi-omics integration in scenarios where spots are partially missing within a single section (Supplementary Fig. 6a–e). These experiments demonstrate the robustness and flexibility of the SMART framework.

Benchmarking SMART’s performance using simulated data
We initially evaluated the performance of SMART using simulated spatial multi-omics data with known ground truth, generated following the method proposed by Townes et al.41. The ground truth of the simulated data defines five distinct spatial factors: factors 1 through 4, representing different cell types, and a background category (Fig. 2a). The simulation includes three distinct modalities, RNA, ADT, and ATAC, which exhibit markedly different expression distributions, reflecting the complementary nature of multi-omics data (Fig. 2b). We compared SMART against several representative methods for multi-omics integration at a clustering resolution of 5 clusters, including MOFA+20, MEFISTO27, SpatialGlue29, SNF26, CellCharter30, MISO31, Seurat WNN23, PRESENT34, COSMOS32 and SpaMultiVAE33. Among existing approaches, these are currently the only methods that support the integration of three omics modalities.

Principal components extracted from each individual omic partially revealed 3–5 distinct factors but failed to clearly distinguish all spatial regions (Fig. 2c), highlighting the necessity of integrating complementary multimodal and spatial information. Although MOFA+, MISO, SNF, PRESENT and SpaMultiVAE can integrate multiple omics, they failed to resolve certain regions. SpatialGlue, MEFISTO and COSMOS successfully identified all factors but struggled with precise boundary delineation between spatial regions, whereas WNN introduced substantial noise into the segmentation results. In contrast, SMART and CellCharter not only accurately identified all factors but also closely matched the ground truth, demonstrating superior performance in spatial domain identification (Fig. 2c, d, Supplementary Fig. 6f).

Integration methods aim to generate a unified embedding (representation) of multi-omics data that preserves the original relationships within each omic. To assess how well these relationships are maintained, we evaluated the consistency between the pairwise distances among spots in the original omics and their corresponding distances in the embedded space. Specifically, we calculated the Euclidean distances for all pairs of spots before and after embedding, and based on these, computed the Pearson correlation coefficient to assess the similarity between the original features and the embedded representations. SMART and MOFA+ demonstrated the highest consistency between the original and embedded representations across all modalities, particularly with RNA and ADT (Fig. 2e). These results indicate that both methods maximally preserved the original features of each omics modality during integration, while SMART further incorporated spatial information throughout this process. Within the clusters identified by SMART, we also demonstrated the correlation between each cluster and the individual omics modalities. This analysis reveals that certain clusters tend to be more associated with specific omics features, reflecting the complementary integration of modalities achieved by SMART (Fig. 2f). Moreover, since cells of the same type are often spatially clustered, such as clone populations of T cells42, we evaluated the overall spatial coherence of the embeddings using Moran’s I, a measure of spatial autocorrelation. A higher Moran’s I value indicates a more orderly spatial distribution. However, for certain datasets with complex spatial domain patterns, Moran’s I may be relatively low. SMART achieved Moran’s I scores approaching 1, demonstrating excellent spatial clustering performance (Fig. 2g).

To quantitatively compare the performance of SMART with existing methods, we evaluated clustering accuracy using several standard metrics: Adjusted Rand Index (ARI), Adjusted Mutual Information (AMI), Normalized Mutual Information (NMI), Homogeneity (Homo), Mutual Information (MI), FMI (Fowlkes-Mallows Index) and V-Measure. Across all metrics, SMART consistently achieved the highest performance, followed by CellCharter. In contrast, MISO and SNF did not produce comparable results (Fig. 2h).

SMART is a robust model applicable not only to multi-omics data but also to single-omics modalities. We evaluated its performance separately on RNA, ADT, and ATAC data, as well as their combinations, using various metrics (Fig. 2i). Repeated experiments conducted ten times with different random seeds demonstrated that SMART achieves strong performance even when utilizing only one modality, though slightly lower than results obtained with three modalities. To investigate differences in the embeddings produced by SMART between single-omics and multi-omics data, we compared the k-nearest neighbor graphs derived from SMART embeddings in both scenarios. Specifically, we computed embeddings using SMART for each individual modality (SMART-ADT, SMART-RNA, SMART-ATAC) as well as for the integration of all three modalities (SMART-ADT+RNA+ATAC). For each embedding, we constructed a graph using the k-nearest neighbors (k=10) and recorded all edges. By comparing the edges across these graphs, we found that only 12.1% of the edges in the three-omics embedding were unique, which is lower than the proportion of unique edges found in any single-omics embedding (ATAC: 21.2%; ADT: 17.6%; RNA: 16.1%) (Fig. 2j). This indicates that the tri-modal embedding captures complementary features by integrating information from all modalities.

SMART integrates spatial transcriptomic and proteomic data
To evaluate the effectiveness of SMART on real-world data, we applied SMART and several comparison methods to a co-detected transcriptome and proteome dataset from human lymph node section A1, generated using the 10x Visium Spatial Platform. Hematoxylin and eosin (H&E)-based annotations were used as the ground truth (Fig. 3a). The outer region of the tissue is primarily composed of pericapsular adipose tissue and the capsule, while the inner region includes the cortex, medullary sinuses, and medullary cords. In addition to the previously compared methods, we also included scMM22, TotalVI25, MultiVI28, COSMOS32 and SpaMultiVAE33 for RNA-protein integration, resulting in a total of thirteen comparison methods used to assess the performance of SMART.

The results with a cluster number of 7 demonstrate that SMART not only successfully identified the cortex (cluster 2) and pericapsular adipose tissue (cluster 3), but also more accurately delineated the medullary sinuses (cluster 1) and medullary cords (cluster 5) compared to existing methods (Fig. 3b). In addition, SMART detected smaller structures such as follicles (cluster 6) and the capsule (cluster 4,7) (Fig. 3b, Supplementary Fig. 7). While most other methods were able to reliably identify the cortex, medullary sinuses, medullary cords and pericapsular adipose region, MEFISTO, SNF, COSMOS and CellCharter fail to separate the medullary sinus from the medullary cords due to over-integration of spatial information. In the UMAP (Uniform Manifold Approximation and Projection) visualization, SMART, PRESENT, MISO and SpatialGlue exhibit well-defined cluster boundaries corresponding to the ground truth labels, demonstrating their effectiveness in identifying distinct tissue regions (Fig. 3c).

We further compared the performance of different methods using supervised evaluation metrics, and the results show that SMART demonstrates a significant advantage in quantitative assessments when the number of clusters is set to 7 (Fig. 3d). Considering that the optimal number of clusters may vary across datasets, we additionally evaluated the stability of SMART across a range of clustering resolutions (from 5 to 10 clusters). The results indicate that SMART consistently outperforms other methods under all settings, highlighting its robustness across different clustering granularities (Fig. 3e). In the spatial autocorrelation evaluation, SMART exhibits a moderate performance, as its clustering results closely align with the ground truth labels but do not display particularly pronounced spatial patterns (Fig. 3f). Additionally, for each cluster, we calculated the Pearson correlation coefficients between the original transcriptomic or proteomic features and the unified embeddings generated by SMART by comparing the pairwise relationship among spots before and after embeddings. The results show that SMART exhibits a high degree of consistency between the original and embedded representations (Fig. 3g). Specifically, SMART placed greater emphasis on protein features in clusters 1 and 2, while RNA features contributed more prominently in clusters 3, 4, 5, 6 and 7 (Fig. 3h).

To validate the accuracy of the spatial domains identified by SMART, we extracted spatially specific marker genes and proteins for selected regions (Fig. 3h, i). For example, CD3E and CCR7 show high expression in both RNA and ADT modalities within the cortex (Cluster 3), indicating that this region harbors a higher abundance of T cells compared to other spatial domains (Supplementary Fig. 8). Similarly, in the ADT modality, the medullary sinus (Cluster 1) may have been grouped as a distinct class despite the absence of known spatially specific marker proteins, but it can be reliably annotated based on the expression of spatially enriched genes such as CCN1. These findings demonstrate that SMART effectively leverages the complementary strengths of transcriptomic and proteomic data to identify spatial domains with high biological relevance.

We further evaluated SMART on an additional sample, human lymph node section D1, and observed that it consistently outperformed other methods. These results demonstrate SMART’s strong generalization capability in integrating transcriptomic and proteomic data (Supplementary Figs. 9–11).

SMART integrates spatial transcriptomic and chromatin accessibility data
In addition to integrating spatial transcriptomic and proteomic data, SMART can also fuse spatial transcriptomics with chromatin accessibility. We evaluated SMART’s performance on brain datasets from four developing mice at distinct embryonic stages (E11.0, E13.5, E15.5, and E18.5)2. These datasets were generated using MISAR-seq, a technique that enables spatially resolved joint profiling of chromatin accessibility and gene expression.

Since TotalVI and SpaMultiVAE is not applicable to epigenomic data, we compared SMART with other representative methods, including scMM, WNN, SNF, MultiVI, PRESENT, MOFA+, MEFISTO, MISO, COSMOS, CellCharter and SpatialGlue. We used the unsupervised clustering results from Jiang et al.2 as artificial annotations, which closely match the anatomical structures observed in H&E-stained images of brain at different developmental stages. On the E18.5_S1 brain section, the clustering results for ten regions showed that only WNN, SMART and SpatialGlue produced clear boundaries between different brain areas. Both methods successfully delineated regions such as dorsal pallium (DPallm), portions of the diencephalon, and hindbrain. while these region in other methods were disperse (Fig. 4a, c). However, SMART additionally detected the boundary of a small structure, cartilaga-1, which was not as smoothly defined by SpatialGlue (Fig. 4c). In the manually annotated UMAP visualizations of different methods, the embeddings produced by SMART, WNN, and SpatialGlue exhibited relatively clear boundaries between distinct categories (Fig. 4b, c).

In terms of unsupervised evaluation, SMART better preserved the original multi-omics relationships among spatial spots and ranked third in spatial autocorrelation assessment (Fig. 4d), indicating its effectiveness in identifying continuous spatial domains within the brain. Moreover, we computed the correlations between the original transcriptomic or epigenomic features and the embeddings generated by SMART. The results showed that SMART embeddings exhibited strong correlations with the original features (Fig. 4e), and each SMART cluster tended to align more closely with one specific omic modality (Fig. 4f). In the supervised evaluation using quantitative metrics, SMART also achieved the best performance on the E18.5_S1 section (Fig. 4g).

We further evaluated SMART on the remaining three sections: E11.0_S1, E13.5_S1, and E15.5_S1, which contain 5, 7, and 11 clusters, respectively. The clustering results indicate that, compared with other methods, SMART more effectively reconstructs brain structure across developmental stages. For example, in E15.5_S1, SMART accurately distinguishes the dorsal pallium medial (DPallm) and ventral (DPallv) regions, while in E11.0_S1, it clearly identifies the primary brain and mesenchyme. Moreover, SMART outperformed most methods in terms of supervised evaluation metrics, except on E11.0_S1 where it was surpassed by MOFA+ (Fig. 4c, Supplementary Figs. 12–14).

To quantitatively compare the overall performance, we computed supervised clustering metrics for the results of all spatial multi-omics integration methods across the four sections. SMART consistently achieved the highest scores, highlighting its effectiveness in identifying spatial domains and integrating spatial transcriptomic and chromatin accessibility data (Fig. 4h). These findings further confirm the robustness and superiority of SMART in analyzing spatial RNA and ATAC-seq data.

SMART enables efficient integration of spatial multi-omics data
SMART is an efficient model with fewer parameters and lower computational complexity, enabling the analysis of large-scale datasets. To further demonstrate SMART’s advantages in computational efficiency and resource utilization for multi-omics integration, we evaluated its performance on one of the largest currently available spatial transcriptomics and epigenomics datasets. This dataset, obtained by CUT&Tag–RNA-seq, co-profiles transcriptomic data and H3K27me3 epigenetic marks in the P22 mouse brain, encompassing 9752 spots, 25,881 genes, and 70,470 peaks.

As the dataset lacks ground-truth labels, we determined the number of clusters to be 12 based on internal clustering validation metrics, including mean FMI, SCI (Silhouette Coefficient), and DBI (Davies-Bouldin Index) (Supplementary Fig. 15a, b). While all methods successfully identified major anatomical layers such as the cerebral cortex (CTX), caudoputamen (CP), and genu of the corpus callosum (ccg), SMART, COSMOS, and CellCharter’s integration results exhibited fewer noise artifacts and more clearly defined layer boundaries (Fig. 5a and Supplementary Fig. 15c–e). While CellCharter, MEFISTO, and COSMOS also showed relatively distinct cluster boundaries and achieved high Moran’s I scores for spatial autocorrelation, they tended to overemphasize spatial smoothness at the expense of preserving true anatomical structures (Supplementary Fig. 15f). In comparative analyses of runtime and memory usage, SMART consistently demonstrated the shortest runtime and lowest memory consumption, whereas MEFISTO required the most computational resources (Fig. 5b).

To further validate the efficiency of SMART, we applied it to a large-scale spatial transcriptomics and proteomics co-profiling dataset, the Stereo-CITE-seq dataset of the mouse spleen. Stereo-CITE-seq is a multi-omics technology that integrates spatial transcriptomics (Stereo-seq) with spatial proteomics (CITE-seq), achieving subcellular spatial resolution of up to 500 nanometers. It enables simultaneous measurement of both mRNA and protein expression levels on a single tissue section. Given the high resolution (500 nm) of the raw spatial data, neighboring detection points are commonly aggregated into larger spatial units, or bins, to facilitate analysis and improve the signal-to-noise ratio. For instance, Bin10 denotes the aggregation of 10×10 neighboring detection points into one unit, covering an area of 5µm×5µm for downstream analysis.

We extracted spatial grid data at six resolution levels from the raw dataset (Bin200 to Bin10), with spatial resolution increasing progressively from 100µm (Bin200) to 5µm (Bin10). Correspondingly, the number of spatial locations (spots) increased from 2001 to 756,430. The dataset includes a total of 29,034 genes and 128 ADTs. Considering that most state-of-the-art spatial multi-omics integration methods support GPU acceleration, we compared their GPU memory consumption and training time under a unified GPU environment to evaluate scalability and computational efficiency.

For consistency, we set the number of clusters to 6 across all analyses. SMART maintained strong spatial continuity in its clustering results across different resolutions, with several spatial structures stably identified across adjacent bin sizes. In contrast, clustering results based on RNA or ADT modalities alone showed instability at certain resolutions, with ambiguous cluster boundaries (Fig. 5c). Regarding resource utilization, aside from SpaMultiVAE (which was configured with a batch size of 2000), all methods used a batch size equal to the number of spots, leading to GPU memory usage being directly proportional to the number of spots. Under the same data scale, SMART exhibited the lowest memory usage. Notably, all other methods failed to complete computations on the Bin20 dataset with about 190K spots, whereas SMART ran smoothly even on the largest Bin10 dataset with over 750K spots (Fig. 5d). In terms of training time, SMART completed training on the Bin10 dataset with over 750K spots in only 56 seconds, significantly outperforming all other methods (Fig. 5e). This is attributed to the rapid convergence of the SMART model and the high efficiency of the SAGEConv architecture when handling large-scale graph structures.

In summary, SMART not only demonstrates strong adaptability and stability in spatial multi-omics integration, but also significantly outperforms existing methods in terms of computational efficiency and resource usage, highlighting its broad potential for large-scale spatial data analysis.

SMART enables the integration of multi-omics data across multiple sections
Spatial omics data from biological tissue samples are often derived from multiple tissue sections. To enable multi-omics integration across sections, we developed SMART-MS, an extension of SMART that supports multi-section data integration, batch effect correction, and the construction of cross-section spatial neighbor graphs to align omics features across tissue sections.

We first evaluated the performance of SMART-MS and other methods on a human tonsil dataset. As a critical component of the peripherally lymphoid system, the tonsil plays a central role in mucosal immune defense. It exhibits complex internal architecture and pronounced spatial heterogeneity, characterized by densely arranged lymphocyte clusters. The follicular zone is enriched in B cells and often contains germinal centers; the surrounding mantle zone also consists primarily of B cells; and the interfollicular zone between follicles is a T cell–rich region. The outer regions include epithelial and connective tissue areas, which may contain non-lymphoid cell types such as plasma cells and epithelial-related cells.

The dataset consists of three tissue sections co-profiled with spatial transcriptomics (RNA) and proteomics (ADT) using the 10x Genomics CytAssist Visium platform. UMAP visualization of PCA-reduced features revealed a clear batch effect in the third section, likely due to the fact that the first two are consecutive sections and thus more similar (Supplementary Fig. 16a). In addition, major tissue regions were annotated based on H&E-stained images and used as ground truth for computing supervised metrics.

We compared SMART-MS with several integration methods capable of batch effect removal, including MultiVI, Present-BC, TotalVI, and MOFA+, as well as RNA- or ADT-derived features corrected by Harmony. When setting the number of clusters to 6, we observed that all methods except TotalVI achieved good batch effect removal (Supplementary Fig. 16b). Moreover, while all methods successfully identified the germinal center, MultiVI poorly distinguished the follicular region, and Present-BC and TotalVI failed to accurately detect the epithelial and connective tissue zones. In contrast, SMART-MS accurately identified the follicular and germinal center regions, as well as the outer tonsillar plasma cell/epithelial zones and the interfollicular T cell–enriched regions (Fig. 6a, Supplementary Fig. 16c). The utility of SMART-MS clustering was further validated by the co-expression of marker genes and proteins, such as CD19 in the follicular zone, CR2 in the germinal center, and CD3E and CD4 in T cell–rich areas, across both RNA and ADT modalities (Fig. 6c, d). Furthermore, the proportions of spatial domains were highly consistent across sections (Fig. 6e), and analysis of SMART-MS embeddings revealed modality-specific preferences for each cluster (Fig. 6f).

For quantitative evaluation, we used previously defined supervised metrics for biological signal preservation, and iLISI and kBET scores to assess batch effect removal. SMART-MS achieved the highest overall score among all compared methods and substantially outperformed others in both biological information retention and batch effect correction (Fig. 6b). To control for potential bias from fixed clustering numbers, we also evaluated clustering performance across a range of cluster numbers (4–8). SMART-MS consistently achieved the highest ARI scores both across the three sections collectively and for each individual section (Fig. 6g). In terms of spatial autocorrelation, SMART-MS also attained the highest Moran’s I score (Fig. 6h). These results demonstrate that SMART-MS effectively integrates multi-section data and accurately identifies spatial domains.

To further demonstrate the generalizability of SMART, we conducted additional experiments on two mouse spleen sections generated by SPOTS, three high-resolution mouse thymus sections from Stereo-CITE-seq, and three mouse postnatal brain sections from spatial ATAC-RNA-seq. Although these datasets lack manual annotations to serve as ground-truth labels, SMART-MS was still able to identify distinct spatial structures, for example by distinguishing cell types in the mouse spleen (Supplementary Fig. 17). The similarity metric used for comparing the two sections is cosine similarity. Moreover, it consistently outperformed other methods in terms of batch effect removal and spatial autocorrelation (Supplementary Figs. 18–19).

Methods
Ethics statement
This study exclusively used publicly available datasets. No new human or animal samples were collected, and no experiments involving human participants or animals were performed by the authors. Therefore, ethical approval was not required for this study. Sex and/or gender was not considered in the study design or analysis, as this work focuses on computational method development rather than biological comparisons between sexes or genders, and sex- or gender-disaggregated information was not consistently available across the public datasets used.

Data
Simulated data were generated using the method outlined by Townes et al.41, which is designed to produce synthetic datasets with specific spatial structures, facilitating the validation of the model’s ability to identify and process spatial features effectively. The simulation generated multivariate counts with spatial correlation patterns. We use the ggblocks simulation which is based on the Indian Buffet Process, where each latent factor represents a typical spatial pattern defined over a 36×36 grid of locations (N=1296 spatial locations). For the RNA and ATAC modalities, we generated spatial expression matrices of size 1296 cells×1000 genes (peaks) characterized by four factors and following a zero-inflated negative binomial distribution (ZINB). For the protein modality, we generated a spatial expression matrix of size 1296 cells×100 proteins characterized by four factors and following a negative binomial distribution (NB). The negative binomial distribution introduces randomness by modeling the variability of discrete events. This variability is considered noise, representing the uncertain portion of the data and simulating the random fluctuations observed in real-world data.

10x Genomics CytAssist Visium datasets were generated using the 10x Genomics CytAssist Visium platform, which enables the joint profiling of transcriptome and protein expression. They include the human lymph node dataset used in SMART for spatial transcriptomics and proteomics integration, and the three-section tonsil dataset used in SMART-MS for multi-section integration. This platform integrates spatial whole-transcriptome sequencing with multiplexed protein detection on a single tissue section via next-generation sequencing (NGS), with a spatial resolution of 55µm, a spot spacing of 100µm, and an imaging area of 6.5mm×6.5mm. The lymph node dataset consists of two tissue sections: Human Lymph Node A1 (3484 spots) and D1 (3359 spots), each containing expression profiles of 18,085 genes and 31 proteins. The tonsil dataset includes three sections with 4326, 4519, and 4521 spots, respectively. Each section contains 18,085 genes; the first two sections include 31 proteins, while the third section includes 35 proteins.

MISAR-seq mouse brain datasets were generated by measuring spatial transcriptome and chromatin accessibility in the mouse brain using MISAR-seq², a microfluidic indexing–based spatial assay for transposase-accessible chromatin and RNA sequencing. MISAR-seq enables spatially resolved joint profiling of chromatin accessibility and gene expression. In this dataset, the tissue is positioned on a microfluidic chip, where a grid-based spatial barcoding system assigns unique DNA barcodes across 2500 grids, each 50×50µm, covering approximately 5–20 cells per grid. This dataset includes eight sections of the mouse fetal brain at embryonic days, i.e., E11.0, E13.5, E15.5, and E18.5. The number of grids covered by the sections ranges from 1263 to 2248, with a total of 32,285 sequenced genes and peak counts varying from 60,112 to 143,879.

Spatial Epigenome–Transcriptome mouse brain datasets originate from the method proposed by Zhang et al.1, including spatial ATAC–RNA-seq and CUT&Tag–RNA-seq, which enable simultaneous detection of chromatin accessibility or histone modifications (e.g., H3K27me3, H3K27ac, or H3K4me3) together with gene expression within a single tissue section at near single-cell resolution. In the P22 mouse brain coronal sections, a 100×100 barcode grid (pixel size: 20µm) was used to cover the entire hemisphere region, with most pixels capturing 1–3 cells. The RNA+H3K27me3 dataset used to evaluate the scalability of SMART contains 9752 spots, 70,470 peaks, and 25,881 genes. Meanwhile, the RNA+ATAC dataset used to assess multi-section integration with SMART-MS includes three sections with 2372, 2497, and 9215 spots, respectively, along with 161,514 peaks and 18,107 genes.

STARmap-RIBOmap-Align datasets were generated by applying STARmap, a high-resolution spatial transcriptomics technology developed by Wang et al.46, and RIBOmap, a three-dimensional in situ spatial translatomics method introduced by Zeng et al.47, to consecutive mouse brain tissue sections, enabling joint measurement of transcriptomic and translatomic profiles for 5,413 genes at single-cell and molecular resolution. The STARmap section contained 59,165 spots, and the RIBOmap section contained 58,692 spots. Using the CAST projection algorithm introduced by Tang48, spots from the STARmap section were aligned to those in the RIBOmap section, resulting in dual-omics data for 58,692 spots.

The SPOTS mouse spleen dataset was generated using Spatial PrOtein and Transcriptome Sequencing (SPOTS)⁴ to profile spatial transcriptomic and proteomic data for assessing multi-section integration with SMART-MS. Similar to 10X Human Lymph Node dataset, SPOTS also offers a spatial resolution of 55µm, with a distance of 100µm between spots, covering an imaging area of 6.5mm×6.5mm. This dataset includes two sections, SPOTS Spleen Replicate 1 and SPOTS Spleen Replicate 2, containing 2647 and 2759 spots, respectively, with each section capturing the expression of 32,285 genes and 21 antibody-derived tags (ADTs).

Stereo-CITE-seq datasets were generated using the method proposed by Liao et al.6, which combines CITE-seq with Stereo-seq to enable simultaneous profiling of the transcriptome and proteome on the same tissue section at subcellular spatial resolution (0.5µm) with high reproducibility and precision. This technique achieves a spatial resolution of up to 0.22µm, with a spot spacing of 0.5µm and an imaging area of 200mm². The mouse spleen dataset used to evaluate the scalability of SMART was processed into multiple resolution levels, including Bin10 (5µm), Bin20 (10µm), Bin50 (25µm), Bin100 (50µm), Bin150 (75µm), and Bin200 (100µm), comprising 756,430; 189,867; 30,652; 7,782; 3507; and 2001 spots, respectively. In addition to spot-level representations generated by spatial binning, we also used the image-guided cell segmentation results provided by the Stereo-CITE-seq pipeline (cellbin.gef), in which RNA and protein signals are aggregated at the single-cell level. These data were used to evaluate SMART’s applicability to single-cell–segmented spatial data. This dataset includes expression data for 29,034 genes and 128 ADTs. For evaluating multi-section integration with SMART-MS, we used three mouse thymus sections at Bin50 resolution (25µm), which contain 4253, 4646, and 4228 spots, respectively. Each section captures expression profiles for 23,221 to 23,960 genes and 19 ADTs.

Data preprocessing
Spatial transcriptomic data were preprocessed by first removing genes expressed in fewer than 10 spots to minimize the impact of low-abundance signals. The top 3000 or 5000 highly variable genes were then selected to retain features contributing most to data variability. Expression counts were normalized by scaling the total expression in each spot to 10,000 to account for differences in sequencing depth, followed by logarithmic transformation to reduce the influence of highly expressed genes and approximate a normal distribution. The data were subsequently scaled to zero mean and unit variance.

Spatial chromatin accessibility data were preprocessed by first applying a TF–IDF transformation to accessible chromatin regions, with a scaling factor of 10,000 to downweight commonly accessible regions and emphasize features with higher variability across spots. Peak counts within each spot were then normalized by scaling the total signal to 10,000 to correct for differences in sequencing depth. A logarithmic transformation was subsequently applied to stabilize variance and reduce the influence of highly accessible regions, preparing the data for downstream analyses.

Spatial protein data were preprocessed by first applying a centered log-ratio transformation to remove scale differences across proteins. The data were then standardized to zero mean and unit variance to ensure that all protein features were on a comparable scale for downstream analyses.

The SMART framework
SMART is a deep learning model that leverages graph neural networks and metric learning to integrate spatially-resolved multi-modal omics into unified embeddings. For each modality, SMART extracts principal components (PCs) using principal component analysis (PCA) and constructs spatial neighboring graphs with PCs as node features. Spatial graphs are built based on the coordinates of spatial units using a k-nearest-neighbor (kNN) strategy. In spot-based analyses, nodes correspond to spots or bins, whereas in single-cell–segmented analyses, nodes correspond to individual cells, with cell centroids used as spatial coordinates. For single-cell–segmented data, radius within one cell distance to select the nearest cells around can also be used in spatial graph construction. Then, the model employs SAGEConv (Sample and Aggregate Convolution) to aggregate both the spatial information and the PCs from a specific modal omics, thereby synthesizing a integrate representation of the omics. Ultimately, these representations are combined into a unified intermodal embedding.

However, using spatial neighboring graphs for aggregation may neglect the feature correlations even in long distance. Therefore, we further adjust the graph aggregation using metric learning with triplet loss to ensure the mutual correlation between spots or bins in the original omics. The loss functions of reconstruction to the original omics and the triplet loss are crucial to guarantee the representation of the original omic intact after embedding with spatial information.

In a spatial multi-omics dataset featuring three distinct omics modalities, the inputs to SMART consist of characteristics for each modality X1 2Rm×n1, X2 2Rm×n2, and X3 2Rm×n3 and the spatial coordinates S 2Rm×2. Here m represents the number of spots in the tissue section, while n1, n2, and n3 correspond to the number of features in the transcriptome, proteome, and epigenome. The output of SMART is a unified embedded representation Z 2RN×f in the low-dimensional latent space, which integrates information from multiple spatial omics. The parameter f is denoted as the dimension in the latent space. If there are two omics, the inputs become X1 2Rm×n1, X2 2Rm×n2 and the rest of the operation is the same. Overall, the main components of SMART can be categorized into five modules: principal component analysis, spatial neighboring graph construction, SAGEConv encoder, triplet construction, and SAGEConv decoder. Each module is elaborated in the following sections.

Principal component analysis
We first apply PCA to the preprocessed data from each modality: X1 2Rm×n1, X2 2Rm×n2, and X3 2Rm×n3, in order to reduce the dimensionality of the data to d1, d2 and d3 dimensions, respectively. Specifically, after applying PCA, we obtain the dimensionality-reduced feature matrices: X1 2Rm×d1, X2 2Rm×d2 and X3 2Rm×d3. By retaining the most representative principal components, we achieve the dimensionality reduction. Typically, the dimensionality of the transcriptomics and chromatin accessibility modalities is reduced to 30, while the dimensionality of the proteomics modality is determined based on the number of ADTs.

Spatial neighboring graph construction
To learn the spatial coordination of omics, we constructed a spatial neighbor graph with each spot or bin as node and principal components as node feature. Each node (spot or bin) was connected to its k nearest neighbors according to the Euclidean distance between spots on the coordinates. Consequently, the spatially-resolved omics was converted into an undirected spatial neighbor graph G=(V,E), where V represents m spots and E represent the set of connecting edges among the spots in their k nearest neighbors. The number of neighbors k was set to 4 for datasets with a quadrilateral spatial layout (e.g., SPOTS, MISAR-seq, and Stereo-CITE-seq), and to 6 for 10X Visium data with a hexagonal lattice. We denoted A 2Rm×m as the adjacency matrix of the graph G and Aij = 1 when there is an edge between node i and node j, otherwise Aij = 0.

SAGEConv encoder and multimodal feature integration
SAGEConv (Sample and Aggregate Convolution) is a convolution layer designed to efficiently capture the graph structure and learn high-quality representation for graph features, particularly well-suited for large-scale graph data in spatial multi-omics. Its samples a subset of the neighboring nodes and aggregates their features, thus reducing computational complexity. SAGEConv employs various aggregation functions and is stacked in multiple layers to enhance node representation. For omics i (i 2f1, 2, 3g), we use the principal components Xi as input to SAGEConv encoder to learn the graph-specific representation Hi of each node. hli represents node v’s representation of the original feature of omics i through the l-th (l 2f1, 2, ..., Lg) layer of SAGEConv encoder. The formula is as follows:

h i l N(v) = f(N(v))

hli = g(σ(Wi l [hli-1; hli N(v)]))

where f(x) is an aggregator function and we use the mean function as the aggregate function which formula is as follows:

f(N(v)) = 1/|N(v)| Σ u2N(v) h(u l-1)

N(v) represents the set of neighbors of node v in the spatial neighbor graph G=(V,E). Wi denote a trainable weight matrix and σ(x)=max(0,x) is a nonlinear activation function. The normalization function g(x)= x/||x||2 applies L2 normalization to the updated node embeddings, ensuring that the feature vector for each node has a unit Euclidean norm.

In the output of omics i embeddings hL 2Rf, f is the dimension of latent embedded representation. By default, f is set to 64. We use the fully connected layer to integrate the SAGEConv output of different omics. Assuming integrating three omics, we first perform concatenation, i.e., h = [hL1; hL2; hL3] 2R3f, and obtain latent embedded representation Zv 2Rf that integrates all modalities using fully connected layer

Zv = W*h + b

where W denotes a trainable weight matrix that transforms the input into another feature space, and b denotes a trainable bias vector. The number of GraphSAGE encoder layers was set to two based on the results of an ablation study (Supplementary Fig. 1a).

SAGEConv decoder
SAGEConv decoder is designed to reconstruct the principal components of different omics from the latent embedded representation. For omics i (i 2f1, 2, 3g), we use final latent embedded representation Z as input to SAGEConv decoder to reconstruct the graph-specific representation h e i l of each node. The decoder is composed of multiple stacked layers to enhance reconstruction capabilities. h e i 0 is denoted as the representation of node v reconstruction feature of omics i through the l-th (l 2f1, 2, ..., Lg) layer of SAGEConv decoder. In particular, h e i 0 = Z. The formula is as follows:

h e i l = f(N(v))

h e i l = g(σ(Wi l [h e i l-1; h e i l N(v)]))

where f(x) is an aggregator function as same as formula (3). Wi denote a trainable weight matrix and σ(x)=max(0,x) is a nonlinear activation function. The normalization function g(x)= x/||x||2 applies L2 normalization to the updated node embeddings, ensuring that the feature vector for each node has a unit Euclidean norm. Finally, we get the reconstructed feature h e i L 2Rdi of omics i. The number of GraphSAGE decoder layers was set to two based on the results of an ablation study (Supplementary Fig. 1a).

Reconstruction loss
To guarantee the latent representation appropriately encode and preserve the information of expression features from all the omics, we enforced that different omic features can be recover through the SAGEConv decoder. We applied the reconstruction loss to maximize the similarity between the output of the decoder and the principal components of each omics. Assuming ex iv 2Rdi is principal components of omics i for node v, which is the input to the SAGEConv encoder, the reconstruction feature output by the SAGEConv decoder is h e i L iv 2Rdi. The target is to minimize the difference between h e i L iv and ex iv. Therefore, objective function of the reconstruction loss is:

L recon = Σ I i=1 αi Σ N v=1 ||ex iv - h e i L iv||2

where I represent the number of omics, αi is the weight factor used to adjust the contribution of modality i, and N represents the number of spots in the section, also referring to the number of nodes in the spatial neighboring graph. SMART allow the adjustment of α to meet possible requirements on depending more on one or two omics. In our experiments, we consistently set α to 1. During training, the model will try to minimize the reconstruction loss L recon.

Triplet construction
The spatial neighboring graph is only based on spatial structure and neglects the relationships among spots (for example, spots in the same type) in relatively long distance. Therefore, we adjust the weight in the graph aggregation using metric learning based on the relationship of omic features. We construct triplets, including anchor points, positive points, and negative points among omic features, and regulate the graph aggregation using triplet loss.

To construct the triplets according to omic feature relationships, we calculate the Euclidean distance between the principal components of each omics. For each spot, we select the top k nearest neighbors to form the nearest neighboring set (where k is set to 3 by default). If spot j and spot i are mutually in the nearest neighbor set of each other, then spot i and j serve as the anchor sample ai and positive sample pi. The negative sample ni is chosen from the m×r farthest set of spot i, where m is the number of the total spots r is a ratio set to 0.6 by default. For each omics, a set of triplets Ttri={a1, p1, n1, a2, p2, n2, ..., as, ps, ns}, s represents the number of triples in the triplet set in this modality.

Triplet loss
To enable the adjustment of graph aggregation and unified representation according to features, we apply triplet loss in metric learning, specifically using the features’ relationship represented by triplet. Based on the triplet set Ttri={a1, p1, n1, a2, p2, n2, ..., as, ps, ns}, for omics i, we try to ensure that the representation of anchor spots is closer to positive samples than negative samples in the latent space. The objective function of triplet loss is given by the equation:

L triplet = Σ I i=1 αi * 1/si Σ si (a,p,n)2Ttri max(||Za - Zp||2 - ||Za - Zn||2 + τ, 0)

where I represent the number of modalities, αi is the weight factor used to adjust the contribution of modality i, Z is the latent embedded representation, and τ (default 1.0) is the margin used to enforce the distance between positive and negative pairs. SMART allows the adjustment of α to meet possible requirements on depending more on one or two omics. In our experiments, we consistently set α to 1. During training, the object is to minimize the triplet loss L triplet.

Model training of SMART
To obtain a better unified representation of spatial multi-omics, SMART includes spatial information and multi-omic relationships using the reconstruction loss and triplet loss. The model is trained by minimizing overall loss function as follows:

L = λL recon + (1-λ)L triplet

where L recon is the reconstruction loss described in Eq. (7) and L triplet is the triplet loss described in Eq. (8), λ represents the weighting coefficient for the reconstruction loss in the overall loss function. It equals a value between 0 and 1, and is typically set to 0.5. The model was trained using the Adam optimizer, with training parameters adjusted for different datasets. However, the batch size was consistently set to one graph. To prevent the model from overfitting expression features while neglecting spatial structure, we implemented an early stopping strategy based on the slope of the loss functions. Specifically, training was automatically terminated when the rate of change (slope) of either the reconstruction loss or the triplet loss fell below a predefined threshold of 0.0001. This approach ensures that the model does not excessively optimize expression features at the expense of spatial structure in pursuit of lower reconstruction loss, nor does it overemphasize similarity in expression values via the triplet loss. The training process was conducted on a single NVIDIA RTX 3090 Ti GPU using the PyTorch and PyTorch Geometric frameworks.

The SMART-MS framework and training
To integrate multi-sections spatial multi-omics data and map the cellular features from different sections into a common latent space, capturing the biological heterogeneity shared across tissue sections, we developed the SMART-MS model, specifically designed for multi-sections spatial multi-omics data. SMART-MS follow the design principles of SMART, with the addition of modules for multi-sections data integration, batch effect correction, and cross-section spatial neighbor graph construction. The training process remains consistent with that of SMART.

Multi-sections data integration
In a spatial multi-omics dataset, assuming there are t sections of multi-omics data, for section i and modality j, the raw input data is Xij 2Rmi×nij. Here mi represents the number of spots in the tissue section i, while nij correspond to the eigenvalues of modality j in the tissue section i. The final matrix obtained by integrating all sections for omics i, we try to ensure that the representation of anchor spots is closer to positive samples than negative samples in the latent space. The objective function of triplet loss is given by the equation: Xj 2R(Σti=1 mi)×Tj nij, where Σti=1 mi is the number of intersections of features across sections. If modality j is RNA or protein, the intersection operation identifies overlapping regions that are accessible in the chromatin in both datasets (i.e., peaks that appear in both datasets). Specifically, the intersection operation detects portions of peak regions from two ATAC-seq datasets that overlap, meaning that the peaks in both datasets cover the same genomic region.

Batch effect correction
For modality j, we apply PCA to the preprocessed data from multiple sections integration for dimensionality reduction, resulting in batch-effect-corrected input data X e j 2R(Σti=1 mi)×pj, where pj is the dimension after dimensionality reduction. Next, we apply Harmony49 to remove batch effects from the input data. Harmony removes batch effects by performing low-dimensional embedding and batch alignment, eliminating differences between batches while preserving the biological variation in the data. It calculates batch differences and iteratively adjusts the spatial representation of samples, enabling samples from different batches to be reasonably aligned in a unified latent space, thereby improving the accuracy of downstream analyses. Finally, the batch-effect-corrected feature matrix is denoted as Hj 2R(Σti=1 mi)×pj.

Triplet construction in multi-sections
In the multi-section integration task, to more effectively align omic features across different tissue sections, we extended the construction of triplets to a cross-section setting. Specifically, each triplet consists of an anchor and a negative sample from the same section, while the positive sample is selected from a different section.

The triplet construction proceeds as follows: we first enumerate all possible section pairs and compute the Euclidean distances between spots based on low-dimensional features obtained after Harmony-based batch correction. For a spot i from section 1, which serves as the anchor a, we identify the farthest N1×r spots within section 1 as negative sample candidates, where N1 denotes the total number of spots in section 1 and r is a predefined ratio (default: 0.6). One spot is then randomly sampled from this candidate pool as the negative sample n. Correspondingly, in the section 2, if the feature of spot j is also among the top k nearest neighbors of j, then j is selected as the positive sample p of a.

Assuming there are b sections in total, for each omics, the complete triplet set for this omics can be expressed as the union over all unordered section pairs:

Ttri = [ 1≤x<y≤b Tx,y

where Tx,y denotes the number of triplets generated from section pair x and y.

Cross-section spatial neighbor graph construction
For each section i across multiple sections, we construct the spatial neighbor graph Ai 2Rmi×mi for section i using the k-nearest neighbor (kNN) algorithm, just as in SMART for constructing single-section spatial neighbor graph. Finally, the cross-modal spatial neighbor graph can be represented by the following formula:

A = diag(A1, A2, ..., At)

where t represents the number of sections.

After obtaining the spatial neighbor graph A for multi-sections integration and the feature matrix H for modality H, the subsequent steps are the same as those in SMART.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Review on \"SMART: Spatial Multiomics Aggregation with Graphical Metric Learning\"\nSummary of the Manuscript\nThe manuscript introduces SMART, a deep learning model utilizing graphical neural networks (GNNs) and metric learning to integrate and analyze spatial multi-omics data. SMART employs a modular, stacking-based framework that allows it to handle multi-omics datasets across different spatial resolutions efficiently. A variant, SMART-MS, is also proposed for integrating multi-section datasets. The study validates SMART’s performance on simulated datasets, real-world transcriptomics and proteomics data, and chromatin accessibility studies, showing superior spatial domain identification compared to existing methods. The authors highlight SMART’s computational efficiency, scalability, and applicability to multi-omics and multi-section data, addressing limitations in existing integration approaches.\nMajor Comments\n1. Model Design and Training Concerns\nThe manuscript presents an interesting use of SAGEConv as an encoder and decoder to generate spatial-informed expression representations. However, I have concerns regarding the model’s design and training scheme. SMART is initialized based on spatial coordinates and then trained to minimize aggregated neighborhood expression differences in the expression space through triplet loss and reconstruction loss. The triplet loss ensures the final embeddings would retain information about expression similarity across input data, while reconstruction loss prevents the final embeddings from collapsing by ensuring the captures of original expression variance. However, there does not seem to be a mechanism preventing the model from converging solely based on expression data while neglecting spatial information. Instead, the user appears to rely on some empirical convergence cutoff to retain spatial information in the model’s latent embedding output. The authors should discuss this potential limitation and clarify whether any explicit constraints exist to enforce spatial structure retention.\n2. Comparison to Other Latent Representations\nIt would be beneficial to compare SMART’s latent embeddings to those generated by other methods, such as BANKSY (Singhal V, et al. Nat Genet. 2024;56(3):431-441.), which appends single-cell self-expression profiles with neighborhood expression information, including expression gradients. In methods like BANKSY, the weighting of spatial information influences whether embeddings are more representative of individual cell types or spatial domains. Does SMART exhibit a similar trade-off? If so, what are the control parameters that allow tuning between cell-type-specific and spatially influenced embeddings? A discussion on this aspect would strengthen the manuscript.\n3. Clarity of Model Architecture\nThe manuscript does not explicitly state critical architectural details, such as the number of layers in the encoder and decoder. This lack of clarity makes it difficult to assess the model’s complexity and reproducibility. The authors should provide explicit details about the layer structure, and other relevant hyperparameters.\n4. Single-Cell vs. Spot-Based Analysis\nThe manuscript does not clearly indicate whether any of the real-data results are at true single-cell resolution or if they are all based on spatially binned spots. If all results are spot-based, the authors should describe how the raw data were processed into spots. If single-cell resolution was analyzed, the manuscript should explicitly state which results pertain to single-cell analyses and discuss whether SMART is equally applicable to both single-cell and spot-based datasets. Additionally, the manuscript should clarify whether optimal parameters for graph construction (e.g., k in kNN) and SAGEConv settings (e.g., number of convolution layers) vary based on spatial resolution differences (e.g., single-cell vs. 50 µm spot-based data). Recommendations for different dataset resolutions would be useful for future users of SMART.\n5. Data Integration and Omics Alignment\nSMART integrates multi-omics data using a two-step process: (1) embedding spatial and expression similarities within a dataset and (2) integrating multi-omics data across tissue sections/slides. While this approach is effective, the integration of different omics across slides appears to rely on batch correction via the Harmony package, a standard method in single-cell analysis. The integration of different omics within the same tissue section relies on shared cells that contain multi-omics data. However, SMART does not seem to support integration across tissue sections where each section has its own omics data (e.g., one section for transcriptomics, another for proteomics). The authors should clarify whether SMART can handle such cases and, if not, explicitly state this limitation.\n6. Pooling Layer Training Impact\nIn SMART, multi-omics embeddings are concatenated before being processed by a trainable fully connected pooling layer. It is unclear how the training of this pooling layer influences the final output. How does this approach compare to using the concatenated embeddings directly for downstream tasks? Furthermore, the model does not seem to include a loss function to ensure alignment between different data modalities. This limitation suggests that SMART may not be applicable for integrating different tissue sections with distinct omics data. A discussion on this limitation and potential solutions would improve the manuscript.\nMinor Comments\n7. Inconsistencies in Figure Labels\nThere are inconsistencies between the tissue section names in Figure 4c and the figure captions for Figures S8-S10. The spatial plots in Figure S10 appear to be significantly different from those in Figure 4c (E11.0_S1). The authors should verify and correct these inconsistencies.\n8. Clarification of Repeated Experiments (Page 4, Line 149)\nThe manuscript mentions that experiments were repeated ten times, but it does not explain how test data were generated across these runs. Were different downsampling rates or binning window sizes used in each experiment? Clarifying this would help interpret the reported results.\nOverall, this paper is well written and presents a promising approach for spatial multi-omics integration. Addressing the above concerns would improve clarity, reproducibility, and applicability.", "reviewer_2": "Review of\n\"SMART: Spatial Multiomics Aggregation with Graphical Metric Learning\" by Zheng et al.\nSummary: this paper proposes a method for training a machine learning model to classify tissues spatially. The approach works by building a spatial k-nearest-neighbors graph separately for each omic, and then propagating information between nodes with graph convolution (specifically SAGEConv). Information from each omics head is aggregated by a fully connected neural network in a latent space embedding, and then decoded. The final model is trained with a combination of reconstruction loss (measuring how well the model preserves each node's information through the latent space) and triplet loss (enforcing that spatially similar nodes ). The authors validate the proposed approach by applying it to several models with different types of multiomic data (both real and synthetic datasets). The paper extensively references existing literature in bioinformatics. The authors also showcase several proposed applications of their method.\nWhile the experiments presented are fairly compelling, I have concerns about the novelty of the approach, as well as concerns about the presentation of the paper. At this time, I believe the paper needs substantial revision before it is suitable for publication.\nThis review is structured as follows: I will first present what I perceive to be the main general strengths and weaknesses of the paper, and then give a limited number of specific line edits.\nMain Strengths:\n-The paper combines several methods from the machine learning literature into an end-to-end pipeline for analyzing multiomic data.\n-The paper presents a variety of experiments which show that the model is able to learn a latent embedding that merges these omics into a single high-dimensional space.\n-The authors consider a wide variety of applications where both spatial data and multi-omic data are relevant.\n-The visualizations show that the model is making predictions which are spatially consistent.\n-The authors consider a variety of metrics to compare their models’ performance to preexisting methods, and cite these methods appropriately.\nMain Weaknesses:\n-I am a machine learning researcher and so am editing/reviewing with that in mind. I think the authors could present this material differently as proof of concept for a pipeline for analyzing multi-omic data. As it stands, many of my criticisms below come from the paper making claims about the novelty of the machine learning aspect of the paper, without using the standard methodology from machine learning to justify those claims. If the authors reduced their claims (e.g. rewrote the paper as mostly an innovation in bioinformatics) then many of my criticisms below would no longer apply.\n-I don’t think that it is accurate for the paper to describe SMART as a “graph metric learning” technique. Graph metric learning refers to the process of learning a distance metric d(G_1, G_2) which compares two graphs. The approach discussed in the paper is instead using triplet loss and reconstruction loss to find an embedding of the spatial graph.\n-The paper does not cite enough of the relevant machine learning literature, and does not do enough to highlight how the proposed approach differs from previous work applying machine learning to multiomics data. I would also suggest that the authors should look more deeply into current best practices for multimodal machine learning.\n-The paper does not motivate the chosen architecture, either theoretically or empirically. Some unanswered questions that I had while reading the paper:\n---Why is it important/necessary for the three omics to have separate spatial graphs? Since all of the data is representing the same physical tissue, wouldn’t it potentially make more sense to have a single spatial graph with masked feature vectors? The authors need to discuss in detail why different spatial graphs are a desirable feature for the model.\n---Why was SAGEConv used, rather than some other message-passing architecture?\n---As stated above, triplet loss is typically used to train a metric learning model. The goal in these cases is to learn an embedding such that Euclidean distance in embedding space corresponds to some “soft” measure of similarity such as semantic content of an image. We may only have binary labels of this semantic similarity (are two images in the same category or not). Triplet loss is used because in these cases “A should be closer to B than to C” is a prior which is easily expressed as a mathematical function of the labels as well as d(A,B), d(B,C). But in this case, it seems like what is actually wanted is that the spatial embedding should smoothly vary across the spatial graph. Triplet loss is also quite expensive to sample. I think it would make more sense to have a loss term that encouraged Laplacian smoothness; if there’s some reason why this wouldn’t work the authors should justify it with experiments or argument.\n---Furthermore, why is the triplet loss calculated on the reconstruction, rather than on the latent embedding vectors? The latter would be more common. This should also be justified.\nThe above questions should be answered, and justified with either theoretical arguments or empirical measurements that show that these architecture choices make a difference to the problem in question.\n-The authors put error bars on many of the plots, but there is no indication of how the error bars are calculated. Do they represent different initializations of the model, or different folds of the data? I suspect that the reported values are calculated on training data, which would unfortunately invalidate them. Best practice would be to train on some of the data and evaluate the model on held-out testing data. Since this is not discussed in the “data preprocessing” section, I see no indication that it was done.\n-Additionally to the prior points, the paper does not perform many of the experiments that would be considered standard to demonstrate the efficiency/accuracy of a new machine learning method. For example, I would expect to see some of the following:\n---Ablation experiments which demonstrate how different parts of the learning pipeline contribute to the model’s performance;\n---Experiments which compare different methods of building the spatial graph that the model uses for each omic;\n---Experiments which compare different methods for graph convolution;\n---Experiments which compare different methods for data preprocessing;\n---Experiments which quantify the degree to which batch effects are present;\n---Experiments which examine the performance of the model if the relative weight of the reconstruction loss and triplet loss are varied.\n-The paper suffers from grammar and translation issues throughout. I have highlighted some of these below in my “line edits” section, but in general the entire paper needs to be thoroughly edited to make sure that it conforms to standard English grammar and terminology.\n-The paper does not present the quantitative results in a way that is easily readable - for example, the bar chart/box plot should be accompanied by a table that lists the actual values. The authors discuss several metrics that they use to demonstrate their model’s superiority, so those values should be listed somewhere. Reported values need to be compared empirically to other, similar machine learning approaches.\n-There are various places where the authors make unsubstantiated claims about what other models can or cannot do. For instance, the authors state on line 42 that SpaGCN “cannot” handle multi-omics data, which I believe is false. The SpaGCN paper does not have experiments with multi-omics, so we can’t say either way. The authors state that SpatialGlue “cannot” handle a unified spatial representation, when this is not the intent of approaches like SpatialGlue - that paper is trying to predict by aligning the spatial and feature graphs. These claims should be reduced in scope, e.g. “prior work has not effectively demonstrated the integration of spatial and multi-omic data.”\n-The paper uses vague, nontechnical language throughout. Sometimes this is okay as a way to provide a reader with intuition about how a model works, but it is not a substitute for a detailed technical explanation (including equations) about how the model works.\n-The figures are extremely difficult to read/interpret. In general I would suggest increasing the number of figures and splitting up the subfigures, as well as making sure all legends are larger and consistent.\nLine edits (note, this is non-comprehensive - as stated above the entire paper could use a thorough editing pass. I am trying to give detailed feedback for the first few pages as examples of what needs to be improved throughout.):\nLine 12 - what is meant by “comprehensive aspect”? This is not a standard term.\nLine 13 - “spatial domain” should be plural.\nLine 15 - this is the first appearance of the acronym SMART in the body of the paper so it should be spelled out.\nLine 15 - “graphical neural net” -> “graph neural net”. This error appears many places in the paper.\nLine 27 - “as the next generation” should be “as next generation”. This grammar error (spurious use of the definite article “the”) appears many places in the paper (line 56, line 57, line 67, line 89, line 157).\nLine 30 - “simultaneously detection” -> “simultaneous detection”\nLine 36 - “identify spatial domain” is a clause fragment - it should be made clear what is being identified in the spatial domain. This error appears again on line 45.\nLine 57 - “SMART construct” -> “SMART constructs”\nLine 58 - what is a “graph inclination” - nonstandard term.\nLine 58 - use of the nontechnical word “spot” when the technical term “vertex” is intended. This error appears many places in the paper.\nLine 73 - “graphical” - “graph”\nLine 73 - as stated above, this is not really a graph metric learning model.\nLine 83 - avoid using anthropomorphizing language which makes it sound like the model has independent agency. The model doesn’t “apply”, “perceive”, or “focus on” anything. Other parts of the paper which similarly anthropomorphize the paper should be edited to use more technical language.\nLine 86 - 88: The sentence starting “Calculating similarity….” does not make sense and needs to be reworded.\nLine 115 - this is not “theoretical” model performance, it is empirical performance on simulated data.\nLine 120 - the word “factor” is used here, but has already been used in a different sense in the preceding discussion of principal components. I suspect that what is meant here is “category”, which should be used instead.\nLine 156 - what does 13.9% of embeddings overlapping mean? How was embedding overlap measured? This is not made clear anywhere in the paper.\nLine 174 - UMAP does not preserve metrics, so it is not valid to claim that UMAP embeddings make it “evident” that a metric learning model is working.\nNote: the remainder of the paper contains errors in this vein.", "reviewer_3": "This manuscript introduces SMART, a Graph Neural Network (GNN)-based framework for integrating spatial multi-omics data. By using GraphSAGE for spatial feature aggregation and triplet loss for enhanced representation learning, SMART achieves a unified latent representation for every spot. The method enables more biologically meaningful embeddings and is extended through SMART-MS to handle adjacent tissue sections. The authors provide thorough comparisons with numerous existing methods, reinforcing SMART's superiority, and have made their source code publicly available on GitHub, enhancing the work's transparency.\nWhile SMART presents an innovative and scalable solution, several methodological and evaluation-related limitations must be addressed to enhance the manuscript's rigor and impact. Below, I outline major and minor concerns that require the authors' attention.\n**Major Comments**\n1. Triplet loss is one of SMART's key contributions, but the threshold defining \"60% distant spots\" as negatives is fixed without discussing its validity. The effects of the margin parameter τ and comparisons of different triplet selection methods are insufficient. A sensitivity analysis of triplet selection should be conducted to quantitatively demonstrate the impact of different selection strategies. Additionally, in the conceptual figure, the meaning of the triplet loss may be somewhat unclear and could benefit from a more intuitive explanation.\n2. The authors use the latent states estimated by SMART to perform spatial clustering and then compare the resulting clusters with pre-annotated clusters. However, details about how the clustering was conducted and how its parameters were chosen appear to be lacking. From the provided .ipynb files in GitHub, it seems that the number of clusters is manually specified. In practical scenarios where one does not have access to ground-truth annotations or cluster quality metrics, some objective index is needed to determine this cluster count. For instance, scNiche (Qian et al., Nat Commun 2025) uses the Fowlkes-Mallows Index to determine the value of k in k-means clustering. Although using the same approach as scNiche is not necessary, it is important to use an objective criterion—documented in the Methods—to prevent arbitrary clustering choices.\n3. The current manuscript compares SMART with methods such as MOFA+, MEFISTO, SpatialGlue, and PRESENT. However, direct comparisons with more recently introduced spatial multi-omics integration methods (e.g., COSMOS, SpaMultiVAE, CellCharter) are not provided. Furthermore, the authors should describe how each method used for comparison was configured, including how they determined the number of clusters. MultiVI, in particular, seems to underperform noticeably across several metrics, which could indicate unfavorably chosen settings compared to those used for other methods.\n4. Although some comparative experiments are presented, it remains unclear how performance changes if specific components are removed or replaced (e.g., turning off the triplet loss, or substituting GraphSAGE with a simpler GCN or GAT). A more detailed ablation study would be valuable to quantify the individual contributions of the triplet loss and the GraphSAGEConv architecture.\n5. The authors demonstrate that the latent spaces obtained via SMART form well-separated clusters on UMAP plots (Fig. 3c, Fig. 4b, 4c) and that different replicates are successfully integrated (Fig. 6a, 6g). However, it is essential to specify the settings used for UMAP and to consider whether UMAP-based comparisons are entirely objective. It may be prudent to avoid drawing firm conclusions from UMAP plots, as parameter choices may affect how the data are displayed.\n6. In Figure 6, the authors emphasize the utility of SMART-MS, which extends SMART by handling adjacent tissue slices. However, there is insufficient explanation of how exactly SMART and SMART-MS were compared in Figure 6j. If the original SMART can also be applied to adjacent slices, the manuscript could potentially include comparisons between SMART-MS and other methods, similar to the benchmarking in other figures. Additionally, SMART-MS examples focus largely on RNA + protein data, and it remains to be seen how it handles slices with different omics compositions (e.g., integrating an RNA+ATAC section with an RNA+protein section).\n7. Many of the presented datasets (e.g., mouse brain, lymph node) feature relatively well-defined layers or regions. It is unclear how SMART would perform on tissue types where distinct cell populations are heavily intermixed—such as tumors with a high degree of spatial heterogeneity. Testing the triplet loss and reporting domain segmentation metrics on such challenging datasets would clarify SMART's robustness and generality.\n**Minor Comments**\n1. In Fig. 6f, the authors compare two slices, but it is unclear what similarity metric is being used in this comparison.\n2. In Fig. 2g, the colors in the box plots are difficult to discern. Furthermore, additional clarification is needed for the \"ten replicate experiments.\" Were multiple simulated datasets used, or were experiments repeated on the same dataset?\n3. The authors should describe how they determined that SMART's training had converged in the methods section (e.g., use of early stopping).\n4. In Figs. 3h, 3i, and 6f, the authors show heatmaps. It might be helpful to rearrange the spots and genes within each cluster to highlight differences more clearly.\n5. Key hyperparameters—such as the margin in the triplet loss, the number of nearest neighbors (k), and the negative sampling ratio—are described briefly, but the manuscript does not fully explain how these values were explored or optimized. Supplementary Materials (or the main text) should include more details on the parameter search space, optimization criteria, and best practices to facilitate reproducibility.\n6. In several figure captions and tables, the terms \"spots\" and \"cells\" appear to be used interchangeably. This may confuse readers as to whether the data are spot-level or single-cell level. Clarifying and standardizing these terms throughout the manuscript (including captions) will improve readability.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Authors’ Response to Reviewers’ Comments\nPaper SMART: Spatial multi-omic aggregation using graph neural networks and metric\ntitle: learning\nAuthors: Zhihua Du, Qiyi Chen, Jinmiao Chen*, Xubin Zheng*\nWe would like to express our sincere gratitude to the editor and the reviewers for their careful\nreview of the previous version of our manuscript. We are pleased to inform you that we have\ncompleted the revision of the manuscript according to your comments and suggestions. For your\nconvenience, the corresponding revisions are highlighted as follows: yellow for Reviewer #1, green\nfor Reviewer #2, and blue for Reviewer #3.\nWe also thank Reviewer #4 for co-reviewing our manuscript. The related comments and our\ncorresponding revisions can be found in the response to that co-reviewer.\nReviewer #1\nComment:\nThe manuscript introduces SMART, a deep learning model utilizing graphical neural\nnetworks (GNNs) and metric learning to integrate and analyze spatial multi-omics data. SMART\nemploys a modular, stacking-based framework that allows it to handle multi-omics datasets\nacross different spatial resolutions efficiently. A variant, SMART-MS, is also proposed for\nintegrating multi-section datasets. The study validates SMART’s performance on simulated\ndatasets, real-world transcriptomics and proteomics data, and chromatin accessibility studies,\nshowing superior spatial domain identification compared to existing methods. The authors\nhighlight SMART’s computational efficiency, scalability, and applicability to multi-omics and\nmulti-section data, addressing limitations in existing integration approaches.\nResponse:\nWe sincerely thank you for carefully reviewing our manuscript, recognizing the value of our\nwork, and providing constructive suggestions. We have revised the manuscript and provided\nclarifications accordingly. All revisions have been highlighted in yellow in the manuscript.\nMajor comment 1:\nModel Design and Training Concerns\nThe manuscript presents an interesting use of SAGEConv as an encoder and decoder to\ngenerate spatial-informed expression representations. However, I have concerns regarding the\nmodel’s design and training scheme. SMART is initialized based on spatial coordinates and then\ntrained to minimize aggregated neighborhood expression differences in the expression space\nthrough triplet loss and reconstruction loss. The triplet loss ensures the final embeddings would\nretain information about expression similarity across input data, while reconstruction loss\nprevents the final embeddings from collapsing by ensuring the captures of original expression\nvariance. However, there does not seem to be a mechanism preventing the model from\nconverging solely based on expression data while neglecting spatial information. Instead, the\nuser appears to rely on some empirical convergence cutoff to retain spatial information in the\nmodel’s latent embedding output. The authors should discuss this potential limitation and clarify\nwhether any explicit constraints exist to enforce spatial structure retention.\nResponse:\nWe thank the reviewer for the comment. To capture spatial information, we included spatial\ngraph neural networks and early stopping, which have been proved to be effective in spatial\ntranscriptomics methods, such as STAGATE9, STAligner43, GraphST10. We would like to clarify in\ndetail:\nSpatial graph construction: SMART builds a k-nearest neighbor graph based on spatial\ncoordinates. As a result, both message propagation and node aggregation in the graph neural\nnetwork are inherently constrained by the spatial topology, ensuring that spatial information is\nintegrated from the beginning of training.\nSAGEConv encodes spatial context: Instead of simple fully connected layers, we use\nSAGEConv, which aggregates information from spatial neighbors at each layer. This allows node\nembeddings to incorporate expression features from nearby spatial locations, effectively imposing\nan implicit spatial constraint. This design aligns with mainstream spatial transcriptomics methods\nsuch as spaGCN7, STAGATE9, and STAligner43, which also embed spatial context via message passing\nrather than explicit adjacency reconstruction.\nEarly stopping prevents overfitting to expression features: To avoid overfitting to expression\nfeatures and neglecting spatial structure, we introduce an early stopping mechanism based on the\nslope of the loss curve. Training halts automatically when the change in reconstruction or triplet\nloss stabilizes, helping preserve spatial integrity in the learned embeddings.\nThank you for the insightful suggestions. We have also added this discussion to the revised\nmanuscript.\nRevision (line 402):\nTo incorporate spatial information, SMART builds a k-nearest neighbor graph based on spatial\ncoordinates. Both message propagation and node aggregation in the graph neural network are\ninherently constrained by the spatial topology, ensuring that spatial information is integrated from\nthe beginning of training. Moreover, SAGEConv, which aggregates information from spatial\nneighbors at each layer, allows node embeddings to incorporate expression features from nearby\nspatial locations, effectively imposing an implicit spatial constraint. This design aligns with\nmainstream spatial transcriptomics methods such as spaGCN7, STAGATE9, and STAligner43. To avoid\noverfitting to expression features and neglecting spatial structure, we introduced an early stopping\nmechanism based on the slope of the loss curve. Training halts automatically when the change in\nreconstruction or triplet loss stabilizes, helping preserve spatial integrity in the learned\nembeddings.\nReferences:\n7. Hu, J. et al. SpaGCN: Integra(cid:415)ng gene expression, spa(cid:415)al loca(cid:415)on and histology to iden(cid:415)fy\nspa(cid:415)al domains and spa(cid:415)ally variable genes by graph convolu(cid:415)onal network. Nat Methods 18, 1342–\n1351 (2021).\n9. Dong, K. & Zhang, S. Deciphering spa(cid:415)al domains from spa(cid:415)ally resolved transcriptomics with\nan adap(cid:415)ve graph a(cid:425)en(cid:415)on auto-encoder. Nat Commun 13, 1739 (2022).\n10. Long, Y. et al. Spa(cid:415)ally informed clustering, integra(cid:415)on, and deconvolu(cid:415)on of spa(cid:415)al\ntranscriptomics with GraphST. Nat Commun 14, 1155 (2023).\n43. Zhou, X., Dong, K. & Zhang, S. Integra(cid:415)ng spa(cid:415)al transcriptomics data across different\ncondi(cid:415)ons, technologies and developmental stages. Nature Computa(cid:415)onal Science 3, 894–906 (2023).\nMajor comment 2:\nComparison to Other Latent Representations\nIt would be beneficial to compare SMART’s latent embeddings to those generated by other\nmethods, such as BANKSY (Singhal V, et al. Nat Genet. 2024;56(3):431-441.), which appends\nsingle-cell self-expression profiles with neighborhood expression information, including\nexpression gradients. In methods like BANKSY, the weighting of spatial information influences\nwhether embeddings are more representative of individual cell types or spatial domains. Does\nSMART exhibit a similar trade-off? If so, what are the control parameters that allow tuning\nbetween cell-type-specific and spatially influenced embeddings? A discussion on this aspect\nwould strengthen the manuscript.\nResponse:\nYes. In SMART, the trade-off between cell/spot specificity and spatial structure modeling can\nbe adjusted via the triplet loss weight and the reconstruction weight in the spatial graph. The\ntriplet loss emphasizes similarity among spots of the same type, regardless of their spatial distance.\nIn contrast, the reconstruction loss, computed through a GraphSAGE-based neural network that\nincorporates spatial graphs during message passing, constrains the embeddings to reflect the\nunderlying spatial structure.\nSMART introduces a tunable parameter (cid:2019)∈[0,1] to control the trade-off between spatial\ncontinuity and expression specificity:\nℒ =(cid:2019)ℒ +(1−(cid:2019))ℒ , (cid:2019)∈[0,1]\n(cid:2928)(cid:2915)(cid:2913)(cid:2925)(cid:2924) (cid:2930)(cid:2928)(cid:2919)(cid:2926)(cid:2922)(cid:2915)(cid:2930)\nwhere ℒ denotes the total loss, with ℒ and ℒ representing the reconstruction loss and\n(cid:2928)(cid:2915)(cid:2913)(cid:2925)(cid:2924) (cid:2930)(cid:2928)(cid:2919)(cid:2926)(cid:2922)(cid:2915)(cid:2930)\ntriplet loss. Increasing (cid:2019) emphasizes spatial locality, while decreasing it prioritizes expression-based\nspot type separation.\nMoreover, the number of neighbors (cid:1863) in the spatial graph also affects model behavior. It\nsignificantly influences spatial structure modeling. For example, when (cid:1863)=0, the model performs\nwell in identifying spot types but poorly in capturing spatial domains (Supplementary Fig. S5).\nUnlike SMART, BANKSY lacks an explicit spatial graph and instead relies on expression\ngradients and feature concatenation. Moreover, BANKSY is limited to single-omic data, whereas\nSMART is designed for multi-omic integration. Therefore, a direct performance comparison\nbetween SMART and BANKSY is not feasible.\nRevision (line 412, 707, Supplementary Fig. S5):\nLine 412: In SMART, the trade-off between spot specificity and spatial structure modeling can\nbe adjusted via the triplet loss weight and the reconstruction weight in the spatial graph. The triplet\nloss emphasizes similarity among spots of the same type, regardless of their spatial distance. In\ncontrast, the reconstruction loss, computed through a GraphSAGE-based neural network that\nincorporates spatial graphs during message passing, constrains the embeddings to reflect the\nunderlying spatial structure. SMART introduces a tunable parameter (cid:2019)∈[0,1] to control the trade-\noff between spatial continuity and expression specificity. Increasing (cid:2019) emphasizes spatial locality,\nwhile decreasing it prioritizes expression-based spot type separation. Moreover, the number of\nneighbors (cid:1863) in the spatial graph also affects model behavior. It significantly influences spatial\nstructure modeling. For example, when (cid:1863)=0, the model performs well in identifying spot types but\npoorly in capturing spatial domains (Supplementary Fig. S5).\nLine 707: The model is trained by minimizing overall loss function as follows.\nℒ =(cid:2019)ℒ +(1−(cid:2019))ℒ (9)\n(cid:2928)(cid:2915)(cid:2913)(cid:2925)(cid:2924) (cid:2930)(cid:2928)(cid:2919)(cid:2926)(cid:2922)(cid:2915)(cid:2930)\nwhere ℒ is the reconstruction loss described in equation (7) and ℒ is the triplet loss\n(cid:2928)(cid:2915)(cid:2913)(cid:2925)(cid:2924) (cid:2930)(cid:2928)(cid:2919)(cid:2926)(cid:2922)(cid:2915)(cid:2930)\ndescribed in equation (8), (cid:2019) represents the weighting coefficient for the reconstruction loss in the\noverall loss function. It takes a value between 0 and 1, and is typically set to 0.5, assigning equal\nimportance to the reconstruction loss and the triplet loss.\nFig. S5. Ablation study for joint cell-type classification and spatial domain detection in\nSTARmap-RIBOmap-Align dataset. a, Spatial domain annotation across consecutive mouse brain\ntissue sections. b, Cell type identification in consecutive mouse brain tissue sections. c-d, Heatmap\nof ARI (c) and NMI (d) for cell type classification (left) and spatial domain segmentation (right)\nacross various loss combinations and numbers of nearest neighbors (K = 0, 4, 16, 64) when the\nnumber of clusters is fixed at 7.\nFig. S4d Impact of triplet-to-reconstruction loss weight ratio.\nMajor comment 3:\nClarity of Model Architecture\nThe manuscript does not explicitly state critical architectural details, such as the number of\nlayers in the encoder and decoder. This lack of clarity makes it difficult to assess the model’s\ncomplexity and reproducibility. The authors should provide explicit details about the layer\nstructure, and other relevant hyperparameters.\nResponse:\nWe appreciate the reviewer’s comment and have addressed the issue accordingly. SMART\nuses a two-layer GraphSAGE encoder and a two-layer GraphSAGE decoder. The number of\nneighbors k was set to 4 for datasets with a quadrilateral spatial layout (e.g., SPOTS, MISAR-seq,\nand Stereo-CITE-seq), and to 6 for 10X Visium data with a hexagonal lattice. Other relevant\nhyperparameters are also stated in the revised manuscript.\nMoreover, we conducted ablation studies to evaluate the impact of varying the number of\nlayers (1, 2, 3, 4) on model performance. Results show that the two-layer configuration achieves\nthe best balance among accuracy, spatial clustering quality, and training stability, across both\nsimulated and real datasets. Detailed results are provided in the Supplementary Materials,\nincluding tests on the simulated tri-omics dataset (Fig. S1a) and the 10x lymph node datasets A1\nand D1 (Fig. S5b).\nRevision:\nLine 646: The number of GraphSAGE encoder layers was set to two based on the results of an\nablation study (Supplementary Fig. S1a).\nLine 615: The number of neighbors k was set to 4 for datasets with a quadrilateral spatial\nlayout (e.g., SPOTS, MISAR-seq, and Stereo-CITE-seq), and to 6 for 10X Visium data with a\nhexagonal lattice.\nSupplementary Figures:\nFig. S1a Performance comparison with different numbers of encoder and decoder layers (1 to\n4) in simulated dataset.\nFig. S5b Performance comparison with different numbers of encoder and decoder layers (1 to\n4) in 10X human lymph node A1 and D1 dataset.\nMajor comment 4:\nSingle-Cell vs. Spot-Based Analysis\nThe manuscript does not clearly indicate whether any of the real-data results are at true\nsingle-cell resolution or if they are all based on spatially binned spots. If all results are spot-\nbased, the authors should describe how the raw data were processed into spots. If single-cell\nresolution was analyzed, the manuscript should explicitly state which results pertain to single-\ncell analyses and discuss whether SMART is equally applicable to both single-cell and spot-based\ndatasets. Additionally, the manuscript should clarify whether optimal parameters for graph\nconstruction (e.g., k in kNN) and SAGEConv settings (e.g., number of convolution layers) vary\nbased on spatial resolution differences (e.g., single-cell vs. 50 µm spot-based data).\nRecommendations for different dataset resolutions would be useful for future users of SMART.\nResponse:\nWe thank the reviewer for pointing out this confusion. Most real datasets used in this study,\nsuch as 10X Visium, SPOTS, and MISAR-seq, are spot-level spatial multi-omics data, where each\nspot typically covers 3–10 cells. We also include datasets at single-cell resolution, such as Stereo-\nCITE-seq (spatial resolution ~500 nm) and RIBOmap-STARmap-aligned datasets, which\napproximate single-cell or even subcellular resolution. Data processing details are provided in the\nMethods section.\nSMART is designed as a general framework for spatial multi-omics analysis, capable of\nhandling both spot-level and single-cell-resolution data. Its architecture does not rely on specific\nspatial granularity, demonstrating strong generalization across platforms. Experiments on different\nresolution data confirm SMART’s robust performance across resolutions.\nRegarding graph construction, we first explored a radius-based method, where the spatial\nneighborhood radius is determined by global spot density, typically set to the average distance\nbetween adjacent spots. In ablation experiments, this radius was defined to include the (cid:1866)-hop\nspatial neighborhood. We then adopted a spatial k-nearest neighbor (k-NN) strategy, selecting (cid:1863)\nbased on the dataset's spatial topology. We found that SMART achieved best performance when\n(cid:1863)=6 for technologies using hexagonal layouts (e.g., 10X Visium) and (cid:1863)=4 for technologies using\nrectangular grids (e.g., SPOTS, MISAR-seq, Stereo-CITE-seq). Notably, a 1-hop radius corresponds\nto (cid:1863)=6 or (cid:1863)=4 depending on grid structure (Supplementary Fig. S2a,b and Fig S3e,f).\nRevision:\nLine 615: The number of neighbors k was set to 4 for datasets with a quadrilateral spatial\nlayout (e.g., SPOTS, MISAR-seq, and Stereo-CITE-seq), and to 6 for 10X Visium data with a\nhexagonal lattice.\nSupplementary Figures:\nFig. S2a Impact of different K values in spatial graph construction with KNN in simulated\ndataset.\nFig. S2b Impact of different radius values in spatial graph construction (radius values 1–4\ndenote including spots within 1–4 hops from each spot) in simulated dataset.\nFig. S3e Impact of different K values in spatial graph construction with KNN in 10X human\nlymph node A1 and D1 dataset.\nFig. S3f Impact of different radius values in spatial graph construction (radius values 1–4\ndenote including spots within 1–4 hops from each spot) in 10X human lymph node A1 and D1\ndataset.\nMajor comment 5:\nData Integration and Omics Alignment\nSMART integrates multi-omics data using a two-step process: (1) embedding spatial and\nexpression similarities within a dataset and (2) integrating multi-omics data across tissue\nsections/slides. While this approach is effective, the integration of different omics across slides\nappears to rely on batch correction via the Harmony package, a standard method in single-cell\nanalysis. The integration of different omics within the same tissue section relies on shared cells\nthat contain multi-omics data. However, SMART does not seem to support integration across\ntissue sections where each section has its own omics data (e.g., one section for transcriptomics,\nanother for proteomics). The authors should clarify whether SMART can handle such cases and,\nif not, explicitly state this limitation.\nResponse:\nSMART currently supports two scenarios for multi-omics integration: (1) integration of\nmultiple modalities within a single tissue section, and (2) integration across multiple sections.\nFor multi-section integration, we apply Harmony for batch correction, but also constructing spatial\ngraphs and unified embeddings across sections (Fig. 1).\nHowever, we acknowledge that SMART does not yet support integration across sections with\ncompletely non-overlapping modalities (e.g., RNA in one section and protein in another with no\nshared spots). We have stated this limitation in the revised manuscript, and we plan to explore in\nfuture work.\nBesides, SMART supports integration with partially missing modalities. When only partial\nomics data are available for subsets of cells or spots within the same section, SMART can still\neffectively integrate spatial multi-omics, allowing us to assess integration under complex missing-\nmodality conditions (Fig. S6).\nRevision (line 470):\nSMART does not yet support integration across sections with completely non-overlapping\nmodalities (e.g., RNA in one section and protein in another with no shared spots).\nFigures:\nFig. S6. Performance of SMART in integrating multiple modalities when expression values\nare partially missing in specific modalities at certain spatial spots. a-e, Performance of SMART in\nintegrating multiple modalities when only 35% (a), 50% (b), 65% (c), 80% (d) and 95% (e) of spatial\nspots retain expression values in each modality. From left to right: input data of the RNA modality,\nADT modality, and ATAC modality; Venn diagram showing the intersection of available spots across\nmodalities; and clustering results after SMART integration.\nMajor comment 6:\nPooling Layer Training Impact\nIn SMART, multi-omics embeddings are concatenated before being processed by a trainable\nfully connected pooling layer. It is unclear how the training of this pooling layer influences the\nfinal output. How does this approach compare to using the concatenated embeddings directly\nfor downstream tasks? Furthermore, the model does not seem to include a loss function to\nensure alignment between different data modalities. This limitation suggests that SMART may\nnot be applicable for integrating different tissue sections with distinct omics data. A discussion\non this limitation and potential solutions would improve the manuscript.\nResponse:\nThank you for the comment. We have compared concatenation followed by fully connected\npooling layer to direct concatenation. Results show that the pooling layer yields superior\nperformance in spatial clustering and structural preservation (Fig. S4e), validating its effectiveness.\nAlthough SMART does not explicitly incorporate a cross-modality alignment loss (e.g.,\ncontrastive loss), it leverages triplet loss and precomputed mutual nearest neighbor (MNN) pairs\nto align modalities in the same graph structure. Based on partially overlapping spots with multi-\nomics information, this design encourages consistent expression structure across modalities. As a\nresult, SMART is well-suited for mosaic-like multi-omics data within a single slice, where modalities\nare partially missing. We validated this capability on a simulated dataset. Even under clear cluster\nboundaries, SMART accurately recovered spatial structure and achieved effective modality fusion\n(Fig. S6).\nWe have added this limitation and potential solutions in the revised manuscript.\nRevision (line 468):\nIn particular, the current lack of explicit modeling of inter-modality relationships may limit\nSMART’s ability to capture complex biological interplay across omics layers. SMART does not yet\nsupport integration across sections with completely non-overlapping modalities (e.g., RNA in one\nsection and protein in another with no shared spots). In the near future, we plan to incorporate\nmodules that model inter-modality interactions while preserving spatial domain identification.\nMinor comment 7:\nInconsistencies in Fig. Labels\nThere are inconsistencies between the tissue section names in Fig. 4c and the figure\ncaptions for Figures S8-S10. The spatial plots in Fig. S10 appear to be significantly different from\nthose in Fig. 4c (E11.0_S1). The authors should verify and correct these inconsistencies.\nResponse:\nThank you for pointing out the mistakes. We have reviewed the manuscript and corrected all\nthe tissue section names to ensure consistency.\nMinor comment 8:\nClarification of Repeated Experiments (Page 4, Line 149)\nThe manuscript mentions that experiments were repeated ten times, but it does not explain\nhow test data were generated across these runs. Were different downsampling rates or binning\nwindow sizes used in each experiment? Clarifying this would help interpret the reported results.\nResponse:\nReproducibility was assessed by repeating each experiment 10 times with different random\nseeds under the same parameter settings, allowing for evaluation of model stability. We have\nadded description in the revised manuscript.\nRevision (line 185):\nRepeated experiments conducted ten times with different random seeds demonstrated that\nSMART achieves strong performance even when utilizing only one modality, though slightly lower\nthan results obtained with three modalities.\nReviewer #2\nMain Strengths:\n-The paper combines several methods from the machine learning literature into an end-to-\nend pipeline for analyzing multiomic data.\n-The paper presents a variety of experiments which show that the model is able to learn a\nlatent embedding that merges these omics into a single high-dimensional space.\n-The authors consider a wide variety of applications where both spatial data and multi-omic\ndata are relevant.\n-The visualizations show that the model is making predictions which are spatially consistent.\n-The authors consider a variety of metrics to compare their models’ performance to\npreexisting methods, and cite these methods appropriately.\nResponse:\nWe sincerely appreciate your thoughtful comments and constructive suggestions. We are\npleased that our methodological approach was recognized and that you found the conclusions to\nbe well supported by the results. In response to your comments, we have provided explanations\nand made revisions, which are highlighted in green in the manuscript.\nComment 1:\nI am a machine learning researcher and so am editing/reviewing with that in mind. I think the\nauthors could present this material differently as proof of concept for a pipeline for analyzing multi-\nomic data. As it stands, many of my criticisms below come from the paper making claims about the\nnovelty of the machine learning aspect of the paper, without using the standard methodology from\nmachine learning to justify those claims. If the authors reduced their claims (e.g. rewrote the paper\nas mostly an innovation in bioinformatics) then many of my criticisms below would no longer apply.\nResponse:\nWe sincerely thank you for the constructive feedback from a machine learning perspective.\nIndeed, the primary goal of SMART is to provide a practical and scalable graph neural network-\nbased framework for integrating spatial multi-omics data and identifying spatial structures and\nbiological regions within tissues. While we adopt standard machine learning components such as\ngraph neural networks (i.e., graphSAGE) and triplet loss, the core contribution of this work lies in\nits bioinformatics innovation, addressing domain-specific challenges in a concise and efficient\nmanner. We have revised the manuscript to highlight the practical applicability and bioinformatics\nsignificance of our approach in the context of spatial multi-omics integration.\nComment 2:\nI don’t think that it is accurate for the paper to describe SMART as a “graph metric learning”\ntechnique. Graph metric learning refers to the process of learning a distance metric d(G_1, G_2)\nwhich compares two graphs. The approach discussed in the paper is instead using triplet loss\nand reconstruction loss to find an embedding of the spatial graph.\nResponse:\nWe sincerely thank you for pointing out the misuse of terminology. The strategy employed in\nSMART is more accurately described as a graph-based embedding learning approach, where triplet\nloss and reconstruction loss are jointly used to guide the learning of low-dimensional node\nrepresentations, modeling the relationship between expression features and spatial structure\nwithin a spatial graph. To avoid ambiguity, we have revised the manuscript to use more appropriate\nterminology. Specifically, we have replaced “graphical metric learning” with “graph neural\nnetworks and metric learning” where applicable, and removed all inaccurate or misleading\ndescriptions.\nRevision:\nTitle: SMART: Spatial multi-omic aggregation using graph neural networks and metric learning\nAbstract (line 16): Here, we present SMART (Spatial Multi-omic Aggregation using gRaph neural networks and meTric learning), a computational framework for spatial multi-omic integration.\nLine 88: SMART is a computational method using graph neural networks combined with\nmetric learning to integrate multiple omics modalities and spatial tissue distribution into a unified\nlatent representation (Fig 1a).\nComment 3:\nThe paper does not cite enough of the relevant machine learning literature, and does not\ndo enough to highlight how the proposed approach differs from previous work applying machine\nlearning to multiomics data. I would also suggest that the authors should look more deeply into\ncurrent best practices for multimodal machine learning.\nResponse:\nWe have added more references about multimodal machine learning and highlighted our\ndifference from the previous works on multi-omics in the revised manuscript.\nRevision:\nLine 129: Recently, multimodal machine learning methods have been proposed such as\ncontrastive learning-based methods14–17, dynamically learning modality gap18, and hierarchical\nmultimodal metric learning19.\nLine 47: Although numerous computational methods have been proposed for multi-omic\nintegration, such as MOFA+20, StabMap21, scMM22, Seurat WNN23, CiteFuse24, totalVI25, SNF26,\nMEFISTO27, and multiVI28, they do not incorporate the spatial coordinates and are therefore not\ndemonstrated the capability to identify spatial domains within tissue samples. Recently,\nSpatialGlue29, CellCharter30, MISO31, COSMOS32, SpaMultiVAE33, and PRESENT34 were proposed to\nintegrate multi-omics data with spatial information. However, MISO, CellCharter, and SpaMultiVAE\nintegrate multi-omics features merely through simple concatenation or basic operations, failing to\neffectively capture and utilize the complementary characteristics among different omics layers,\nwhich results in suboptimal integration performance. Although COSMOS constructs graph models\nbased on spatial adjacency, such approaches primarily capture local spatial information and may\noverlook functionally similar regions that are spatially distant. SpatialGlue constructs separate\ngraphs for spatial coordinates and omics features rather than generating a unified graph\nrepresentation that jointly models both types of information. Moreover, its dual-attention\nmechanism leads to increased computational complexity with the number of omics modalities and\nhas not demonstrated to support multi-section analysis. PRESENT mainly models specific omics\nmodalities, and its applicability and scalability to emerging omics technologies remain to be further\nevaluated. In addition, its computationally intensive statistical parameter estimation process\nfurther limits its performance. Therefore, there is an urgent need for a computation method that\ncan construct a unified spatial omics graph representation and efficiently process the spatial multi-\nomics data from both single and multiple tissue sections.\nReferences:\n14. Radford, A. et al. Learning Transferable Visual Models From Natural Language Supervision. in\nProceedings of the 38th Interna(cid:415)onal Conference on Machine Learning (2021).\n15. Yao, W., Liu, C., Yin, K., Cheung, W. K. & Qin, J. Addressing Asynchronicity in Clinical\nMul(cid:415)modal Fusion via Individualized Chest X-ray Genera(cid:415)on. Advances in Neural Informa(cid:415)on Processing\nSystems 37, 29001–29028 (2024).\n16. Jaume, G. et al. Modeling Dense Mul(cid:415)modal Interac(cid:415)ons Between Biological Pathways and\nHistology for Survival Predic(cid:415)on. in 2024 IEEE/CVF Conference on Computer Vision and Pa(cid:425)ern\nRecogni(cid:415)on (CVPR) 11579–11590 (2024). doi:10.1109/CVPR52733.2024.01100.\n17. Song, Q., Gong, T., Gao, S., Zhou, H. & Li, J. QUEST: Quadruple Mul(cid:415)modal Contras(cid:415)ve\nLearning with Constraints and Self-Penaliza(cid:415)on. Advances in Neural Informa(cid:415)on Processing Systems 37,\n28889–28919 (2024).\n18. Yang, Y., Wan, F., Jiang, Q.-Y. & Xu, Y. Facilita(cid:415)ng Mul(cid:415)modal Classifica(cid:415)on via Dynamically\nLearning Modality Gap. Advances in Neural Informa(cid:415)on Processing Systems 37, 62108–62122 (2024).\n19. Zhang, H., Patel, V. M. & Chellappa, R. Hierarchical Mul(cid:415)modal Metric Learning for\nMul(cid:415)modal Classifica(cid:415)on. in 2017 IEEE Conference on Computer Vision and Pa(cid:425)ern Recogni(cid:415)on (CVPR)\n2925–2933 (IEEE, Honolulu, HI, 2017). doi:10.1109/CVPR.2017.312.\n20. Argelaguet, R. et al. MOFA+: a sta(cid:415)s(cid:415)cal framework for comprehensive integra(cid:415)on of mul(cid:415)-\nmodal single-cell data. Genome Biol 21, 111 (2020).\n21. Ghazanfar, S., Guiben(cid:415)f, C. & Marioni, J. C. Stabilized mosaic single-cell data integra(cid:415)on using\nunshared features. Nat Biotechnol (2023) doi:10.1038/s41587-023-01766-z.\n22. Minoura, K., Abe, K., Nam, H., Nishikawa, H. & Shimamura, T. A mixture-of-experts deep\ngenera(cid:415)ve model for integrated analysis of single-cell mul(cid:415)omics data. Cell Rep Methods 1, 100071\n(2021).\n23. Hao, Y. et al. Integrated analysis of mul(cid:415)modal single-cell data. Cell 184, 3573-3587.e29\n(2021).\n24. Kim, H. J., Lin, Y., Geddes, T. A., Yang, J. Y. H. & Yang, P. CiteFuse enables mul(cid:415)-modal analysis\nof CITE-seq data. Bioinforma(cid:415)cs 36, 4137–4143 (2020).\n25. Gayoso, A. et al. Joint probabilis(cid:415)c modeling of single-cell mul(cid:415)-omic data with totalVI. Nat\nMethods 18, 272–282 (2021).\n26. Wang, B. et al. Similarity network fusion for aggrega(cid:415)ng data types on a genomic scale. Nat\nMethods 11, 333–337 (2014).\n27. Velten, B. et al. Iden(cid:415)fying temporal and spa(cid:415)al pa(cid:425)erns of varia(cid:415)on from mul(cid:415)modal data\nusing MEFISTO. Nat Methods 19, 179–186 (2022).\n28. Ashuach, T. et al. Mul(cid:415)VI: deep genera(cid:415)ve model for the integra(cid:415)on of mul(cid:415)modal data. Nat\nMethods 20, 1222–1231 (2023).\n29. Long, Y. et al. Deciphering spa(cid:415)al domains from spa(cid:415)al mul(cid:415)-omics with Spa(cid:415)alGlue. Nat\nMethods (2024) doi:10.1038/s41592-024-02316-4.\n30. Varrone, M., Tavernari, D., Santamaria-Mar(cid:417)nez, A., Walsh, L. A. & Ciriello, G. CellCharter\nreveals spa(cid:415)al cell niches associated with (cid:415)ssue remodeling and cell plas(cid:415)city. Nature Gene(cid:415)cs 56, 74–\n84 (2024).\n31. Coleman, K. et al. Resolving (cid:415)ssue complexity by mul(cid:415)modal spa(cid:415)al omics modeling with\nMISO. Nat Methods 22, 530–538 (2025).\n32. Zhou, Y. et al. Coopera(cid:415)ve integra(cid:415)on of spa(cid:415)ally resolved mul(cid:415)-omics data with COSMOS.\nNature Communica(cid:415)ons 16, 27 (2025).\n33. Tian, T., Zhang, J., Lin, X., Wei, Z. & Hakonarson, H. Dependency-aware deep genera(cid:415)ve\nmodels for mul(cid:415)tasking analysis of spa(cid:415)al omics data. Nature Methods 21, 1501–1513 (2024).\n34. Li, Z. et al. Cross-modality representa(cid:415)on and mul(cid:415)-sample integra(cid:415)on of spa(cid:415)ally resolved\nomics data. Preprint at h(cid:425)ps://doi.org/10.1101/2024.06.10.598155 (2024).\nComment 4:\n-The paper does not motivate the chosen architecture, either theoretically or empirically.\nSome unanswered questions that I had while reading the paper:\n---Why is it important/necessary for the three omics to have separate spatial graphs? Since\nall of the data is representing the same physical tissue, wouldn’t it potentially make more sense\nto have a single spatial graph with masked feature vectors? The authors need to discuss in detail\nwhy different spatial graphs are a desirable feature for the model.\nResponse:\nWe thank the reviewer for the comment and would like to clarify the following: In SMART, all\nomics modalities share the same adjacency graph, which is constructed based on spatial\ncoordinates. The connectivity between nodes is consistent across modalities; the only difference\nlies in the node features, which are modality-specific and derived from PCA-reduced expression\nprofiles of each omics type. This design preserves the common spatial structure of the tissue while\nallowing each modality to independently capture modality-specific features within a shared spatial\ncontext. We have revised the description of the model architecture in Fig. 1 to make this clearer\nand more intuitive.\nRevision (Fig. 1):\nFig. 1 Framework of SMART designed for spatial multi-omics integration. a SMART overview. The\nSMART framework constructs a spatial neighbor graph from spatial coordinates using k-nearest\nneighbors (KNN). For each modality, normalized and dimensionally reduced features serve as input.\nAnchor, positive, and negative samples are determined via mutual nearest neighbor (MNN)\nmatching for metric learning. SAGEConv encoder processes the spatial graph and input features by\nsampling and aggregating neighborhood information to generate node embeddings. Multi-modal\nembeddings are concatenated and integrated through a dense layer to produce unified\nrepresentations. The model is optimized by jointly minimizing feature reconstruction loss and\ntriplet margin loss in the SAGEConv decoder. b SMART-MS overview. The SMART-MS framework\nintegrates multi-section omics data through horizontal concatenation of expression matrices\nacross tissue sections, followed by joint dimensionally reduction and batch correction with\nHarmony to generate a unified input matrix. For spatial graph construction, the model employs\ndiagonal concatenation of spatial graphs from individual sections. The remaining pipeline\nmaintains consistency with the standard SMART framework. c Triplet samples construction. Single-\nsection triplets use intra-section sampling, while multi-section triplets select positives from other\nsections and negatives from the anchor's section with MNN. d Downstream applications of\nSMARTS and SMART-MS for spatial multi-omics data across technologies, resolutions, and multi-\nsection analyses.\n---Why was SAGEConv used, rather than some other message-passing architecture?\nResponse:\nIn SMART, we chose SAGEConv as the fundamental convolutional unit, primarily due to its\nexcellent scalability and stability. SAGEConv adopts a neighbor sampling strategy, which effectively\nreduces computational and memory burdens when processing large-scale spatial omics data,\nparticularly in scenarios with a large number of nodes and high-dimensional features. Meanwhile,\nits use of a simple mean aggregation mechanism makes it more stable and faster to converge in\nsituations where the feature density varies widely across spatial omics datasets. We compared\nSAGEConv with well-establised graph neural network architectures such as GCNConv, GATConv, and\nGraphConv, and found that SAGEConv outperformed the others in both clustering accuracy and\ntraining convergence (Supplementary Fig. S1c, e). Moreover, compared to directly using fully\nconnected layers, graph neural networks naturally incorporate spatial adjacency between nodes,\nenabling the model to better capture local spatial correlations without significantly increasing\nmodel complexity (Supplementary Fig. S1b).\nRevision (line 129):\nTo validate the design of SMART, we conducted a series of ablation studies, evaluating\ndifferent graph neural network encoders (e.g., GCN38, GAT39,GraphConv40), strategies for selecting\nanchor and positive pairs in metric learning, alternative loss functions and other architectural\ncomponents (Supplementary Table 1 and Supplementary Fig S1-S4).\nFig. S1b Comparison between SAGEConv and fully connected (FC) encoder architectures in\nsimulated dataset.\nFig. S1c Performance across different graph encoders: SAGEConv, GATConv, GCNConv, and\nGraphConv in simulated dataset.\nFig. S1e ARI scores over training epochs for different graph encoder types in simulated dataset.\n---As stated above, triplet loss is typically used to train a metric learning model. The goal in\nthese cases is to learn an embedding such that Euclidean distance in embedding space\ncorresponds to some “soft” measure of similarity such as semantic content of an image. We may\nonly have binary labels of this semantic similarity (are two images in the same category or not).\nTriplet loss is used because in these cases “A should be closer to B than to C” is a prior which is\neasily expressed as a mathematical function of the labels as well as d(A,B), d(B,C). But in this\ncase, it seems like what is actually wanted is that the spatial embedding should smoothly vary\nacross the spatial graph. Triplet loss is also quite expensive to sample. I think it would make more\nsense to have a loss term that encouraged Laplacian smoothness; if there’s some reason why\nthis wouldn’t work the authors should justify it with experiments or argument.\nResponse:\nOur graph structure is constructed based on spatial coordinates, where each node connects\nto its spatially adjacent neighbors. The use of triplet loss is to capture long-range similarity between\nspots of the same cell type. Triplet loss encourages their embeddings to be closer than those of\nnearby but dissimilar spots, ensuring that long-range similarity is preserved in the latent space.\nIn spatial multi-omics data, tissues may exhibit sharp boundaries between distinct cellular\nregions, marked by abrupt changes in gene or protein expression. Under such conditions, applying\nsmoothing regularization (e.g., Laplacian smoothness) can over-emphasize local continuity, leading\nto undesired blurring across boundaries and reduced accuracy in spatial structure identification. In\ncontrast, triplet loss allows flexible specification of anchor-positive pairs based on expression\nsimilarity (e.g., precomputed MNN pairs), while explicitly pushing apart dissimilar anchor-negative\npairs. This approach enhances expression-based cluster separation while preserving local\ncontinuity, thereby improving the model’s ability to capture heterogeneous tissue architecture.\nAblation studies further validate this advantage (Supplementary Fig. S4b).\nRevision:\nFig. S4b Comparison with and without Laplacian smoothing loss in 10X human lymph node\nA1 and D1 dataset.\n---Furthermore, why is the triplet loss calculated on the reconstruction, rather than on the\nlatent embedding vectors? The latter would be more common. This should also be justified.\nThe above questions should be answered, and justified with either theoretical arguments or\nempirical measurements that show that these architecture choices make a difference to the\nproblem in question.\nResponse:\nWe thank the reviewer for pointing out the suboptimal placement of the triplet loss. Following\nthis suggestion, we have revised the model to apply triplet loss to the encoder output (latent\nrepresentations) instead of the decoded space. We have re-evaluated the updated model on both\nsimulated and multiple real datasets. The revised manuscript has included a detailed description\nof the updated architecture (Fig.1) and the corresponding experimental results (Fig. 2-6 and\nSupplementary Fig S1-23).\nThe above questions have been addressed and justified with both theoretical arguments and\nempirical measurements.\nRevision:\nFig. 1-6 and Supplementary Fig S1-23\nLine 695: Based on the triplet set (cid:1846)(cid:3047)(cid:3045)(cid:3036) =(cid:4668)((cid:1853) ,(cid:1868) ,(cid:1866) ),((cid:1853) ,(cid:1868) ,(cid:1866) ),⋯ ⋯,(cid:3435)(cid:1853) ,(cid:1868) ,(cid:1866) (cid:3439)(cid:4669) in\n(cid:3036) (cid:2869) (cid:2869) (cid:2869) (cid:2870) (cid:2870) (cid:2870) (cid:3046)(cid:3284) (cid:3046)(cid:3284) (cid:3046)(cid:3284)\nomics (cid:1861), we try to ensure that the representation of anchor spots is similar to the positive spots\nand different from the negative spots at the same time. The objective function of triplet loss is\ngiven by the following equation:\n(cid:3010) (cid:3046)(cid:3167)\n1\nℒ\n(cid:2930)(cid:2928)(cid:2919)(cid:2926)(cid:2922)(cid:2915)(cid:2930)\n=(cid:3533)(cid:2009)\n(cid:3036)\n⋅\n(cid:1871)\n(cid:3533) (cid:1865)(cid:1853)(cid:1876)(cid:4672)∥∥(cid:1852)\n(cid:3028)\n−(cid:1852)\n(cid:3043)\n∥∥\n(cid:3007)\n(cid:2870) −∥∥(cid:1852)\n(cid:3028)\n−(cid:1852)\n(cid:3041)\n∥∥\n(cid:3007)\n(cid:2870) +(cid:2028),0(cid:4673) (8)\n(cid:2919)\n(cid:3036)(cid:2880)(cid:2869) ((cid:3028),(cid:3043),(cid:3041))∈(cid:3021)(cid:3295)(cid:3293)(cid:3284)\n(cid:3284)\nwhere (cid:1835) represents the number of modalities, (cid:2009) is the weight factor used to adjust the\n(cid:3036)\ncontribution of modality (cid:1861) , (cid:1852) is the latent embedded representation, and τ (default 1.0) is the\nmargin used to enforce the distance between positive and negative pairs.\nComment 5:\n-The authors put error bars on many of the plots, but there is no indication of how the error\nbars are calculated. Do they represent different initializations of the model, or different folds of\nthe data? I suspect that the reported values are calculated on training data, which would\nunfortunately invalidate them. Best practice would be to train on some of the data and evaluate\nthe model on held-out testing data. Since this is not discussed in the “data preprocessing”\nsection, I see no indication that it was done.\nResponse:\nIn this study, error bars in Fig. 2i, Fig. S1 and Fig. S2 represent variability due to multiple runs\nwith different random initializations under the same data split. Specifically, we trained the model\nindependently using different random seeds (typically 10 times) and reported the mean and\nstandard deviation to reflect performance fluctuations arising from initialization and training\nrandomness. Error bars in Fig. 6g, Fig. S3 and Fig. S4, indicate performance variation under different\nnumbers of clusters, used to evaluate the model's robustness to hyperparameter choices.\nRegarding data splitting, since this is an unsupervised learning task, we follow the standard\npractice in spatial omics analysis by training and evaluating the model on the entire tissue section.\nIn such settings, the primary goal is to reconstruct the spatial organization (e.g., spatial domains\nwithin tissue) rather than generalize to unseen data. Labels are not used during training but are\nonly employed for computing evaluation metrics such as ARI and NMI. Therefore, we train and\nevaluate on the full dataset to ensure consistency and comparability with previous spatial omics\nstudies.\nRevision:\nFig. 2i caption: Bar plots of five evaluation metrics evaluating the performance of different\nomics combinations across ten replicate experiments. Error bars in bar plots represent standard\ndeviations over 10 repeated experiments with different random seeds.\nFig. 3e caption: Box plots of seven evaluation metrics across different methods, with the\nnumber of clusters varying from 4 to 10.\nFig. 3f caption: Box plots of Moran’s I scores for different methods, with cluster numbers\nranging from 4 to 10.\nFig. 4d caption: Box plots of Moran’s I scores for different methods, with cluster numbers\nranging from 7 to 15.\nFig. 4h caption: Box plot of seven evaluation metrics to evaluate the performance of\ncombinations of different omics with four sections (E11.0_S1, E13.5_S1, E15.5_S1, E18.5_S1).\nFig. 6h caption: Box plots of Moran’s I scores on section 1, section 2, and section 3 for\ndifferent methods, with cluster numbers ranging from 4 to 8.\nSimilar descriptions have also been added to Supplementary Fig. S1, S2, S3, S4, S9e-f, S12e-f,\nS13e-f, S14e-f, S15d, S18e, S19e.\nComment 6:\n-Additionally to the prior points, the paper does not perform many of the experiments that\nwould be considered standard to demonstrate the efficiency/accuracy of a new machine learning\nmethod. For example, I would expect to see some of the following:\n---Ablation experiments which demonstrate how different parts of the learning pipeline\ncontribute to the model’s performance;\nResponse:\nAccording to the reviewer’s suggestion, we conducted systematic ablation and comparative\nexperiments in the revised manuscript. We systematically remove key components of the model,\nincluding the triplet loss, reconstruction loss, and the pooling fusion layer, to assess the\ncontribution of each module to overall performance (Supplementary Table 1).\nRevision (line 129):\nTo validate the design of SMART, we conducted a series of ablation studies, evaluating\ndifferent graph neural network encoders (e.g., GCN38, GAT39,GraphConv40), strategies for selecting\nanchor and positive pairs in metric learning, alternative loss functions and other architectural\ncomponents (Supplementary Table 1 and Supplementary Fig S1-S4).\nSupplementary Table 1. Ablation study of SMART on datasets A1 and D1.\nModel Configuration A1 (ARI) D1 (ARI)\nw/o PCA (all genes) 0.2338 0.2200\nw/o SAGEConv encoder (fully connected encoder) 0.2416 0.1955\nw/o fully connected layer (concatenation fusion) 0.3066 0.2526\nw/o triplet loss 0.2829 0.3024\nw/o reconstruction loss 0.3224 0.3162\nSMART (full model) 0.3341 0.3291\n---Experiments which compare different methods of building the spatial graph that the\nmodel uses for each omic;\nResponse:\nWe compared two strategies, k-nearest neighbor (kNN) graphs with different k values and\nradius-based graphs constructed using spatial distances, to evaluate their impact on clustering\nperformance under varying data densities. SMART achieved best performance when (cid:1863)=6 for\ntechnologies using hexagonal layouts (e.g., 10X Visium) and (cid:1863)=4 for technologies using rectangular\ngrids (e.g., SPOTS, MISAR-seq, Stereo-CITE-seq). Notably, a 1-hop radius corresponds to (cid:1863)=6 or (cid:1863)=4\ndepending on grid structure (Supplementary Fig. S2a,b and Fig S3e,f).\nRevision:\nLine 615: The number of neighbors k was set to 4 for datasets with a quadrilateral spatial\nlayout (e.g., SPOTS, MISAR-seq, and Stereo-CITE-seq), and to 6 for 10X Visium data with a\nhexagonal lattice.\nFig. S2a Impact of different K values in spatial graph construction with KNN in simulated\ndataset.\nFig. S2b Impact of different radius values in spatial graph construction (radius values 1–4\ndenote including spots within 1–4 hops from each spot) in simulated dataset.\nFig. S3e Impact of different K values in spatial graph construction with KNN in 10X human\nlymph node A1 and D1 dataset.\nFig. S3f Impact of different radius values in spatial graph construction (radius values 1–4\ndenote including spots within 1–4 hops from each spot) in 10X human lymph node A1 and D1\ndataset.\n---Experiments which compare different methods for graph convolution;\nResponse:\nWe conducted a systematic comparison of different well-established graph convolution\nmethods, including GCNConv, GATConv, GraphConv, and SAGEConv, and found that SAGEConv\nachieved the best performance.\nRevision (line 129):\nTo validate the design of SMART, we conducted a series of ablation studies, evaluating\ndifferent graph neural network encoders (e.g., GCN38, GAT39,GraphConv40), strategies for selecting\nanchor and positive pairs in metric learning, alternative loss functions and other architectural\ncomponents (Supplementary Table 1 and Supplementary Fig S1-S4).\nFig. S1c Performance across different graph encoders: SAGEConv, GATConv, GCNConv, and\nGraphConv in simulated dataset.\nFig. S1e ARI scores over training epochs for different graph encoder types in simulated dataset.\n---Experiments which compare different methods for data preprocessing;\nResponse:\nWe compared different data preprocessing strategies, including no processing, highly variable\ngene (HVG) selection, PCA dimensionality reduction, and non-negative matrix factorization (NMF),\nto assess their impact on modeling expression structure. The results indicate that PCA-based\npreprocessing yields the best performance.\nFig. S3. a Performance comparison with different data preprocessing methods.\n---Experiments which quantify the degree to which batch effects are present;\nResponse:\nIn the multi-slice experiments using SMART-MS, we incorporated quantitative metrics to\nevaluate batch effect removal, enabling a systematic assessment of the extent of batch effects\nacross slices.\nRevision (Fig. 6b):\nFig. 6b Biological conservation scores and batch correction scores across different integration\nmethods.\n---Experiments which examine the performance of the model if the relative weight of the\nreconstruction loss and triplet loss are varied.\nResponse:\nWe conducted a loss weight sensitivity analysis, systematically testing different ratios\nbetween reconstruction loss and triplet loss (e.g., 1:1, 1:2, 2:1) to evaluate their impact on the\nstructure of the embedding space and clustering performance. This analysis helps clarify how the\nloss composition influences training dynamics. The results show that a balanced ratio (1:1) yields\nthe best overall performance.\nFig. S4d Impact of triplet-to-reconstruction loss weight ratio.\nMinor Comment 7:\n- I have highlighted some of these below in my “line edits” section, but in general the entire\npaper needs to be thoroughly edited to make sure that it conforms to standard English grammar\nand terminology.\nResponse:\nWe thank the reviewer for the thorough and detailed suggestions. We have carefully reviewed\nand corrected the manuscript thoroughly to ensure grammatical accuracy and precise wording.\n-The paper does not present the quantitative results in a way that is easily readable - for\nexample, the bar chart/box plot should be accompanied by a table that lists the actual values.\nThe authors discuss several metrics that they use to demonstrate their model’s superiority, so\nthose values should be listed somewhere. Reported values need to be compared empirically to\nother, similar machine learning approaches.\nResponse:\nFollowing most articles in bioinformatics, we visualized the performance comparison using\ncharts. But in the revised manuscript, we have added the corresponding numerical values in the\nappendix file metrics_source_data.xlsx for reference.\n-There are various places where the authors make unsubstantiated claims about what other\nmodels can or cannot do. For instance, the authors state on line 42 that SpaGCN “cannot” handle\nmulti-omics data, which I believe is false. The SpaGCN paper does not have experiments with\nmulti-omics, so we can’t say either way. The authors state that SpatialGlue “cannot” handle a\nunified spatial representation, when this is not the intent of approaches like SpatialGlue - that\npaper is trying to predict by aligning the spatial and feature graphs. These claims should be\nreduced in scope, e.g. “prior work has not effectively demonstrated the integration of spatial\nand multi-omic data.”\nResponse:\nWe sincerely thank the reviewer for the helpful suggestions to improve the quality of our\nmanuscript. We have revised the relevant claims accordingly.\nRevision:\nLine 41: Graph neural network-based approaches have demonstrated promising performance\nin modeling spatial information within spatial transcriptomics, such as SpaGCN7, CCST8, STAGATE9,\nGraphST10, conST11, DeepST12, and SpaceFlow13, but these approaches were originally developed\nfor spatial transcriptomics data and have not yet been applied to spatial multi-omics data\nintegration.\nLine 57: SpatialGlue constructs separate graphs for spatial coordinates and omics features\nrather than generating a unified graph representation that jointly models both types of information.\nMoreover, its dual-attention mechanism leads to increased computational complexity with the\nnumber of omics modalities and has not demonstrated to support multi-section analysis.\n-The paper uses vague, nontechnical language throughout. Sometimes this is okay as a way\nto provide a reader with intuition about how a model works, but it is not a substitute for a\ndetailed technical explanation (including equations) about how the model works.\nResponse:\nWe thank the reviewer for the thorough and detailed suggestions. We have carefully reviewed\nand corrected the manuscript thoroughly to ensure grammatical accuracy and precise wording.\n-The figures are extremely difficult to read/interpret. In general I would suggest increasing\nthe number of figures and splitting up the subfigures, as well as making sure all legends are\nlarger and consistent.\nResponse:\nWe apologize for any inconvenience caused during reading. Due to the large number of\nexperiments and the journal’s limitation on the number of figures (<6), we had to combine multiple\nsubfigures. However, we have revised and reorganized the figures, and increased the legend font\nsize as much as possible. If any parts remain unclear, we are happy to make further adjustments.\nMinor Comment 8:\nLine 12 - what is meant by “comprehensive aspect”? This is not a standard term.\nRevision (line 13):\nSpatial multi-omics enables the exploration of tissue microenvironments and heterogeneity\nfrom the perspective of different omics modalities across distinct spatial domains within tissues.\nLine 13 - “spatial domain” should be plural.\nRevision (line 14): across distinct spatial domains within tissues.\nLine 15 - this is the first appearance of the acronym SMART in the body of the paper so it\nshould be spelled out.\nRevision (line 16):\nHere, we present SMART (Spatial Multi-omic Aggregation using gRaph neural networks and\nmeTric learning), a computational framework for spatial multi-omic integration.\nLine 27 - “as the next generation” should be “as next generation”. This grammar error\n(spurious use of the definite article “the”) appears many places in the paper (line 56, line 57, line\n67, line 89, line 157).\nRevision (line 28):\nIn recent years, spatial single-omics technologies, such as spatial transcriptomics,\nepigenomics, and metabolomics have established a vital role and are regarded as next generation\ntechniques in biological and medical research.\nRevision (line 67):\nIn this work, we propose SMART (Spatial Multi-omic Aggregation method using gRaph neural\nnetworks and meTric learning), an unsupervised deep learning framework that leverages graph\nsampling, aggregation and metric learning for spatial multi-omic integration.\nRevision (line 69):\nSMART constructs a unified graph by incorporating spatial coordinates and omic features.\nRevision (line 81):\nFinally, we applied the SMART-MS model, a variant of SMART for Multi-Section analysis, to\nintegrate spatial transcriptomics and proteomics data from mouse spleen and thymus across\nmultiple tissue sections.\nRevision (line 103):\nTherefore, we applied principal component analysis (PCA) to each omics, reducing high-\ndimensional expression data to lower-dimensional representations that retain biologically\nmeaningful patterns.\nRevision (line 192):\nBy comparing the edges across these graphs, we found that only 12.1% of the edges in the\nthree-omics embedding were unique, which is lower than the proportion of unique edges found in\nany single-omics embedding (ATAC: 21.2%; ADT: 17.6%; RNA: 16.1%) (Fig. 2j).\nWe have thoroughly polished the manuscript and made numerous additional revisions\nthroughout the text, which are not listed individually here.\nLine 30 - “simultaneously detection” -> “simultaneous detection”\nRevision (line 29):\nThe emergence of spatial multi-omics enables simultaneous detection of different modal\nomics within the same tissue section, which offers new perspectives for in-depth analysis and\nunderstanding of gene regulation and microenvironment.\nLine 36 - “identify spatial domain” is a clause fragment - it should be made clear what is\nbeing identified in the spatial domain. This error appears again on line 45.\nResponse:\nSpatial domains refer to distinct anatomical structures or cell types within a tissue section,\nwhich are identified based on spatially resolved molecular profiles. In the context of spatial omics,\nthese are commonly referred to as spatial domains. We have added an explanation in the revised\nmanuscript.\nRevision (line 37):\nDifferent omics can provide complementary information of the tissues, but also pose an\nurgent demand for computational methods capable of integrating multi-omics data and accurately\nidentifying distinct spatial domains, such as anatomical structures or cell types, within tissues.\nLine 57 - “SMART construct” -> “SMART constructs”\nRevision (line 69):\nSMART constructs a unified graph by incorporating spatial coordinates and omic features.\nLine 58 - what is a “graph inclination” - nonstandard term.\nRevision (line 70):\nIt learns the graph representations using graph neural networks and refines the aggregation\nprocess based on the relationships among omic spots through metric learning, thereby integrating\nmulti-omics data with spatial context into a unified latent space.\nLine 58 - use of the nontechnical word “spot” when the technical term “vertex” is intended.\nThis error appears many places in the paper.\nResponse:\nIn this paper, a spot refers to a defined, fixed location on a tissue section in spatial omics,\nwhere RNAs and ADT are captured and measured. Each spot represents a physical area on the\ntissue slide that contains a mixture of molecules from the cells within that region. To better\nillustrate the input data format, we have included schematic diagram in Fig. 1.\nLine 73 - “graphical” - “graph”\nLine 73 - as stated above, this is not really a graph metric learning model.\nResponse:\nWe have removed all instances of “graphical” throughout the manuscript and replaced them\nwith the more appropriate term “graph”. “graph metric learning model”is also revised to “graph\nneural networks and triplet loss”.\nLine 83 - avoid using anthropomorphizing language which makes it sound like the model\nhas independent agency. The model doesn’t “apply”, “perceive”, or “focus on” anything. Other\nparts of the paper which similarly anthropomorphize the paper should be edited to use more\ntechnical language.\nRevision:\nline 92: To account for this, we applied metric learning with triplet loss to adaptively adjust\nthe latent representation.\nLine 98: Instead of analyzing raw or highly variable omic features, we applied principal\ncomponents, also referred to as factors, which reflect omic variation and synergy for further\nanalysis, aligning with the biological premise that genes function cooperatively.\nLine 102: Therefore, we applied principal component analysis (PCA) to each omics, reducing\nhigh-dimensional expression data to lower-dimensional representations that retain biologically\nmeaningful patterns.\nLine 676: SMART allows the adjustment of (cid:2009) to meet possible requirements on depending\nmore on one or two omics.\nLine 86 - 88: The sentence starting “Calculating similarity….” does not make sense and needs\nto be reworded.\nRevision (line 101):\nDirectly similarity calculations based on raw omic features can be misleading, as zero\nexpression from different spots may be incorrectly interpreted as similar.\nLine 115 - this is not “theoretical” model performance, it is empirical performance on\nsimulated data.\nRevision (line 140): Benchmarking SMART's performance using simulated data\nLine 120 - the word “factor” is used here, but has already been used in a different sense in\nthe preceding discussion of principal components. I suspect that what is meant here is\n“category”, which should be used instead.\nResponse:\nWe thank the reviewer for raising this point regarding potential confusion. In the original\npaper generating the simulated data, the authors used the term “Factor,” and other related studies\non simulated datasets also employ this term. To stay consistent with the original wording, we have\nmodified the description of principal components by removing the term “Factor.”\nRevision (line 98):\nInstead of analyzing raw or highly variable omic features, we applied principal components,\nwhich reflect omic variation and synergy for further analysis, aligning with the biological premise\nthat genes function cooperatively.\nLine 156 - what does 13.9% of embeddings overlapping mean? How was embedding\noverlap measured? This is not made clear anywhere in the paper.\nRevision (line 189):\nSpecifically, we computed embeddings using SMART for each individual modality (SMART-ADT,\nSMART-RNA, SMART-ATAC) as well as for the integration of all three modalities (SMART-\nADT+RNA+ATAC). For each embedding, we constructed a graph using the k-nearest neighbors (k=10)\nand recorded all edges. By comparing the edges across these graphs, we found that only 12.1%\n(after adjusting the placement of the triplet loss, this value decreased from 13.9% to 12.1%) of the\nedges in the three-omics embedding were unique, which is lower than the proportion of unique\nedges found in any single-omics embedding (ATAC: 21.2%; ADT: 17.6%; RNA: 16.1%) (Fig. 2j). This\nindicates that the tri-modal embedding captures complementary features by integrating\ninformation from all modalities.\nLine 174 - UMAP does not preserve metrics, so it is not valid to claim that UMAP\nembeddings make it “evident” that a metric learning model is working.\nRevision (line 215):\nIn the UMAP visualization, SMART, PRESENT, MISO and SpatialGlue exhibit well-defined\ncluster boundaries corresponding to the ground truth labels, demonstrating their effectiveness in\nidentifying distinct tissue regions.\nOnce again, we sincerely thank you for your detailed and constructive comments. We have\nthoroughly revised the manuscript, and your suggestions have significantly improved the overall\nquality of our work.\nReviewer #3\nComment:\nThe method enables more biologically meaningful embeddings and is extended through\nSMART-MS to handle adjacent tissue slices. The authors provide thorough comparisons with\nnumerous existing methods, reinforcing SMART's superiority, and have made their source code\npublicly available on GitHub, enhancing the work's transparency. While SMART presents an\ninnovative and scalable solution, several methodological and evaluation-related limitations\nmust be addressed to enhance the manuscript's rigor and impact.\nResponse:\nWe sincerely thank the reviewer for recognizing the value of our work and acknowledging it\nas an innovative, scalable solution. We have addressed your concerns and incorporated the\ncorresponding revisions, which are highlighted in blue in the revised manuscript.\nMajor Comment 1:\nTriplet loss is one of SMART's key contributions, but the threshold defining \"60% distant\nspots\" as negatives is fixed without discussing its validity. The effects of the margin parameter τ\nand comparisons of different triplet selection methods are insufficient. A sensitivity analysis of\ntriplet selection should be conducted to quantitatively demonstrate the impact of different\nselection strategies. Additionally, in the conceptual figure, the meaning of the triplet loss may be\nsomewhat unclear and could benefit from a more intuitive explanation.\nResponse:\nWe thank the reviewer for the insightful comments regarding the triplet loss design and\nnegative sample selection strategy in our framework.\n(1) Regarding the choice of defining the \"60% most distant spots\" as negative samples, this\nparameter was empirically determined based on prior experience. We have conducted a sensitivity\nanalysis by varying the negative sampling threshold (20%, 40%, 60%, and 80%) and evaluated the\nresulting effects on clustering consistency and embedding quality. As shown in the revised\nSupplementary Fig. S2d and Fig. S3h, the 60% threshold provides the most stable performance\nacross multiple metrics.\nNotably, the 60% threshold also implicitly incorporates moderately similar samples as\nnegatives, which balances discriminability and robustness. This design aligns well with the concept\nof \"semi-hard negatives\" commonly used in triplet loss strategies.\n(2) To further analyze the role of the margin parameter τ in the triplet loss, we have conducted\nadditional experiments using τ ∈ {0.1, 0.2, 0.5, 1.0, 2.0} across multiple datasets. The results\nindicate that τ = 0.5 yields the most consistent and robust performance, and we now recommend\nthis setting as the default. The sensitivity analysis is included in the revised Supplementary Fig. S4a.\nFor the construction of anchor-positive pairs, we employed a mutual nearest neighbors (MNN)\nstrategy, in which we selected node pairs that were among each other's top-n nearest neighbors.\nWe have now included an ablation study analyzing the impact of different n values on training\nstability and representation quality (Supplementary Fig. S3g) .\n(3) Regarding to the representation of triplet loss in the conceptual figure, we have redesigned\nthe Fig. 1 to clearly label the definitions of anchor, positive, and negative samples, as well as the\noptimization relationship among them. This updated figure provides a more intuitive depiction of\nthe core concept and mechanism of triplet loss.\nAlso, in the main text, we have revised the relevant section to explicitly describe the triplet\nsampling strategy, including how the 60% threshold for negatives was determined and validated,\nand how the margin parameter τ was tuned through sensitivity analysis. These details are now\nincluded in the revised Results section to improve clarity and preempt possible confusion.\nRevision (line 427):\nTo construct negative samples for triplet loss, we selected the top 60% most distant nodes\n(measured in Euclidean distance) as negatives. A sensitivity analysis across different thresholds\n(20%, 40%, 60%, and 80%) revealed that 60% yields the most stable and accurate results across\nmultiple datasets (Supplementary Fig. S2). This design also aligns well with the concept of \"semi-\nhard negatives\" commonly used in triplet loss strategies. We also studied the effect of the margin\nparameter (τ) in the triplet loss, comparing τ ∈ {0.1, 0.2, 0.5, 1.0, 2.0}, and found that τ = 0.5\nprovided robust performance across datasets (Supplementary Fig. S4a), which we adopt as the\ndefault value in SMART. For the construction of anchor-positive pairs, we employed a mutual\nnearest neighbors (MNN) strategy, in which we select node pairs that are among each other's top-\nn nearest neighbors. To evaluate the effect of this design, we conducted an ablation study across\ndifferent n values, and analyzed their impact on training stability and representation quality\n(Supplementary Fig. S3g).\nSupplementary Figures:\nFig. S2d Influence of distance ratio for negative sample selection (e.g., 0.2 indicates selection\nfrom the farthest 20% of spots).\nFig. S3h Influence of distance ratio for negative sample selection (e.g., 0.2 indicates selection\nfrom the farthest 20% of spots).\nFig. S4a Effect of different margin values in triplet loss function.\nFig. S3g Impact of different N values of mutual nearest neighbor (MNN) pairs (N denotes the\nnumber of mutual nearest neighbors—each pair must be among each other’s top-N nearest\nneighbors).\nFigures:\nFig. 1c Triplet samples construction. Single-section triplets use intra-section sampling, while\nmulti-section\nMajor Comment 2:\nThe authors use the latent states estimated by SMART to perform spatial clustering and\nthen compare the resulting clusters with pre-annotated clusters. However, details about how the\nclustering was conducted and how its parameters were chosen appear to be lacking. From the\nprovided .ipynb files in GitHub, it seems that the number of clusters is manually specified. In\npractical scenarios where one does not have access to ground-truth annotations or cluster\nquality metrics, some objective index is needed to determine this cluster count. For instance,\nscNiche (Qian et al., Nat Commun 2025) uses the Fowlkes-Mallows Index to determine the value\nof k in k-means clustering. Although using the same approach as scNiche is not necessary, it is\nimportant to use an objective criterion—documented in the Methods—to prevent arbitrary\nclustering choices.\nResponse:\nWe appreciate the reviewer’s thoughtful comments regarding the clustering process and the\nchoice of the number of clusters (K). To clarify, our study involves three types of scenarios:\n(1) Datasets with ground-truth annotations:\nFor benchmark datasets that contain pre-annotated ground-truth domains (e.g., DLPFC,\nbreast cancer slices), we did not arbitrarily fix K to a value that favors our method. Instead, we\nperformed evaluations across a range of K values (e.g., from 4 to 10) and reported clustering\nperformance (ARI, NMI, Moran’s I, etc.) accordingly (Fig. 3e-f, Fig. 4d, and Fig. 6h). In all\ncomparative evaluations, we ensured the same K was used across competing methods to\nguarantee fair and unbiased comparison. The chosen K for each dataset is explicitly stated in the\nfigure captions (Fig. 3e, Fig. S9e, Fig. S12e, Fig. S13e, Fig. S14e).\n(2) Datasets without ground-truth annotations:\nFor real-world datasets lacking reference labels (e.g., mouse brain), we adopted a principled\nunsupervised strategy to determine K. Specifically, we used a combination of cluster validity indices\nincluding the mean Fowlkes-Mallows Index (FMI), Silhouette Coefficient (SCI), and Davies-Bouldin\nIndex (DBI). These metrics helped identify a stable and biologically meaningful number of clusters.\nWe have now clarified this process in the Results section and revised the Fig.S15. We also included\nrelevant code in the GitHub repository for reproducibility.\n(3) Biologically informed clustering (user-defined K):\nIn practical applications, domain experts often guide the choice of cluster number based on\nprior knowledge, such as tissue morphology from H&E staining or anatomical structures. SMART\nsupports such use cases by allowing users to manually specify K, enabling flexibility for biological\ninterpretation and downstream analysis.\nThese details have been added to the Result section for clarity. The specific modifications are\nas follows:\nRevision:\nLine 218: We further compared the performance of different methods using supervised\nevaluation metrics, and the results show that SMART demonstrates a significant advantage in\nquantitative assessments when the number of clusters is set to 7 (Fig. 3d). Considering that the\noptimal number of clusters may vary across datasets, we additionally evaluated the stability of\nSMART across a range of clustering resolutions (from 4 to 10 clusters). The results indicate that\nSMART consistently outperforms other methods under all settings, highlighting its robustness\nacross different clustering granularities (Fig. 3e).\nLine 294: As the dataset lacks ground-truth labels, we determined the number of clusters to\nbe 12 based on internal clustering validation metrics, including mean FMI, SCI (Silhouette\nCoefficient), and DBI (Davies-Bouldin Index) (Supplementary Fig S15 a,b).\nSupplementary Figures:\nFig. S15a Mean FMI score across varying cluster numbers.\nFig. S15b Silhouette Coefficient score and Davies-Bouldin Index across varying cluster\nnumbers.\nMajor Comment 3:\nThe current manuscript compares SMART with methods such as MOFA+, MEFISTO,\nSpatialGlue, and PRESENT. However, direct comparisons with more recently introduced spatial\nmulti-omics integration methods (e.g., COSMOS, SpaMultiVAE, CellCharter) are not provided.\nFurthermore, the authors should describe how each method used for comparison was\nconfigured, including how they determined the number of clusters. MultiVI, in particular, seems\nto underperform noticeably across several metrics, which could indicate unfavorably chosen\nsettings compared to those used for other methods.\nResponse:\nWe thank the reviewer for pointing out that the comparison scope was limited.\n(1) We have expanded our evaluation in the revised manuscript to include more recently\nintroduced spatial multi-omics integration methods, such as COSMOS, SpaMultiVAE, CellCharter,\nand MISO. These methods represent significant advancements in spatial multi-modal analysis and\nare highly relevant to our work. The results show that SMART outperforms these methods across\nmultiple key metrics (Fig. 2h, Fig. 3e, Fig. 4h), further validating its strengths in multi-modal\nintegration and spatial structure recognition.\n(2) Regarding the comparison methods, we supplemented the configuration along with the\ndetails on how the number of clusters was determined in our Github code repository. For each\nmethod, the cluster number was based on either manual annotations or available ground truth\nlabels, and we ensured that the number of clusters was consistent across all methods for fair\ncomparison.\n(3) Concerning the reviewer’s specific mention of MultiVI, we provide the following\nexplanation. MultiVI is a general-purpose deep generative model originally designed for multi-\nmodal single-cell data. It primarily relies on variational inference for feature fusion, but does not\nexplicitly model spatial information. As a result, it faces limitations when applied to spatial multi-\nomics data, as structural information is not adequately captured, which negatively impacts its\nperformance. We performed parameter tuning for MultiVI in our revised experiments. However, it\nstill performed relatively poorly on spatial datasets. This aligns with the performance of MultiVI in\nprevious studies, such as SpatialGlue and PRAGA.\nFig. 2i in SpatialGlue（Long, Y. et al. Deciphering spatial domains from spatial multi-omics\nwith SpatialGlue. Nat Methods (2024) doi:10.1038/s41592-024-02316-4.）\nTable 1 in Praga (Huang, X. et al. PRAGA: Prototype-aware Graph Adaptive Aggregation for\nSpatial Multi-modal Omics Analysis. AAAI (2025) doi:10.1609/aaai.v39i1.32010)\nWe have made the following revisions to the revised manuscript and Figures:\nRevision:\nLine 205 : we also included scMM16, TotalVI19, MultiVI22, COSMOS26 and SpaMultiVAE27 for\nRNA-protein integration....\nLine 253: ... including ....COSMOS, CellCharter ....\nLine 180: Across all metrics, SMART consistently achieved the highest performance, followed\nby CellCharter.\nFigures:\nFig. 2h Bar plot displaying seven evaluation metrics to assess the performance of different\nmethods.\nFig. 3e Box plots of seven evaluation metrics across different methods, with the number of\nclusters varying from 4 to 10.\nFig. 4h Box plot of seven evaluation metrics to evaluate the performance of combinations of\ndifferent omics with four sections (E11.0_S1, E13.5_S1, E15.5_S1, E18.5_S1).\nMajor Comment 4:\nAlthough some comparative experiments are presented, it remains unclear how\nperformance changes if specific components are removed or replaced (e.g., turning off the triplet\nloss, or substituting GraphSAGE with a simpler GCN or GAT). A more detailed ablation study\nwould be valuable to quantify the individual contributions of the triplet loss and the\nGraphSAGEConv architecture.\nResponse:\nWe appreciate the reviewer’s insightful suggestion to evaluate the individual contributions of\nkey components within the SMART architecture. In response, we have included a comprehensive\nablation study in the revised manuscript to quantify the effect of two major components.\n(1) Effect of the triplet loss function\nWe conducted experiments under three conditions: using only the reconstruction loss, using\nonly the triplet loss, and using both losses together. We evaluated the spatial clustering consistency\nusing supervised metrics across multiple real datasets. As shown in Fig. S4c, the removal of the\ntriplet loss notably degraded the model’s ability to discriminate expression structures, especially\nin tissues with complex organization such as the human lymph node. This supports the conclusion\nthat the triplet loss plays a key role in enhancing semantic separation in the latent embedding\nspace.\n(2) Effect of the GraphSAGEConv graph encoder\nWe replaced the default GraphSAGEConv encoder with fully-connected encoder (i.e., without\nGraphSAGEConv), GCNConv, GATConv, and GraphConv, while keeping all other settings identical.\nAs shown in Figures S1b-e, GraphSAGE consistently achieved better clustering accuracy, faster\nconvergence, and greater training stability across all tested datasets.\nWe have added these results and corresponding explanations to the revised manuscript and\nSupplementary Figures.\nRevision:\nLine 437: To quantify the effect of the triplet loss, we conducted experiments under three\nconditions: using only the reconstruction loss, using only the triplet loss, and using both losses\ntogether. We evaluated the spatial clustering consistency using supervised metrics across multiple\nreal datasets. As shown in Fig. S4c, the removal of the triplet loss notably degraded the model’s\nability to discriminate expression structures, especially in tissues with complex organization such\nas the human lymph node. This supports the conclusion that the triplet loss plays a key role in\nenhancing semantic separation in the latent embedding space.\nLine 424: We replaced the default GraphSAGEConv with different graph encoders, GCNConv,\nGATConv, and GraphConv, keeping other parameters constant. Figures S1c-e display the\nGraphSAGEConv encoder consistently demonstrated better stability, faster convergence, and\nhigher clustering accuracy.\nSupplementary Figures:\nFig. S4c Effects of triplet loss, reconstruction loss, and their combination.\nFig. S1. b Comparison between SAGEConv and fully connected (FC) encoder architectures in\nsimulated dataset.\nFig. S1c Performance across different graph encoders: SAGEConv, GATConv, GCNConv, and\nGraphConv.\nFig. S1d Training loss curve of the SMART model over 150 epochs.\nFig. S1e ARI scores over training epochs for different graph encoder types.\nMajor Comment 5:\nThe authors demonstrate that the latent spaces obtained via SMART form well-separated\nclusters on UMAP plots (Fig. 3c, Fig. 4b, 4c) and that different replicates are successfully\nintegrated (Fig. 6a, 6g). However, it is essential to specify the settings used for UMAP and to\nconsider whether UMAP-based comparisons are entirely objective. It may be prudent to avoid\ndrawing firm conclusions from UMAP plots, as parameter choices may affect how the data are\ndisplayed.\nResponse:\nThank you for your comment regarding the use of UMAP for visualizing the latent spaces.\nWe have used the default settings for UMAP across all experiments. We agree with the reviewer that\nUMAP is primarily a visualization tool. In this study, UMAP was used solely for visualization\npurposes. The model’s performance was evaluated using quantitative metrics derived from\nclustering analyses. These metrics are independent of UMAP and provide more objective\nevaluations of the model’s ability to integrate replicates and form well-separated clusters.\nTherefore, UMAP should be considered as a complementary visualization result, while the\nconclusions in the manuscript are based on more robust quantitative analyses.\nMajor Comment 6:\nIn Fig. 6, the authors emphasize the utility of SMART-MS, which extends SMART by handling\nadjacent tissue slices. However, there is insufficient explanation of how exactly SMART and\nSMART-MS were compared in Fig. 6j. If the original SMART can also be applied to adjacent slices,\nthe manuscript could potentially include comparisons between SMART-MS and other methods,\nsimilar to the benchmarking in other figures. Additionally, SMART-MS examples focus largely on\nRNA + protein data, and it remains to be seen how it handles slices with different omics\ncompositions (e.g., integrating an RNA+ATAC section with an RNA+protein section).\nResponse:\nThank you for your comment. Currently, SMART is designed to analyze individual tissue slices\none at a time, while SMART-MS extends this capability by aligning and analyzing multiple adjacent\nslices. To avoid confusion, we have removed the comparison with SMART in the revised manuscript\nFig. 6j and instead opted to compare SMART-MS with multi-omics integration methods that\nsupport multiple slices (Fig. 6b).\nAt present, multi-slice cross-modal alignment is not supported, but we plan to improve this\nfunctionality in future versions. We have added this limitation in discussion.\nWe have made the following revisions to the revised manuscript and Figures:\nRevision:\nLine 370: For quantitative evaluation, we used previously defined supervised metrics for\nbiological signal preservation, and c scores to assess batch effect removal. SMART-MS achieved the\nhighest overall score among all compared methods and substantially outperformed others in both\nbiological information retention and batch effect correction (Fig. 6b).\nLine 472: SMART does not yet support integration across sections with different omics\ncompositions (e.g., integrating an RNA+ATAC section and an RNA+protein section).\nFigures:\nFig. 6b Biological conservation scores and batch correction scores across different integration\nmethods.\nMajor Comment 7:\nMany of the presented datasets (e.g., mouse brain, lymph node) feature relatively well-\ndefined layers or regions. It is unclear how SMART would perform on tissue types where distinct\ncell populations are heavily intermixed—such as tumors with a high degree of spatial\nheterogeneity. Testing the triplet loss and reporting domain segmentation metrics on such\nchallenging datasets would clarify SMART's robustness and generality.\nResponse:\nThank you for your insightful comment. Currently, the tumor multi-omics datasets we have\ncollected include the 10X breast cancer dataset and the glioblastoma dataset. While these datasets\nlack manual annotation information, we performed additional experiments on these datasets and\nfound that SMART, when applied to high spatial heterogeneity data, successfully identifies\ncontinuous spatial domains, especially when integrating multi-omics data as opposed to using\nsingle-omics data alone. However, due to the absence of ground-truth annotations, we are unable\nto report quantitative domain segmentation metrics for these datasets.\nWe have made the following revisions to the revised manuscript and Supplementary Figures:\nRevision:\nLine 459: SMART still performs well on tissue types with high spatial heterogeneity. To further\nvalidate this, we conducted additional experiments using tumor datasets, including the 10X breast\ncancer and glioblastoma datasets44,45. However, the lack of manual annotations in these datasets\nlimited their applicability for fully quantitative evaluation. Our results show that SMART, when\napplied to multi-omics data (RNA and protein), can successfully identify continuous spatial domains\neven in highly heterogeneous tissues (Supplementary Fig. S20–S23). Notably, compared to using\nsingle-omics data alone, the integration of multi-omics data significantly enhances the ability to\ncapture spatial structure.\n44. Visium CytAssist Gene and Protein Expression Library of Human Breast Cancer, IF, 6.5mm\n(FFPE). 10x Genomics h(cid:425)ps://www.10xgenomics.com/datasets/gene-and-protein-expression-library-\nof-human-breast-cancer-cytassist-ffpe-2-standard.\n45. Visium CytAssist Gene and Protein Expression Library of Human Glioblastoma, IF, 11mm\n(FFPE). 10x Genomics h(cid:425)ps://www.10xgenomics.com/datasets/gene-and-protein-expression-library-\nof-human-glioblastoma-cytassist-ffpe-2-standard.\nSupplementary Figures:\nFig. S20 SMART integrates multi-omics 10x Visium CytAssist human breast cancer section. a\nHuman breast cancer tissue section (H&E image) with clustering results derived from PCA of RNA\nor ADT features, compared to embeddings integrated by SMART. b Separate spatial plots of all\nclusters identified by SMART in human breast cancer section.\nFig. S22 SMART integrates multi-omics 10x Visium CytAssist human glioblastoma section. a\nHuman glioblastoma tissue section (H&E image) with clustering results derived from PCA of RNA\nor ADT features, compared to embeddings integrated by SMART. b Separate spatial plots of all\nclusters identified by SMART in human glioblastoma section.\nMinor Comments\n1. In Fig. 6f, the authors compare two slices, but it is unclear what similarity metric is being used\nin this comparison.\nResponse:\nThank you for your comment. We have moved Fig. 6f to the Supplementary Figures（Fig.S17\nf）. The similarity metric used for comparing the two slices is cosine similarity.\nWe have made the following revisions to the revised manuscript and Supplementary Figures:\nRevision:\nLine 384：The similarity metric used for comparing the two slices is cosine similarity.\nFig. S17c Cosine similarity between the distance matrix computed from SMART-MS's\nintegrated embedding and those derived from each omics across varying cluster numbers.\n2. In Fig. 2g, the colors in the box plots are difficult to discern. Furthermore, additional\nclarification is needed for the \"ten replicate experiments.\" Were multiple simulated datasets\nused, or were experiments repeated on the same dataset?\nResponse:\nThank you for your comment. We revised Fig. 2g into bar plots in the revised figures Fig. 2i to\nimprove clarity.\nRegarding the \"ten replicate experiments,\" we performed 10 repetitions of the same\nexperiment on the same dataset, each with different random seeds to ensure robustness. We will\nclarify this in the figure legend and the manuscript for better understanding.\nRevision:\nLine 185: Repeated experiments conducted ten times with different random seeds\ndemonstrated that SMART achieves strong performance even when utilizing only one modality,\nthough slightly lower than results obtained with three modalities.\nFigures:\nFig. 2i Bar plots of five evaluation metrics evaluating the performance of different omics\ncombinations across ten replicate experiments\n3. The authors should describe how they determined that SMART's training had converged in the\nmethods section (e.g., use of early stopping).\nResponse:\nThank you for your comment. We will add a description in the Methods section regarding the\nuse of early stopping criteria.\nRevision:\nLine 715: To prevent the model from overfitting expression features while neglecting spatial\nstructure, we implemented an early stopping strategy based on the slope of the loss functions.\nSpecifically, training was automatically terminated when the rate of change (slope) of either the\nreconstruction loss or the triplet loss fell below a predefined threshold of 0.0001.\n4. In Figs. 3h, 3i, and 6f, the authors show heatmaps. It might be helpful to rearrange the spots\nand genes within each cluster to highlight differences more clearly.\nResponse:\nThank you for your suggestion. We have revised the heatmaps (Figs. 3h, 3i, and 6f) into Figs\n3i,3j and Fig.S17 c to improve clarity.\nRevision:\nFigures:\nFig. 3 Integration of 10X Visium CytAssist Gene and Protein co-profiling multi-omics data\nhuman lymph node section A1 using SMART. i RNA expression of region-specific markers in\nSMART’s clusters. j Protein expression of region-specific markers in SMART’s clusters.\nSupplementary Figures:\nFig. S17c Cosine similarity between the distance matrix computed from SMART-MS's\nintegrated embedding and those derived from each omics across varying cluster numbers.\n5. Key hyperparameters—such as the margin in the triplet loss, the number of nearest neighbors\n(k), and the negative sampling ratio—are described briefly, but the manuscript does not fully\nexplain how these values were explored or optimized. Supplementary Materials (or the main\ntext) should include more details on the parameter search space, optimization criteria, and best\npractices to facilitate reproducibility.\nResponse:\nThank you for your comment. We conducted ablation experiments to explore and optimize\nkey hyperparameters, such as the margin in the triplet loss, the number of nearest neighbors (k),\nand the negative sampling ratio. Detailed results of these experiments can be found in the\nsupplementary Fig. S2.\nRevision:\nSupplementary Figures:\nFig. S2 Further ablation studies of SMART on key hyperparameters and modules. a Impact\nof different K values in spatial graph construction with KNN. b Impact of different radius values in\nspatial graph construction (radius values 1–4 denote including spots within 1–4 hops from each\nspot). c Impact of different N values of mutual nearest neighbor (MNN) pairs (N denotes the\nnumber of mutual nearest neighbors—each pair must be among each other’s top-N nearest\nneighbors). d Influence of distance ratio for negative sample selection (e.g., 0.2 indicates selection\nfrom the farthest 20% of spots). e Comparison with and without Laplacian smoothing loss. f Effect\nof different margin values in triplet loss function. g Performance comparison between FC-layer\nfusion (concatenating three omics features followed by a fully connected layer) and concatenation\nfusion without further transformation. Error bars in bar plots represent standard deviations over\n10 repeated experiments with different random seeds.\n6. In several figure captions and tables, the terms \"spots\" and \"cells\" appear to be used\ninterchangeably. This may confuse readers as to whether the data are spot-level or single-cell\nlevel. Clarifying and standardizing these terms throughout the manuscript (including captions)\nwill improve readability.\nResponse:\nThank you for pointing this out. We have unified the terminology throughout the manuscript\nand will use \"spots\" consistently.\nAuthors’ Response to Reviewers’ Comments\nPaper SMART: Spatial multi-omic aggregation using graph neural networks and metric\ntitle: learning\nAuthors: Zhihua Du, Qiyi Chen, Weiliang Huang, Jinmiao Chen*, Xubin Zheng*\nWe truly appreciate the editor and reviewers’ careful review of our revised manuscript. We\nare encouraged that the reviewers found the previous revisions to have strengthened the\nmanuscript. We have perused the reviewers’ comments and undertaken additional work to\naddress your concerns to improve both the manuscript and the SMART package. The\ncorresponding revisions are highlighted in yellow.\nReviewer #1\nHigh-level comment to rebuttal letter:\nI appreciate the authors’ thoughtful revisions and the inclusion of additional comparative\nmethods in the updated manuscript. These additions help contextualize SMART’s performance\nwithin the broader landscape of spatial multi-omics integration tools. However, several minor\npoints still warrant clarification to strengthen the manuscript’s claims and improve its clarity.\nResponse:\nWe sincerely thank you for your positive feedback on our revisions and for recognizing the\nvalue of the additional comparative analyses. We have further revised the manuscript based on\nthe current set of comments. We believe the changes further improve the clarity and strength of\nthe manuscript.\nComment 1: Clarification on Application Scope\nIn response to previous major comment 4 of review 1 on “Single-cell vs spot-based analysis”,\nthe manuscript states that SMART is applicable to both spot-level and single-cell-resolution data.\nHowever, all datasets used in the current study are based on spot- or grid-level measurements.\nGiven the increasing use of single-cell segmented spatial data in the field, it would be helpful for\nthe authors to explicitly state whether SMART is optimized for spot-level data or is equally\napplicable to single-cell segmented data.\nIf SMART is primarily designed for spot-level data, this should be clearly stated—ideally at the\nend of the Introduction where the method is introduced. Conversely, if SMART is intended to\ngeneralize to single-cell data, the manuscript would benefit from either a demonstration of such\nan application or a discussion of how the model would need to be adapted (e.g., changes in\nneighborhood graph construction or hyperparameter tuning). Besides, in cases where both spot-\nlevel and single-cell segmented data can be derived from the same source (e.g., data collected\nusing MERFISH or osmFISH at sub-200 nm resolution, or Stereo-CITE-seq at 500nm resolution),\nit would be informative for the authors to comment on whether SMART performs differently\ndepending on the input granularity. Specifically, is SMART optimized for spot-level data due to\nits architectural design, or are there scenarios where single-cell segmentation offers\nadvantages?\nResponse:\nThank you for raising this concern. SMART is equally applicable to single-cell segmented data\nbecause the construction of graph is based on the nearest neighboring spots, which can be directly\nreplaced by the nearest cells in single-cell segmented data. We performed an additional\nexperiment on cell-segmented data, which yielded results similar with those obtained from spot-\nbased data (Supplementary Fig. S24). As this information may be useful for users, we have added\nan illustration of SMART’s equal applicability to single-cell segmented and spot-based data, as you\nsuggested.\nRevision (Fig. S24):\nb\nFig. S24 Demonstration of SMART’s applicability to single-cell segmented and spot-based data.\na. Spatial plot of mouse spleen using SMART on spot-based data. b. Spatial plot of mouse spleen\nusing SMART on cell-segmented data.\nRevision (Line 471-473):\nOf note, SMART is equally applicable to single-cell segmented data by replacing the nearest\nneighboring spots with the nearest cells. Additional experiment on cell-segmented data yields\nsimilar results with those obtained from spot-based data (Supplementary Fig. S24).\nComment 2: Comparative Evaluation in Simulated vs. Real Data\nIn response to previous major comment 2 of reviewer 1 on “Comparison to other latent\nrepresentations”, the authors had clarified the trade-off between cell/spot specificity and spatial\nstructure modeling. Besides, the updated manuscript now includes comparisons with more\nrecent methods, such as COSMOS, SpaMultiVAE, and CellCharter, that incorporate both spatial\ninformation and multi-modal data (Figures 3–5). This is a welcome addition. However, these\nmethods are not included in the simulated data comparisons shown in Figure 2. Including them\nin the simulated setting would provide a more complete picture of SMART’s performance,\nparticularly in controlled scenarios where ground truth is known.\nResponse:\nThank you very much for the previous valuable comment and your acknowledgement, which\nhelp us to improve the quality of our manuscript. We have included CellCharter, COSMOS (with\ntwo omics), and SpaMultiVAE (with two omics) in Figure 2 and Supplementary Figure S6f\n(SpaMultiVAE does not support ATAC as input). The simulated dataset comprises three omics (RNA,\nADT, and ATAC). However, both COSMOS and SpaMultiVAE currently support only two omics as\ninput. One of our aims in using simulated data was to demonstrate SMART’s capability to integrate\nthree-omics data, and the results further highlight its strong performance.\nRevision (Fig. 2c, 2d, 2e, 2g, 2h，Fig. S6f):\nc\nd\ne g h\nFig. 2 Integration of simulated multi-omics data using SMART for accurate spatial region\nidentification. c Clustering results based on PCA features from RNA, ADT, and ATAC, compared\nwith spatial multi omics integration methods. d Umap plots with ground truth based on PCA features\nfrom RNA, ADT, and ATAC, compared with spatial multi omics integration methods. e Pearson\ncorrelation coefficients between the distance matrices derived from various methods' integrated\nembeddings and those calculated from the individual omics. g Bar plot illustrating Moran’s I scores\nfor different methods. h Bar plot displaying seven evaluation metrics to assess the performance of\ndifferent methods.\nCOSMOS\nFig. S6f Clustering results of RNA and ATAC integration using COSMOS.\nComment 3: Clarification on Figure S5\nThe rebuttal letter references Figure S5 in the context of ablation studies, particularly in response\nto the question regarding trade-offs. To improve clarity, please indicate whether panels A and B\nare derived from SMART’s outputs or from manually curated ground-truth annotations. If they\nare based on SMART, a brief description of the experimental setup used to generate these results\nshould be included in the manuscript. Additionally, to provide a more intuitive understanding of\nthe impact of tuning parameters, I suggest including spatial plots of SMART’s outputs under\nseveral representative conditions (e.g. different K values) as listed in Figures S5c–d. This would\nhelp readers visually assess how parameter choices influence the results. Lastly, I noticed that\nthe order of Figures S5 and S6 appears to be reversed in the supplementary information file.\nPlease verify and correct this for consistency.\nResponse:\nThe panels A and B in Figure S5 were derived from the manually curated ground-truth\nannotation released by the STARmap-RIBOmap-Align dataset [1]. We have clarified this in the\ncaption of Supplementary Fig. S5.\nAs for parameter tuning, we appreciate your suggestion on the demonstration. We have\nincluded the spatial plots of SMART’s outputs in Supplementary Fig. S5. As illustrated in the\nprevious revision response, reconstruction loss and large K tends to focus on spatial continuity,\nwhile triplet loss and small K focus more on expression specificity of spot types.\nWe are sorry for the mistake and have rearranged the order of the figures.\nReference:\n1. Zeng, H. et al. Spatially resolved single-cell translatomics at molecular resolution. Science 380,\neadd3067 (2023).\nRevision (Fig. S5):\nFig. S5 Ablation study for joint cell-type classification and spatial domain detection in\nSTARmap-RIBOmap-Align dataset. a Manually curated ground-truth annotation of spatial\ndomain across consecutive mouse brain tissue sections. b Manually curated ground-truth annotation\nof cell type across consecutive mouse brain tissue sections. c, d Heatmap of ARI (c) and NMI (d)\nfor cell type classification (left) and spatial domain segmentation (right) across various loss\ncombinations and numbers of nearest neighbors (K = 0, 4, 16, 64) when the number of clusters is\nfixed at 13. e, f Clustering outputs of SMART annotated by spatial domain (e) and cell type (f)\nacross various loss combinations and numbers of nearest neighbors (K = 0, 4, 16, 64).\nComment 4: Comparative Results and Trade-Offs in Spatial Integration\nIn the real data comparisons (Figures 3–5), the results from CellCharter appear particularly\ncompelling in terms of identifying visually coherent and biologically plausible spatial domain.\nAlthough the manuscript notes that CellCharter fails to recover the medullary sinus in Figure 3,\nthis may be attributable to specific parameter settings (e.g., clustering resolution or spatial\nweighting) rather than a fundamental limitation of the method. This highlights the broader issue\nthat comparative performance across methods may be highly sensitive to parameter choices.\nWhile a comprehensive parameter sweep across all methods is understandably beyond the scope\nof this manuscript, it would be helpful for the authors to discuss when and why SMART might be\npreferred for multi-modal spatial data integration.\nResponse:\nWe sincerely thank the reviewer for the valuable comments on the comparative experiments.\nWe would like to first clarify that for all comparative methods including CellCharter, we used their\ndefault parameters.\nRegarding the preference scenarios of SMART, which may be particularly useful for users,\nwe would like to highlight three typical situations: (1) SMART is preferred for spatially discrete\n(non-contiguous) niches of the same type, such as follicles in spleen. It is because SMART not only\nperforms neighborhood aggregation to capture spatially adjacent spots/cells but also incorporates\na triplet loss to detect similarities among distant spots/cells, while CellCharter only conducts\nneighborhood aggregation. (2) Multi-section spatial multi-omics data. For multiple sections,\nSMART constructs cross-section triplets, which enables better capture of relationships across\nsections. (3) For large-scale datasets. Owing to its streamlined architectural design, SMART can\nreduce both computation time and memory consumption, as demonstrated in Fig. 5b–e.\nWe have added these explanations to the Discussion section for clarification.\nRevision (line 474-481):\nFor better usage of SMART, we would like to highlight three typical situations where SMART\nis preferred: (1) Spatially discrete (non-contiguous) niches of the same type, such as follicles in\nspleen. SMART not only performs neighborhood aggregation to capture spatially adjacent\nspots/cells but also incorporates a triplet loss to detect similarities among distant spots/cells, which\nis capable of spatially discrete structure. (2) Multi-section spatial multi-omics data. For multiple\nsections, SMART constructs cross-section triplets, which enables better capture of relationships\nacross sections. (3) Large-scale datasets. Owing to its streamlined architectural design, SMART can\nreduce both computation time and memory consumption.\nReviewer #2\nGeneral Comment:\nMy comments from the first version of the manuscript have been satisfactorily addressed.\nI believe this paper is ready for publication.\nResponse:\nWe sincerely thank you for your positive evaluation and supportive comments. We are\ngrateful for your time and effort in reviewing our manuscript, and we are pleased that our revisions\nhave addressed your concerns.\nReviewer #3\nGeneral Comment:\nThe authors have addressed all my concerns. The expanded comparison with existing methods\nnow effectively demonstrates SMART's superiority. The deepened discussion on objectively\nselecting the number of clusters is also a valuable addition.\nResponse:\nWe sincerely thank you for the positive feedback and for recognizing our efforts in expanding\nthe method comparison and discussion on cluster selection.\nComment on Article (Figures & GitHub code):\nFor a final revision, I have two minor requests:\n1. Please make Figures 3e and 4h more readable.\n2. Please add the code to reproduce the manuscript's figures to the GitHub repository. The\ncurrent repository is helpful but lacks the specific scripts for figure generation.\nResponse:\nWe appreciate the reviewer’s suggestion. We have improved the readability of Figures 3e and\n4h by changing the style of boxplot. In addition, we have uploaded the scripts for figure generation\nto the GitHub repository, ensuring reproducibility of the figures presented in the manuscript.\nRevision (Fig. 3e, Fig. 4h):\nFig. 3e Box plots of the seven evaluation metrics across different methods, with the number of\nclusters varying from 4 to 10.\nh\nFig. 4h Box plot of seven evaluation metrics to evaluate the performance of combinations of\ndifferent omics with four sections (E11.0_S1, E13.5_S1, E15.5_S1, E18.5_S1).\nComment 1 on code availability:\n- The README file helpfully lists pinned versions of key dependencies (Python 3.9, muon 0.1.6,\nrpy2 3.5.12, scanpy 1.10.2, scikit-learn 1.5.1, torch 2.4.1, torch_geometric 2.3.0, anndata 0.10.8,\nmatplotlib 3.9.2, tqdm 4.66.5, numba 0.60.0, and R 4.3.0) and links to all datasets. However, the\nlack of a requirements.txt file or an automated installation script, combined with missing\ninstructions for PyTorch Geometric's companion packages (e.g., torch-scatter, torch-sparse) and\nessential R packages, presents a barrier to easy setup. This could lead to significant challenges,\nparticularly for GPU-enabled installations and ensuring rpy2/R interoperability.\nResponse:\nThank you for pointing this out. To improve the user-friendliness of SMART, we construct a\nreadme document website: https://smart-tutorials.readthedocs.io. We also included a\nrequirements.txt file (https://github.com/ws6tg/SMART-main/blob/main/requirements.txt) as\nwell as installation instructions for PyTorch Geometric’s companion packages (torch-scatter, torch-\nsparse) and the essential R packages (https://github.com/ws6tg/SMART-\nmain/blob/main/README.md) in SMART’s repository. This ensures that users can set up the\nenvironment with minimal manual intervention.\nComment 2 on code availability:\n- Assuming a user can successfully replicate the environment and obtain the datasets, the\nprovided notebooks seem sufficient to partially reproduce the reported benchmarks. However,\nfull reproducibility of the paper's findings is uncertain. This is due to several factors: random\nseeds are not documented, training and evaluation commands are embedded directly in\nnotebooks rather than being exposed as command-line scripts, and neither pre-processed data\nsnapshots nor figure generation scripts are included.\nResponse:\nWe thank you for the suggestion in full reproducibility. To address this, we have created a\ndocumentary website: https://smart-tutorials.readthedocs.io following SpatialGlue\n[https://spatialglue-tutorials.readthedocs.io] and COSMOS [https://cosmos-\ntutorials.readthedocs.io]. The website contains detailed tutorials including documented random\nseeds and the pre-processed data, and comprehensive SMART API references to guide users in\napplying the modules conveniently. In addition, we have established a new GitHub branch\ndedicated to training and evaluation scripts and also for figure generation\n(https://github.com/ws6tg/SMART-main/tree/SMART-repreduce).\nComment 3 on code availability:\n- A complete end-to-end run was not attempted. Based on my review, installation appears\npossible but would likely require non-trivial manual effort to align the PyTorch Geometric library\n(and its compiled dependencies) with the R/rpy2 environment. Providing clearer setup\ninstructions or an environment file (e.g., environment.yml) would dramatically increase the\nlikelihood of successful user adoption.\nResponse:\nWe acknowledge the potential challenges with environment setup, particularly for GPU-\nenabled systems. To address this, we have added a clearer requirements.txt file\n(https://github.com/ws6tg/SMART-main/blob/main/requirements.txt) and setup instructions\n(https://github.com/ws6tg/SMART-main/blob/main/README.md) that enables users to\nreproduce the environment seamlessly via conda. Moreover, the installation instructions are\nprovided in our documentary website (https://smart-\ntutorials.readthedocs.io/en/latest/installation.html).\nComment 4 on code availability:\n- The repository is usable, albeit with caveats. It supplies the essential materials and data\npointers needed to reproduce the main analyses. However, it currently lacks the out-of-the-box\nenvironment setup and automation that would facilitate broader use. With the suggested\nimprovements, this repository could become a powerful resource for the community.\nResponse:\nWe thank the reviewer for the constructive suggestion. With the above additions—including\na requirements.txt file (https://github.com/ws6tg/SMART-main/blob/main/requirements.txt),\nfigure generation scripts (https://github.com/ws6tg/SMART-main/tree/SMART-repreduce), a\npackaged release (https://pypi.org/project/bio-SMART/) along with a tutorial website with clearer\ndocumentation (https://smart-tutorials.readthedocs.io/en/latest/), we believe the repository is\nnow a more complete, user-friendly, and reusable resource for the community.\nReviewer #4\nGeneral Comment:\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is\npart of the Nature Communications initiative to facilitate training in peer review and to provide\nappropriate recognition for Early Career Researchers who co-review manuscripts.\nResponse:\nWe sincerely thank the reviewer for your careful evaluation and for co-reviewing this\nmanuscript. We believe we have addressed your concerns accordingly.\nComment on code availability:\nI have confirmed that the source code for the model and the code used for the benchmarks are\navailable, but I have not actually run them, and there is insufficient code to reproduce all the\nfigures.\nResponse:\nWe acknowledge the reviewer’s concern and have now uploaded the figure generation scripts\nto our GitHub repository. We have established a new GitHub branch dedicated to figure generation,\nso that users can more easily reproduce the results presented in our manuscript\n(https://github.com/ws6tg/SMART-main/tree/SMART-repreduce).\nAuthors’ Response to Reviewers’ Comments\nPaper title: SMART: Spatial multi-omic aggregation using graph neural networks and metric learning\nAuthors: Zhihua Du, Qiyi Chen, Weiliang Huang, Jinmiao Chen*, Xubin Zheng*\nWe sincerely thank the Editor and all Reviewers for their careful evaluation of our revised manuscript and for\ntheir constructive and insightful comments. We are pleased that Reviewer #3 and Reviewer #4 found the revised\nmanuscript and code availability satisfactory. Below, we provide a point-by-point response to the remaining\ncomments. The corresponding revisions are highlighted in yellow and the original sentences we mention in the\nresponse are highlighted in green.\nReviewer #3\nComment 1:\nI have carefully read the revised manuscript and the point-by-point response. The authors have addressed all of\nmy previous comments and questions appropriately. I do not have any further comments or concerns.\nResponse:\nWe sincerely thank Reviewer #3 for the careful re-evaluation of our manuscript and for the positive feedback.\nWe are grateful that the revisions adequately addressed all previous concerns.\nReviewer #4\nComment 1:\nThe authors provide appropriate tutorials, benchmarks and codes. It is enough to reproduce the results for users\nResponse:\nWe thank Reviewer #4 for this positive assessment. We are pleased that the provided tutorials, benchmarks,\nand code resources are considered sufficient for reproducibility, and we believe these materials will facilitate the\nadoption and application of SMART by the community.\nReviewer #5\nComment 1.1:\nOne point that previous referee#1 raised on the previous version (that the authors are now addressing) was on\nwhether SMART can do both spot-cell or single-cell level analysis. The authors add Fig. S24 and text revision at\nline 471-473 to address this. I firstly copy and paste what the authors exactly wrote for Fig. S24 figure legend\nand main text:\nFig. S24 Demonstration of SMART’s applicability to single-cell segmented and spot-based data. a. Spatial plot of\nmouse spleen using SMART on spot-based data. b. Spatial plot of mouse spleen using SMART on cell-segmented\ndata\nLine 471-473: Of note, SMART is equally applicable to single-cell segmented data by replacing the nearest\nneighboring spots with the nearest cells. Additional experiment on cell-segmented data yields similar results\nwith those obtained from spot-based data (Supplementary Fig. S24).\nFor above replies, I am concerned on the adequacy of these descriptions, as several key methodological details\nnecessary for evaluating this analysis are missing. For example,\nHow do the authors define what they mean by “spot-based data” versus “single-cell segmented data”? They\nneed to specify the criteria used to distinguish between these data types to allow others to carefully evaluate\nwhether their comparison make biological sense.\nResponse:\nWe thank the reviewer for raising this important point and for highlighting the need for a clearer and more rigorous\nclarification of SMART’s applicability to spot-level and single-cell–segmented spatial data. We agree with the\nreviewer. Below, we clarify the relevant concepts, data processing procedures, and model design considerations,\nand we have revised the manuscript accordingly.\n1. Definition of spot-based data and single-cell–segmented data\nSpot-based data refer to spatial omics data that are either directly generated by spatial profiling platforms,\nsuch as 10x Visium [1] and SPOTS [2], or obtained by aggregating signals into fixed spatial grids. In these data, the\nfundamental spatial unit is a spot with a predefined size. In early spot-based technologies, due to limited spatial\nresolution, each spot typically encompassed multiple cells, and the measured molecular signals represented\naggregated expression from all cells within that spatial region (Fig. R1a & R1b), as described by Greenwald et al.\n[4]. With advances in technology, next-generation high-resolution spot-based spatial omics platforms have\nsubstantially improved spatial resolution, such that multiple spatial spots can correspond to a single cell (Fig. R1c).\nThis enables more fine-grained characterization of both intracellular and intercellular spatial heterogeneity, as\ndemonstrated by platforms such as Visium HD (square bin) [5], Stereo-seq (square bin) [6–8], and Slide-seq [13].\nSingle-cell–segmented data refer to spatial omics data in which the basic spatial unit corresponds to an\nindividual biological cell. These data are obtained either directly from high-resolution imaging-based spatial omics\ntechnologies (e.g., MERFISH [3,9] and seqFISH+ [12]) or through image-guided cell segmentation applied to high-\nresolution imaging-based spatial transcriptomics data, such as Visium HD (cell bin) [5] and Stereo-seq (cell bin) [6–\n8, 11,16,17] (Fig. R1d). In this setting, each spatial unit represents a single cell with an independent spatial\ncoordinate and is associated with the RNA and/or protein expression profile of that cell.\nFig. R1 Illustration of the differences between spot-based data and single-cell–segmented data.\na Nucleic acid staining image of a tissue section. b Low-resolution spot-based spatial data overlaid with nucleic acid\nstaining, where a single spot covers multiple cells. c High-resolution spot-based spatial data overlaid with nucleic\nacid staining, where a single cell is represented by multiple spots. d Image-guided cell segmentation, in which\nmultiple spots are aggregated to reconstruct single-cell–level spatial units. Scale bars are indicated in each panel.\nThe two types of data used in this study were both derived from the same data source, namely the spatial\ntranscriptomic and spatial proteomic co-profiling data generated from fresh-frozen mouse spleen tissue using the\nStereo-CITE-seq platform [8]. Stereo-CITE-seq integrates Stereo-seq [6,15] with CITE-seq [14], enabling the\nsimultaneous measurement of mRNA and protein expression on the same tissue section and thereby providing a\nunified spatial multi-omics representation.\nBecause the raw Stereo-seq data have a high spatial resolution (approximately 500 nm or 715 nm), practical\ndownstream analyses typically require aggregating neighboring DNA nanoballs (DNBs) into larger spatial units (i.e.,\nbinning) to improve the signal-to-noise ratio and reduce computational complexity [6]. In this study, each bin was\ntreated as the fundamental spatial unit at the analysis level (also referred to as a spot). For example, under a\nconfiguration with a 500 nm center-to-center DNB spacing, Bin10 denotes the aggregation of 10 × 10 adjacent\nDNBs into a single spatial unit, corresponding to an area of approximately 5 µm × 5 µm. This binning strategy and\nits rationale have been systematically described in the original Stereo-seq publication [6], and we capture the\nrelevant description below for reference.\nThe center-to-center spacing of individual DNBs is approximately 500 or 715 nm.\nAdjacent DNBs are aggregated into bins of different sizes (e.g., 3 × 3, 14 × 14, or 140 × 140 DNBs),\ncorresponding to different physical scales and UMI counts.\nExamples of bin usage in downstream analyses of Stereo-seq data.\nThe above screenshots are all adapted from the cited literature below:\n[6] Chen, A., Liao, S., Cheng, M., Ma, K., Wu, L., Lai, Y., ... & Wang, J. (2022). Spatiotemporal transcriptomic\natlas of mouse organogenesis using DNA nanoball-patterned arrays. Cell, 185(10), 1777-1792.\n2. Construction of spatial data representations at different spatial scales\nTo evaluate the applicability of SMART across different spatial scales, we constructed two types of spatial\ndata representations based on the Stereo-CITE-seq dataset, corresponding to spot-based and cell-segmented\nspatial resolutions in Supplementary Fig. S25.\n·Spot-based data. Raw spatial data were obtained from the tissue.gef files generated by the Stereo-CITE-\nseq platform. By specifying different bin sizes (5, 10, 20, 50, 100, 150, and 200), the original DNA nanoball (DNB)\nsignals were aggregated into fixed-size spatial grids. Spatial multiomics data of different bin sizes are provided by\nthe Stereo-CITE-seq dataset in the STOmics platform (https://en.stomics.tech/col1191/index.html). Each bin\nserves as the fundamental spatial unit for downstream analysis (i.e., a spot), and its molecular expression profile\nreflects the aggregated signals from multiple cells within the corresponding spatial region (analogous to Figure\nR1b), representing a typical spot-based spatial data format.\n·Single-cell–segmented data. Single-cell–segmented data were derived from the cellbin.gef files generated\nby the image-guided cell segmentation pipeline of the Stereo-CITE-seq dataset in the STOmics platform\n(https://en.stomics.tech/col1191/index.html), in which RNA and protein signals are mapped and aggregated into\ntheir corresponding segmented cell regions. Each cellbin corresponds to a single biological cell (Figure R1d) and is\nassociated with an independent spatial coordinate as well as its RNA and protein expression profiles, representing\na single-cell–segmented spatial data format.\nReference:\n[1] Maynard, K. R., Collado-Torres, L., Weber, L. M., Uytingco, C., Barry, B. K., Williams, S. R., ... & Jaffe, A. E.\n(2021). Transcriptome-scale spatial gene expression in the human dorsolateral prefrontal cortex. Nature\nneuroscience, 24(3), 425-436.\n[2] Ben-Chetrit, N., Niu, X., Swett, A. D., Sotelo, J., Jiao, M. S., Stewart, C. M., ... & Landau, D. A. (2023).\nIntegration of whole transcriptome spatial profiling with protein markers. Nature biotechnology, 41(6), 788-793.\n[3] Qian, X., Coleman, K., Jiang, S., Kriz, A. J., Marciano, J. H., Luo, C., ... & Walsh, C. A. (2025). Spatial\ntranscriptomics reveals human cortical layer and area specification. Nature, 1-11.\n[4] Greenwald, A. C., Darnell, N. G., Hoefflin, R., Simkin, D., Mount, C. W., Castro, L. N. G., ... & Tirosh, I. (2024).\nIntegrative spatial analysis reveals a multi-layered organization of glioblastoma. Cell, 187(10), 2485-2501.\n[5] Oliveira, M. F. D., Romero, J. P., Chung, M., Williams, S. R., Gottscho, A. D., Gupta, A., ... & Taylor, S. E.\n(2025). High-definition spatial transcriptomic profiling of immune cell populations in colorectal cancer. Nature\nGenetics, 1-12.\n[6] Chen, A., Liao, S., Cheng, M., Ma, K., Wu, L., Lai, Y., ... & Wang, J. (2022). Spatiotemporal transcriptomic\natlas of mouse organogenesis using DNA nanoball-patterned arrays. Cell, 185(10), 1777-1792.\n[7] Zhao, Y., Li, Y., He, Y., Wu, J., Liu, Y., Li, X., ... & Xu, X. (2025). Stereo-seq V2: Spatial mapping of total RNA\non FFPE sections with high resolution. Cell, 188(23), 6554-6571.\n[8] Liao, S., Heng, Y., Liu, W., Xiang, J., Ma, Y., Chen, L., ... & Xu, X. (2023). Integrated spatial transcriptomic and\nproteomic analysis of fresh frozen tissue based on stereo-seq. bioRxiv, 2023-04.\n[9] Xia, C., Fan, J., Emanuel, G., Hao, J., & Zhuang, X. (2019). Spatial transcriptome profiling by MERFISH reveals\nsubcellular RNA compartmentalization and cell cycle-dependent gene expression. Proceedings of the National\nAcademy of Sciences, 116(39), 19490-19499.\n[10] Kleshchevnikov, V., Shmatko, A., Dann, E., Aivazidis, A., King, H. W., Li, T., ... & Bayraktar, O. A. (2022).\nCell2location maps fine-grained cell types in spatial transcriptomics. Nature biotechnology, 40(5), 661-671.\n[11] Petukhov, V., Xu, R. J., Soldatov, R. A., Cadinu, P., Khodosevich, K., Moffitt, J. R., & Kharchenko, P. V. (2022).\nCell segmentation in imaging-based spatial transcriptomics. Nature biotechnology, 40(3), 345-354.\n[12] Eng, C. H. L., Lawson, M., Zhu, Q., Dries, R., Koulena, N., Takei, Y., ... & Cai, L. (2019). Transcriptome-scale\nsuper-resolved imaging in tissues by RNA seqFISH+. Nature, 568(7751), 235-239.\n[13] Rodriques, S. G., Stickels, R. R., Goeva, A., Martin, C. A., Murray, E., Vanderburg, C. R., ... & Macosko, E. Z.\n(2019). Slide-seq: A scalable technology for measuring genome-wide expression at high spatial resolution. Science,\n363(6434), 1463-1467.\n[14] Stoeckius, M., Hafemeister, C., Stephenson, W., Houck-Loomis, B., Chattopadhyay, P. K., Swerdlow, H., ...\n& Smibert, P. (2017). Simultaneous epitope and transcriptome measurement in single cells. Nature methods, 14(9),\n865-868.\n[15] Wei, X., Fu, S., Li, H., Liu, Y., Wang, S., Feng, W., ... & Gu, Y. (2022). Single-cell Stereo-seq reveals induced\nprogenitor cells involved in axolotl brain regeneration. Science, 377(6610), eabp9444.\n[16] Ståhl, P. L., Salmén, F., Vickovic, S., Lundmark, A., Navarro, J. F., Magnusson, J., ... & Frisén, J. (2016).\nVisualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science, 353(6294), 78-\n82.\n[17] Palla, G., Spitzer, H., Klein, M., Fischer, D., Schaar, A. C., Kuemmerle, L. B., ... & Theis, F. J. (2022). Squidpy:\na scalable framework for spatial omics analysis. Nature methods, 19(2), 171-178.\nRevision (Discussion, Line 470-475; Methods, Line 593-596; Supplementary note, Line 47-66):\nDiscussion, Line 470-475：\nOf note, although SMART is primarily designed for spot-based data, it is applicable to single-cell–segmented data.\nHere, spot-based data refer to datasets where each spatial unit represents a fixed-size region that is neatly arranged\nand may aggregate signals from multiple cells (Supplementary Notes), whereas single-cell–segmented data refer to\ndatasets in which each spatial unit corresponds to an individual biological cell obtained via image-guided\nsegmentation or imaging-based technologies (Supplementary Notes).\nMethods, Line 593-596：\nIn addition to spot-level representations generated by spatial binning, we also used the image-guided cell\nsegmentation results provided by the Stereo-CITE-seq pipeline (cellbin.gef), in which RNA and protein signals are\naggregated at the single-cell level. These data were used to evaluate SMART’s applicability to single-cell–segmented\nspatial data.\nSupplementary note, Line 47-66：\nDefinition of spot-based and single-cell segmented data\nSpot-based data.\nSpot-based spatial data were derived from the tissue.gef files generated by the Stereo-CITE-seq platform.\nRaw spatial signals from DNA nanoballs (DNBs) were aggregated into fixed-size spatial grids by\nspecifying different bin_size values (5, 10, 20, 50, 100, 150, and 200). This binning procedure represents\na standard preprocessing step in the Stereo-seq platform for handling ultra–high-resolution raw data and\nhas been systematically described in the original methodological publication [1]. Under this\nrepresentation, each bin serves as the basic spatial unit at the analysis level (i.e., a spot), and its molecular\nexpression profile reflects the aggregated signals from multiple cells within the corresponding spatial\nregion, constituting a typical spot-level spatial data representation.\nSingle-cell segmented data.\nSingle-cell segmented data were obtained from cellbin.gef files generated by the Stereo-CITE-seq\nplatform using an image-guided cell segmentation pipeline. In this process, RNA and protein signals\nwere independently mapped and aggregated to the corresponding segmented cellular regions. Each\ncellbin corresponds to an individual biological cell and is associated with a unique spatial coordinate as\nwell as matched RNA and protein expression profiles, thereby constituting a single-cell–segmented\nspatial data representation.\n[1] Chen, A., Liao, S., Cheng, M., Ma, K., Wu, L., Lai, Y., ... & Wang, J. (2022). Spatiotemporal transcriptomic atlas\nof mouse organogenesis using DNA nanoball-patterned arrays. Cell, 185(10), 1777-1792.\nComment 1.2:\nIn addition, it is unclear how the use of “nearest neighboring spots” and “nearest cells” differs between the two\nanalyses in terms of model design and parameter settings.\nResponse:\nWe thank the reviewer for raising this question. Below, we clarify the differences between constructing\nspatial graphs based on nearest-neighbor spots and nearest-neighbor cells.\nThe core idea of SMART is to formulate spatial multi-omics data into a spatial graph structure. The distinction\nbetween spot-level and single-cell–level analyses lies solely in the spatial graph construction step (Fig. S24a):\nIn spot-based analyses, nodes in the spatial graph correspond to spots, and node features are represented\nby spot-level principal components. Spatial adjacency is defined based on the Euclidean distances between spot\ncoordinates and constructed using a k-nearest neighbors (kNN) strategy (Fig. S24b). The selection of the parameter\nk has been explained in detail in our previous responses.\nIn single-cell–segmented analyses, nodes in the spatial graph correspond to individual cells, and node\nfeatures are similarly represented by cell-level principal components. Spatial adjacency is defined based on the\nEuclidean distances between cell centroid coordinates. The spatial graph can be constructed using the same kNN\nstrategy or alternatively by using a radius corresponding to approximately one cell diameter (Fig. S24c). In both\ncases, the underlying principle is to capture the immediate local neighborhood of each cell. Empirically, we\nobserved that constructing graphs using the nearest surrounding ring of neighboring cells yields better model\nperformance (Fig. S2a,b and Fig. S3e,f).\nApart from the physical definition of graph nodes, the model architecture, loss functions (including\nreconstruction loss and triplet loss), training procedure, and optimization strategy remain identical across both\nanalyses. No additional model parameters are introduced during graph construction for single-cell–segmented\ndata; cell spatial coordinates are solely used to determine nearest neighbors. Therefore, replacing “nearest-\nneighbor spots” with “nearest-neighbor cells” only changes the formulation of spatial nodes during graph\nconstruction without altering the SMART model design.\nFig. S24 Illustration of the differences between spot-based and single-cell–segmented graph constructions.\na Architecture of SMART. Using “nearest neighboring spots” and “nearest cells” only differs in the spatial graph\nconstruction, but they are all based on the spatial coordinates of spots or cells. b-c Spatial graph in spot-based data\n(b) and single cell-segmented data (c).\nRevision (Methods, Line 624-630; Discussion, Line 475-482):\nMethods, Line 624-630:\nFor each modality, SMART extracts principal components (PCs) using principal component analysis (PCA) and\nconstructs spatial neighboring graphs with PCs as node features. Spatial graphs are built based on the coordinates of\nspatial units using a k-nearest-neighbor (kNN) strategy. In spot-based analyses, nodes correspond to spots or bins,\nwhereas in single-cell–segmented analyses, nodes correspond to individual cells, with cell centroids used as spatial\ncoordinates. For single-cell–segmented data, radius within one cell distance to select the nearest cells around can\nalso be used in spatial graph construction.\nDiscussion, Line 475-482：\nIn spot-based analyses, nodes correspond to spots or bins, spatial graphs are built based on the coordinates of spatial\nunits using a k-nearest-neighbor (kNN) strategy. In single-cell–segmented analyses, nodes correspond to individual\ncells, with cell centroids used as spatial coordinates. kNN or Radius of one cell distance to select the nearest cells\naround can both be used in spatial graph construction (Supplementary Fig. S24). Because SMART formulates spatial\nmulti-omics data as a graph over spatial units, replacing spots with cells only changes the granularity of graph nodes\nwithout altering the model architecture. Apart from the substitution of spatial units, other model components, loss\nfunctions, and hyperparameters remain unchanged for single-cell–segmented data.\nComment 1.3:\nWithout these essential details, the authors simply state that they compared single-cell–segmented and spot-\nbased data and obtained similar clustering results with SMART, supported only by a very brief description. I\ndo not believe this constitutes an adequate response to the reviewer’s comments. A more rigorous and detailed\nexplanation is required to properly address the reviewer’s concerns.\nResponse:\nWe thank the reviewer for raising this question. Descriptions of spot-based and single-cell–segmented data,\nas well as how the model treats these two data types, have been addressed in the above two responses. Here, we\nprovide a consolidated analysis.\nSMART was originally designed with spot-level spatial data as its primary application scenario, as the majority\nof currently available spatial multi-omics datasets are spot-based. However, both from a theoretical perspective\nand based on experimental results, SMART is equally applicable to single-cell–segmented data. Theoretically,\nSMART models spatial multi-omics data as a graph, in which each node represents a spatial unit (either a spot or a\ncell), and edges are constructed based on relationships among nearest neighboring spatial units. All subsequent\noperations and computations are performed on this graph structure. Therefore, for single-cell–segmented data,\nthe only modification required is to replace nearest-neighbor spots with nearest-neighbor cells during graph\nconstruction. This change merely alters the biological interpretation of each node from representing a spot to\nrepresenting a cell, while the objective of graph construction remains the same: to connect the immediate local\nneighborhood of spatial units. Since all downstream operations and computations are graph-based, no further\nchanges to the model or its computations are required.\nFrom an experimental perspective, the additional experiments conducted on cell-segmented data yielded\nresults highly similar to those obtained using spot-level data (Supplementary Fig. S25). As this information may be\nvaluable for users, we have added an illustrative schematic in the revised manuscript to explicitly demonstrate\nSMART’s applicability to both single-cell–segmented and spot-based data. In practice, users only need to replace\nspots with cells when constructing the neighborhood graph, while all other components including model\narchitecture and hyperparameter settings can remain unchanged.\nFig. S25 Demonstration of SMART’s applicability to single-cell segmented and spot-based data. a Spatial plot of\nmouse spleen using SMART on spot-based data. b Spatial plot of mouse spleen using SMART on cell-segmented\ndata.\nIn addition, when the same data source can generate both spot-level data and single-cell–segmented data,\ndifferences in input data quality may influence the performance. In our Stereo-CITE-seq experiments (Fig. 5C),\nfor spot-based data, bin sizes between 20 and 100 yielded better performance compared with overly fine or overly\ncoarse spatial partitions. For single-cell–segmented data, spatial granularity is no longer a primary factor, however,\nperformance may be affected by the accuracy of the cell segmentation algorithm. Overall, for both types of input,\nperformance differences arising from the model itself are likely to be much smaller than those induced by the\nquality and intrinsic characteristics of the input data.\nFinally, we candidly acknowledge that SMART was originally designed with spot-level spatial data as its primary\napplication scenario. However, its graph-based modeling framework is inherently scale-agnostic, enabling direct\napplication to single-cell–segmented spatial data without modifying the core model.\nFig. 5 SMART efficiently integrates large-scale multi-omics datasets. c Clustering results of the mouse spleen at\nmultiple spatial resolutions using PCA features of RNA, ADT, and SMART’s integrated embedding.\nRevision (Discussion, Line 483-495):\nSMART was originally designed for spot-level spatial data as the primary application scenario. However, it is also\napplicable to single-cell–segmented data by simply replacing the meaning of nodes from spots to cells without\nmodifying the network architecture or optimization strategy. An additional experiment on cell-segmented data\nderived from the same Stereo-CITE-seq dataset yields similar results with those obtained from spot-based data\n(Supplementary Fig. S25). When the same data source can simultaneously generate spot-level data and single-cell\nsegmented data, SMART does not exhibit a preference for any particular input form in our experimental results\n(Supplementary Fig. S25). However, different input data quality may influence the model's performance.\nFor example, in our Stereo-CITE-seq experiment (Fig. 5c), settings with a bin size between 20 and 100 yielded\nbetter performance compared to finer or coarser spatial divisions. For single-cell segmented data, spatial granularity\nis no longer a primary factor, but model performance may be affected by the accuracy of the cell segmentation\nalgorithm. For both input types, the differences arising from the quality and characteristics of the input data itself\nare likely much higher than those induced by the model.\nComment 2:\nPrevious Referee#1 also had a question about setting a fair comparison between SMART and recent methods,\nincluding COSMOS, SpaMultiVAE, and CellCharter. The authors have incorporated these methods into their\nanalysis and argue that SMART outperforms previously published state-of-the-art approaches. However, upon\ncarefully examining the figures and results presented, I find the reported performance of COSMOS, SpaMultiVAE,\nand CellCharter on the same datasets to be substantially worse than what has been demonstrated in their\noriginal publications. For example, the dataset shown in Figure 5A was previously analyzed using COSMOS,\nSpatialGlue, and CellCharter, where the reported results are notably stronger than those presented in the current\nSMART manuscript – If readers carefully examine these prior publications and compare the corresponding\nfigures, it is difficult to conclude that SMART represents a better approach. This discrepancy raises concerns\nabout whether these state-of-the-art methods were implemented appropriately and whether the comparisons\nare being conducted under fair and comparable conditions.\nWithout a clear explanation of parameter choices and evaluation criteria, it is difficult to assess the validity of\nthe claimed performance advantages of SMART. A transparent and reproducible comparison is necessary to\nsupport the authors’ conclusions.\nResponse:\nWe thank the reviewer for their careful examination of the comparisons between SMART and recent methods,\nincluding COSMOS, SpaMultiVAE, and CellCharter. We have carefully compared our reproduced results and the\noriginal papers of the benchmarking methods, and also transparently provided details of the parameters in our\nreproduction and evaluation metrics for all the methods in our study.\n1. Differences in results on the P22 mouse brain dataset (Fig. 5a)\nThe discrepancy between the original publication and our manuscript is mainly because the tissue slice used\nin Fig. 5a of our manuscript is different from the slice analyzed in the original studies. We explicitly illustrate these\ndifferences in the figure below (Fig. R3). Since the original SpaMultiVAE study did not use the same dataset as our\nmanuscript, its results are not included in this comparison.\nFig. R3 Clustering results of mouse brain sections (adapted from the original figures in the respective\npublications).\nCOSMOS and CellCharter used the slice labeled with “RNA+ATAC” in their original paper, while we used the\nslice labeled with “RNA+H3K27me3” in our manuscript. It is because P22 mouse brain dataset does not provide\nground-truth annotations and we have already used the MISAR-seq dataset with annotation (Fig. 4) to compare\nthe performance on spatial RNA + ATAC data. So, we would like to demonstrate SMART on another types of omic\ncombination, namely “RNA+H3K27me3”. To ensure a fair comparison, all competing methods in our manuscript\nwere evaluated using a unified clustering strategy based on mclust, following the practice adopted in SpatialGlue.\nWe have added all reproduction parameters of comparative methods and calculation of evaluation metrics in the\nrevised manuscript (Supplementary Note).\n2. Overall comparison\nTo facilitate a fair and comprehensive comparison, we have listed the reproduction parameters for each\nmethod (Supplementary Notes). Except for the unified use of mclust as the clustering method and dataset-specific\nchoices of the number of clusters (explicitly described in the main text and highlighted in green for clarity),\nall other model parameters follow the recommended settings provided in the respective source codes or official\ntutorials.\nBased on these standardized conditions, we summarized and compared the key evaluation metrics across the five\ndatasets used in this study (Supplementary Table 2).\nThe results show that SMART ranked first on all four labeled datasets, reflecting its strong capability in\nidentifying spatial domains. At the same time, we acknowledge that on the mouse brain dataset, SMART did not\nperform as well as some other methods, highlighting a limitation of SMART in modeling spatial smoothness. Overall,\nSMART outperforms other methods on the majority of datasets, demonstrating strong spatial domain\nidentification performance, support for multi-section integration, and the ability to scale to large datasets owing\nto its low computational cost.\nIn this regard, as noted in our previous response, SMART is particularly advantageous in the following three\nscenarios, which we offer as guidance for users: (1) SMART is preferred for spatially discrete (non-contiguous)\nniches of the same type, such as follicles in spleen. It is because SMART not only performs neighborhood\naggregation to capture spatially adjacent spots/cells but also incorporates a triplet loss to detect similarities among\ndistant spots/cells, while CellCharter only conducts neighborhood aggregation. (2) Multi-section spatial multi-\nomics data. For multiple sections, SMART constructs cross-section triplets, which enables better capture of\nrelationships across sections. (3) For large-scale datasets. Owing to its streamlined architectural design, SMART can\nreduce both computation time and memory consumption, as demonstrated in Fig. 5b,d,e.\nThese points were already incorporated into the Discussion in the previous revision. In the current revision,\nwe have added a dedicated section on limitations in the Discussion.\nSupplementary Table 2. Benchmarking performance on different datasets\nNote: N/S represents not support\nFig. 5 SMART efficiently integrates large-scale multi-omics datasets. b Runtime and peak memory usage of various methods on the P22 mouse brain dataset. d GPU memory usage of different\nmethods across spatial resolutions in the mouse spleen dataset. e Runtime comparison of different methods across spatial resolutions in the mouse spleen dataset.\n3. Comparative analysis with COSMOS\nWe put the results and clustering methods together for comprehensive comparison between COSMOS and\nSMART (Fig. R4). First, Fig. 5a of the SMART manuscript uses a tissue slice named “RNA + H3K27me3” in the original\ndataset, whereas the COSMOS original study analyzed a different slice named “RNA + ATAC”. Here, we conducted\nadditional experiments using the RNA + ATAC slice employed in the original COSMOS study. Of note, in the COSMOS\noriginal publication, experiments were performed only on selected regions of the tissue (Fig. R4a) and COSMOS\napplies specific preprocessing steps to the data. We applied SMART to the same preprocessed data provided by\nCOSMOS (but may bring unfairness). In this setting, SMART was applied to all regions of the slice and clustering\nwas performed using the Louvain algorithm, as in the COSMOS original study (Fig. R4c-d). Under these COSMOS’s\nconditions, SMART can only achieve results comparable to COSMOS. Specifically, COSMOS produced more spatially\ncontinuous regions overall, but SMART performed better in certain local areas (Fig. R4b-d). For example, SMART\nmore clearly delineated the layer VI region compared with COSMOS (Fig. R4e), and in the Ct-1 to Ct-5 regions,\nSMART successfully identified five distinct layers, while COSMOS identified only four (Fig. R4c&d). In contrast,\nCOSMOS yielded smoother spatial domains than SMART.\nHowever, the COSMOS original study did not evaluate its method on other labeled datasets used in our\nmanuscript that allow for quantitative assessment of spatial domain identification accuracy. We reproduced\nCOSMOS on other three datasets with all the parameters listed in Supplementary Notes. From the results (Fig. R4f-\ni cut from the manuscript), SMART outperforms COSMOS in identifying spatial domain with higher ARI in three\ndatasets. It is probably because COSMOS tends to ensure region smoothness. Besides, COSMOS is unable to\nsupport multi-slice integration.\nFollowing the reviewer’s suggestion, we have transparently provided all reproduction parameters in the\nSupplementary Notes. The specific numbers of clusters used for each dataset have already explicitly been stated\nin the main text (highlighted in green), and all methods were evaluated using the same clustering numbers. Other\nmodel parameters followed the recommended settings in the respective source codes or official tutorials.\nOverall, SMART performed better than COSMOS in terms of spatial domain identification, although it may\nproduce spatial domains with less smoothness in certain settings. We have acknowledged this limitation in\nDiscussion.\nFig. R4 Comparison between COSMOS and SMART.\na Clustering results in the original COSMOS publication on mouse brain RNA + ATAC data.\nb Reference of the mouse brain coronal section from the Allen Mouse Brain Atlas.\nc Reproduced COSMOS clustering results on the “RNA + ATAC” slice data using the full tissue region.\nd SMART clustering results on the “RNA + ATAC” slice data using the full tissue region. Zoomed-in views of the VI\nregion comparing the reference annotation with COSMOS and SMART results.\ne Clustering results of COSMOS and SMART on the “RNA + H3K27me3” slice with respective settings.\nf-i Clustering results of COSMOS and SMART on the simulated, human lymph node, mouse brain (MISAR-seq), and\nhuman tonsil datasets with respective settings cut out from the manuscript.\n4. Comparison with SpatialGlue\nSpatialGlue evaluated its method on multiple datasets that are also used in our study. Therefore, we\nperformed a one-to-one comparison between the results reported in the original SpatialGlue publication and those\nreproduced in our manuscript, as shown in Fig. R5. The reproduced results similar with those reported in the\noriginal SpatialGlue study.\nAll parameters used in our reproductions are detailed in the Supplementary Note. For consistency, clustering\nwas uniformly performed using mclust, and the specific number of clusters for each dataset is explicitly stated in\nthe main text and kept identical across all methods (highlighted in green). All remaining model parameters followed\nthe recommended settings provided in the respective source codes or official tutorials.\nFig. R5 Comparison of experimental results on the same datasets between the SMART manuscript and the\noriginal SpatialGlue study.\n5. Comparison with CellCharter\nWe put the results and clustering methods together for comprehensive comparison between CellCharter and\nSMART (Fig. R6). First, the main difference between the original CellCharter study and our reproduced results is\nthe different slice we used. “RNA + ATAC” slice data were used in the original study and “RNA + H3K27me3” slice\ndata were used in our study. In their original paper, the number of clusters was automatically determined using its\nbuilt-in ClusterAutoK pipeline. Here, we conducted additional experiments adopting their ClusterAutoK pipeline to\nSMART on both “RNA + ATAC” and “RNA + H3K27me3” slice (Fig. R6a-d). The results show that, on the RNA + ATAC\nslice, SMART exhibits lower spatial continuity of identified regions compared with CellCharter, while the differences\nbetween the two methods are less pronounced on the RNA + H3K27me3 slice. Because this dataset does not\nprovide ground-truth annotations, quantitative accuracy evaluation is not feasible.\nHowever, the original CellCharter study did not evaluate its method on the other labeled datasets used in\nthe present manuscript. We reproduced CellCharter on other three datasets with all the parameters listed in\nSupplementary Notes. From the results (Fig. R6f-i cut from the manuscript), SMART outperformed CellCharter in\nidentifying spatial domain with higher ARI in three datasets. It is probably because CellCharter tends to ensure\nregion smoothness. Besides, CellCharter is unable to support multi-slice integration. For consistency, clustering\nwas uniformly performed using mclust for all methods, following the practice adopted in SpatialGlue, with the\nspecific number of clusters explicitly stated in the main text (highlighted in green) and kept identical across all\nmethods. All remaining model parameters followed the recommended settings in the respective source codes or\nofficial tutorials.\nOverall, SMART performed better than CellCharter in terms of spatial domain identification. These results\nreflect a limitation of our method, namely that SMART may produce spatial domains with less smoothness in\ncertain settings. We have added this limitation in Discussion.\nFig. R6 Comparison between CellCharter and SMART.\na Clustering results in the original CellCharter publication on mouse brain RNA + ATAC data.\nb Clustering results of SMART using CellCharter’s ClusterAutoK on mouse brain RNA + ATAC data.\nc Reproduced CellCharter’s clustering results on the “RNA + H3K27me3” slice data using ClusterAutoK.\nd SMART’s clustering results on the “RNA + H3K27me3” slice data using CellCharter’s ClusterAutoK.\ne Clustering results of CellCharter and SMART on the “RNA + H3K27me3” slice with respective settings.\nf-i Clustering results of CellCharter and SMART on the simulated, human lymph node, mouse brain (MISAR-seq),\nand human tonsil datasets with respective settings cut out from the manuscript.\n6. Comparison with SpaMultiVAE\nWe put the results and clustering methods together for comprehensive comparison between SpaMultiVAE\nand SMART (Fig. R7). SMART performed better than SpaMultiVAE in terms of spatial domain identification.\nParticularly, SpaMultiVAE does not support ATAC-seq and multi-slice integration. For consistency, clustering was\nuniformly performed using mclust for all methods, following the practice adopted in SpatialGlue, with the specific\nnumber of clusters explicitly stated in the main text (highlighted in green) and kept identical across all methods.\nAll remaining model parameters followed the recommended settings in the respective source codes or official\ntutorials.\nFig. R7 Comparison between SpaMultiVAE and SMART.\na-e Clustering results of SpaMultiVAE and SMART on the simulated (a), human lymph node(b), mouse brain (MISAR-\nseq)(c) , mouse brain (RNA+H3K27me3)(d) and human tonsil datasets (e) with respective settings cut out from the\nmanuscript.\n7. Transparency of parameters and reproducibility\nTo enhance the transparency and reproducibility of the comparisons, we have added all reproduction\nparameters in the revised manuscript. The use of mclust as a unified clustering method following the practice\nadopted in SpatialGlue and dataset-specific choices of the number of clusters have explicitly described in the main\ntext highlighted in green (We also tested different clustering numbers, see Fig. 3e, Fig. 4h, Fig 6h. Clustering number\nin Fig. 5 was determined using internal clustering validation metrics, see Lines 298-300). All other model\nparameters follow the recommended settings provided in the respective source codes or official tutorials. The\ndetailed configurations are summarized in Supplementary Notes, Lines 9–46:\nRegarding the evaluation metrics for SMART, we have already provided a detailed description of how all\nmetrics were computed in the original SMART manuscript. For the reviewer’s convenience, these sections have\nbeen highlighted in green in the revised manuscript (Lines 829–934).\nRevision (Discussion, Line 504-510; Supplementary Notes, Lines 9–46; Supplementary Table 2):\nDiscussion, Line 504-510:\nDespite its strong performance in identifying spatial domains and discrete tissue structures, SMART also\nhas limitations. SMART prioritizes feature-driven discrimination of spatial units and the accurate\nidentification of domain spots, rather than explicitly enforcing strong spatial smoothness. As a result, in\ntissues where spatial domains vary continuously with gradual transitions, SMART may yield embeddings\nwith unclear boundaries compared with methods that impose stronger spatial continuity priors. This\nbehavior reflects an inherent trade-off between preserving molecular heterogeneity and enforcing spatial\nsmoothness.\nSupplementary Notes, Lines 9–46:\nBenchmarking Methods for SMART\nTo comprehensively evaluate the performance of SMART, we compared it with 13 representative spatial\nmulti-omics integration methods. All benchmarking methods were executed following official tutorials or\nrecommended settings in the original paper, unless otherwise specified.\nCellCharter was applied with a single-layer encoder–decoder architecture (128 nodes per hidden layer),\na latent dimensionality of 10, dropout rate of 0.1, and batch size of 128. Spatial information was incorporated using\nfour neighborhood aggregation layers with mean aggregation.\nCOSMOS was implemented with a latent dimension of 50 and trained for up to 1,000 epochs with early\nstopping enabled. Spatial regularization was applied using a k-nearest neighbor graph (k = 10), while the spatial\nregularization strength was set to zero to ensure consistency across datasets.\nSpatialGlue was executed following its original configuration, selecting 3,000 highly variable genes as\ninput, constructing a spatial neighbor graph with three nearest neighbors, and reducing dimensionality to 30\nprincipal components. The model was trained for 600 epochs using the Adam optimizer with a learning rate of\n1e−4 and a fixed random seed of 2022.\nSpaMultiVAE was trained for up to 100 iterations with early stopping enabled. The encoder consisted of\ntwo hidden layers (128, 64), while gene and protein decoders used single hidden layers with 128 units. The latent\nspace was decomposed into Gaussian and Gaussian process components, following the default design.\nMEFISTO and MOFA+ were applied using highly variable gene selection (3,000 genes) and PCA-based\npreprocessing. MEFISTO employed sparse Gaussian processes with 1,000 inducing points and 30 latent factors,\nwhile MOFA+ was trained with 10 latent factors and a maximum of 1,000 iterations using the fast convergence\nmode.\nMISO was trained using Adam optimizer with a learning rate of 1e−2 for 1,000 epochs. Input features were\nreduced to 128 principal components before model training.\nscMM was executed using its default objective function with deterministic warmup. The model was trained\nfor 50 epochs with a batch size of 32 and a latent dimensionality of 64.\nMultiVI and totalVI were implemented using the scVI framework. MultiVI was trained with a 64-\ndimensional latent space, two hidden layers in both encoder and decoder, and equal modality weights. For totalVI,\n4,000 highly variable genes were selected, and the model was trained with early stopping enabled.\nPRESENT was applied using 3,000 highly variable genes and a 64-dimensional latent space. The model was\noptimized with the Adam optimizer (learning rate = 1 × 10⁻³, weight decay = 1 × 10⁻⁴) for up to 100 epochs with a\nbatch size of 320. Early stopping based on validation loss was employed with a patience of 20 epochs and a\nminimum improvement threshold of 1 × 10⁻⁴.\nSimilarity Network Fusion (SNF) was applied using PCA-reduced features (50 components), with 10\nneighbors and 20 diffusion iterations.\nWeighted Nearest Neighbor (WNN) integration was performed using 3,000 highly variable genes, 50 PCA\ncomponents, and k = 10 nearest neighbors.\nSupplementary Table 2. Benchmarking performance on different datasets\nSupplementary Table 2. Benchmarking performance on different datasets\nNote: N/S represents not support\nComment 3:\nPrevious Referee#1 had already asked about more clarity regarding the ablation studies, which the authors have\nreplied to and done in the last two rounds of revision. In the most recent review round, the Referee#1 was asking\nthe authors to be extra clear on how tuning parameters/hyperparameters impacts the analysis and outputs. I\nthink the new Figure S5 did a great job to explain all these details.\nResponse:\nWe thank Reviewer #5 for this positive feedback. We are pleased that the revised ablation analysis and\nSupplementary Fig. S5 clearly illustrate the impact of key parameters and hyperparameters on SMART’s\nperformance.\nComment 4:\nI did not find any issue for the scripts.\nResponse:\nWe thank Reviewer #5 for examining the provided scripts. We are pleased to note that no issues were\nidentified, which supports the correctness of our implementation."}]

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