JADE: Joint Alignment and Deep Embedding for Multi-Slice Spatial Transcriptomics
Authors: Yuanchuan Guo
Jun S. Liu
Huimin Cheng
Ying Ma
Venue: NeurIPS 2025 poster ()
Keywords: Spatial transcriptomics
Multi-slice integration
Joint alignment
Deep embedding
Attention mechanisms
Primary area: machine_learning_for_sciences
TL;DR: JADE is a unified framework that simultaneously learns spot-wise alignments and shared low-dimensional embeddings to robustly integrate multi-slice spatial transcriptomics data.

Abstract: As spatial transcriptomics (ST) datasets increasingly span multiple adjacent or replicated slices, effective joint analysis across slices is needed to reconstruct tissue structures and identify consistent spatial gene expression patterns. This requires resolving spatial correspondences between slices while capturing shared transcriptomic features, two tasks that are typically addressed in isolation. Multi-slice analysis remains challenging due to physical distortions, technical variability, and batch effects. To address these challenges, we introduce Joint Alignment and Deep Embedding for multi-slice ST (JADE), a unified computational framework that simultaneously learns spot-wise alignments and shared low-dimensional embeddings across tissue slices. Unlike existing methods, JADE adopts a roundtrip framework in which each iteration alternates between alignment and embedding refinement. To infer alignment, we employ attention mechanisms that dynamically assess and weight the importance of different embedding dimensions, allowing the model to focus on the most alignment-relevant features while suppressing noise. To the best of our knowledge, JADE is the first method that jointly optimizes alignment and representation learning in a shared latent space, enabling robust multi-slice integration. We demonstrate that JADE outperforms existing alignment and embedding methods across multiple evaluation metrics in the 10x Visium human dorsolateral prefrontal cortex (DLPFC) and Stereo-seq axolotl brain datasets. By bridging spatial alignment and feature integration, JADE provides a scalable and accurate solution for cross-slice analysis of ST data.

JADE: Joint Alignment and Deep Embedding for Multi-Slice Spatial Transcriptomics
Yuanchuan Guo
Jun S. Liu" Department of Statistics Tsinghua University
Huimin Cheng"
Department of Statistics Harvard University yguo @g. www.aarrdd...... edu
Department of Biostatistics Boston University
junsliu@tsinghue edu.
huimin23@bu. edu
Ying Ma Department of Biostatistics
Center for Computational Molecular Biology Brown University
ying_ma@bnn haggmmm@rrown.eed
Abstract
As spatially resolved transcriptomics (SRT) datasets increasingly span multiple adjacent replicated slices, effective joint analysis across slices is needed to reconstruct tissue structures and identify consistent spatial gene expression patterns. This requires resolving spatial correspondences between slices while capturing shared transcriptomic features, two tasks that are typically addressed in isolation. Multi-slice analysis remains challenging due physical distortions, technical variability, and batch effects. To address these challenges, we introduce Joint Align- ment and Deep Embedding for multi-slice SRT (JADE), unified computational framework that simultaneously learns spatial location-wise alignments and shared low-dimensional embeddings adopts a roundtrip framework which each iteration alternates between alignment and embedding refinement. To infer alignment, we employ attention mechanisms that dynamically assess and weight the importance of different embedding dimen- sions, allowing the model focus on the most diinmeent-reeeaan features while suppressing noise. To the best of our knowledge, JADE is the first method that jointly optimizes alignment and representation learning in a shared latent space, enabling robust multi-slice integration. We demonstrate that JADE outperforms existing alignment and embedding methods across multiple evaluation metries in the 10x Visium human dorsolateral prefrontal cortex (DLPFC) and Stereo-seq axolotl brain datasets. By bridging spatial alignment and feature integration, JADE provides scalable and accurate solution for cross-slice analysis of SRT data.
tissue slices. Unlike existing methods, JADE
Introduction
Spatially resolved transcriptomics (SRT) technologies provide sigh-ttroughput measurements of gene expression within tissue sections while preserving spatial context [6
61 29]. By enabling the joint study of molecular states and tissue architecture, SRT has transformed our understanding of developmental processes [ [22, disease microenvironments 47
44
48
83 and spatial cellular organization
across diverse biological systems, from cancer [56]
5 60
16] to neuroscience [R] 45
53 77].
As the resolution and scale of SRT continue to improve, there is growing interest in multi- slice SRT datasets, where multiple adjacent replicated tissue sections are profiled to reconstruct 3D structures, map spatial trajectories, or assess reproducibility across individuals and conditions
19 57 21
31 41 35). However, analyzing multi-slice SRT data introduces of unique
Cco-corresponding authors
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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challenges. Each tissue slice may undergo non-linear spatial deformation during sectioning and mounting, while also exhibiting substantial variation in transcript capture efficiency and local tissue composition 779 37 These factors confound the alignment of corresponding regions across slices and obscure shared biological signals. Effective multi-slice integration must therefore address two tightly coupled tasks: spatial alignment and representation learning [39 67 [3). Alignment resolves
spatial location -level correspondences across slices, while representation learning compresses high- dimensional gene expression data into a shared latent space that supports robust downstream analysis. Despite their interconnected nature, existing methods typically address these tasks in isolation, limiting their ability to perform coherent, biologically meaningful integration.
Previous approaches fall into two broad categories. Alignment- bassed methods [57 12 28| (0).. such as PASTE [79), estimate spatial location level mappings across adjacent slices by jointly considering spatial coordinates and gene expression similarity, enabling reconstruction of 3D tissue volumes. However, these methods operate directly on raw expression profiles, which are often sparse, noisy, and affected by batch effects. These batch effects refer to systematic technical variations intro- duced during sample processing or sequencing, which can obscure true biological signals. As result, they do not provide low-dimensional representations that are essential to downstream tasks such as spatial domain detection or trajectory inference. Conversely, representation learning- methods 12 34
80 52, 23 74 (8). such as GraphST [38] and STAGATE [T5). leverage graph neural networks to extract informative -iw-dimesiional embeddings. While effective for extracting latent embeddings and identifying spatial domains, these methods typically process slices independently or jointly without explicitly resolving anatomical correspondences. As result, homologous tissue regions may be represented inconsistently across slices, undermining interpretability and cross-slice comparison. To address the need for joint analysis across samples, integration methods originally developed for single-cell RNA sequencing data 73 18) including Harmony [33, Seurat [57), and seVI [40], do not account for spatial context and assume shared coordinate systems across samples, assumptions that rarely hold in spatial data. Recently, approaches such as STAligner [81] and PRE- CAST 36 have extended integration techniques spatial transcriptomics, but they either require additional input (e.g., batch id or histology image) or do not explicitly model spatial location- alignment. These methods focus on harmonizing latent features across slices but cannot account for physical tissue distortions that are critical for spatial reconstruction.
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Together, these limitations highlight the need for unified framework that resolve spatial correspondences and learn biologically meaningful representations across multiple slices, allowing alignment to guide representation learning, and vice versa. To address this need, we introduce JADE (Joint Alignment and Deep Embedding), a computational framework that integrates multi-slice SRT data by simultaneously learning (1) a probabilistic alignment between spatial locations and (2) a shared fow-dimensional embedding space. JADE performs alignment in the latent space via attention- bassed optimal transport and enforces spatial and transcriptomic consistency through graph- based contrastive learning. This coupling ensures that learned embeddings are mutually aligned and biologically coherent, while correspondences between spatial locations across tissue slices respect both spatial geometry and gene expression structure.
To the best of our knowledge, JADE is the first method jointly optimize spatial location-level alignment and representation learning within a unified, spatially informed model. We benchmark JADE on multi-slice SRT datasets from the human dorsolateral prefrontal cortex (DLPFC) [45] and the regenerating axolotl brain (68), and show that it consistently outperforms state-of-the-art alignment and embedding methods in spatial clustering accuracy, alignment fidelity, and biological interpretability.. JADE offers a scalable and robust solution for integrative spatial analysis, particularly in settings that require the joint resolution of anatomical correspondence and functional representation across complex tissue landscapes.
2 Methods
Problem Definition. Before we present our method JADE, we first formally introduce the problem setup. Consider a pair of SRT slices (S1, Xx)) and X2), where S₁ x2 and S₂ I rep- resent the spatial coordinates of nı and n2 spatial locations in the two tissue slices, and X1 E RT* Xp and X2 R correspond to their respective gene expression matrices, where p represents the same set of genes measured across tissue slices. Given both gene expression and spatial coordinates for the two slices, our objective is to jointly learn: (1) an alignment matrix II E X between
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ADE
Data Input
Downstream
Spatial Transcriptomicss
Reconstructed
Gene Counts
Spatial domain
2n
Encoder
Decoder
Spatial Locatio
Contrastive Leariing
Alignment
Batch effect correction
Gime Counttrast:
Proection
Mothh
Sriinoo Inratione
Positive
Negative
Differential expression
Sloe
Encoder
Decoder
Court Matz
Embeddings
Figure 1: Workflow of JADE. Given slices of SRT data (left box), JADE learns a probabilistic alignment and low-dimensional embeddings simultancously. One unique feature JADE is that embedding and alignment are updated a roundtrip way in which each iteration alternates between alignment and embedding refinement. Downstream applications (right box) include spatial domain detection, batch effeet correction, and differential expression analysis.
these spatial locations, where MT encodes the correspondence between spatial location in slice 1 and spatial location j in slice 2, and (2) the low-dimensional embedding representations H1 and H2.
Overview of JADE. Figure illustrates the workflow of JADE. The pipeline begins with the input of SRT data from two slices (left panel). These inputs are passed through encoders to extract low-dimensional embeddings. Simultaneously, JADE infers cross-slice correspondences via graph attention module to obtain sebeedddng-space aligmment. This module consists projection head, matrix multiplication, softmax. and iterative sinkhorn operations. To enhance generalizability, employ a contrastive learning module that maximizes agreement between spatially neighboring locations while distinguishing dissimilar ones. A key innovation of JADE is its roundtrip learning scheme, in which embeddings and alignments are refined alternately within each training iteration. The outputs of JADE include probabilistic alignment matrix between spatial locations across two tissue slices and embedding representation of each spot. These outputs support downstream analyses such 3D tissue reconstruction (via the alignment matrix), spatial domain detection (via the learned embeddings), batch effect correction, and differential expression analysis. Detailed descriptions of each module are provided in the following sections and the pseudo code shown Appendix The implementation of JADE, along with data preprocessing scripts and pretrained models, is publicly available at httpp://github..omm http://gthhubboomMMaaaaa///A// Iaa-IAD
2.1 Graph Autoencoder
Let Ai E X and A2 R denote the two adjacency matrices of the spatial graph in two slices obtained using the method described in Appendix B Given two SRT slices (A1, X, and (A2,X)), we first encode them independently using graph convolutional networks (GCNs) [2] to obtain initial embeddings. Each encoder aggregates information from neighboring spatial locations to learn now-dimensional embeddings using a one-layer GCN: H1 Relu Á, Wie + bie),
H2 = Relu( X2 W2e + b2e), where A; = A.' is the degree normalized adjacency matrix, ensuring proper feature scaling across neighboring locations. Without normalization, node with more neighbors would accumulate disproportionately large feature values, leading to biased representations, W. and bie trainable weight and bias parameters of the encoder for slice i E (1,2}. ReLU is applied as a nonlinear activation function to enhance feature expressiveness. H1 E R xd and H2 E Raaxd are the latent embeddings of two slices, where d a hyperparameter that defines the latent dimension.
To ensure that the learned embeddings retain key biological information, we decode them back into the original feature space using a GCN-based decoder: X, = Relu(Á, H, Wia + bia), X2 = Relu H, Wid + bıa), where Wad and bid represent trainable parameters the decoder for slice

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d E {1, The reconstruction loss ensures that the decoded outputs X1, X2 accurately recover
the original gene expression profiles Lreonn - || X11 + || X2ll where -|-1|p
denotes the Frobenius norm, measuring the difference between the reconstructed and original feature matrices.
2.2 Graph Attention for Embedding- Alignment
Given embeddings 11, H2, we obtain the alignment matrix IT through the following steps.
Step 1: Compute cross-attention weights. We first compute an attention-bass based similarity matrix C' E [0, 1 x to measure correspondences between embeddings of two slices:
- TH -HFMM" H2
C' Softmax
(I)
Vd
Here M E [ad is learnable línear projection implementing an attention mechanism the model to focus on key cross-slice features.
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enabling
Step 2: Obtain the alignment matrix from cross-attention weights. The cross-attention weights C' encode pairwise embedding similarities, but it is only row-stochastic: each row sums to 1, yet the column totals are unrestricted. This imbalance can lead to biased mappings, where some target locations accumulate disproportionately high mass, while others receive very little.
To achieve balanced alignment, we reinterpret the alignment problem within optimal transport (OT) [62) framework, enforcing both rows and columns to satisfy uniform marginal constraints. In this framework, the alignment matrix satisfy 11 E [0, 1Jmm, x Σz, Uki 1. Each element HL; denotes the amount of probability mass transported from source point i to target point j. with the constraint that the entire matrix satisfies specific marginal distributions. Specifically, we apply the Sinkhorn- Knopp algorithm [55 [3] to transform the raw similarity scores in C into doubly-stochastic alignment matrix II. This iterative procedure alternately normalizes rows and columns, enforcing each row sum to 1/n1 and each column sum to n2, ensuring that every spatial location contributes and receives an equal amount of alignment mass. Thus, the alignment becomes fair and balanced, avoiding situations where few locations dominate the mappings. Additionally, introduce marginal regularization
term into our objective function: Lmarginal = KL 112 1- 11 Lnz This penalty is defined as the KL
divergence between the column sums of II and the desired uniform marginal distribution. In doing so, we explicitly discourage deviations from uniformity, further reinforcing balanced alignments.
Step 3: Spatial and embedding aware alignment losses. To refine the alignment and maintain spatial structure, we define two primary losses motivated by the fused Gromov-Wassersee Wasserstein distance 46 65]: (1) Spatial structure preservation loss (Mis-Maintain Loss) ensures that spatial relationships in both slices remain consistent after alignment Lmaintain = 1 D1 n1 ||e ny [D2
11 D,11I[F, where Dj and D2 are pairwise spatial distance matrices. Each entry diús (for slice 1) and d2ij (for slice 2) represents the squared Euclidean distance between spatial locations i and j. The scaling factors nž and nf ensure that the transported distance matrices IID, and II" IIII remain on the same scale as the original D2 and D2, compensating for the normalization inherent in II. Minimizing Lmaintain encourages spatial locations that were close to each other before alignment remain close after aligmment, while spatial locations that were far apart should continue to be far apart. (2) Embedding alignment loss MMis-mligmment Loss) ensures that the aligned embeddings are close each other, maintaining meaningful biological correspondence falign = n. |H, n2 + ng H2 II Hillr. Similarly, the scaling factors 722 and n ensure that the transported embedding matrices nzIlH2 and n, II' H; remain on the same scale as the original H, and H2. The first term in the above equation minimizes the discrepancy between slice 1 embeddings and their aligned counterparts from slice The second term enforces the same alignment constraint in the reverse direction.
2.3 Self-supervised Graph Contrastive Learning
We refine our embeddings via self-supervised contrastive learning similar to GraphST 38, using the Graph Infomax objective [66] to maximize mutual information between each spot and its local neighborhood. This drives adjacent, biologically similar spots closer in latent space while pushing structurally distinct distant spots apart.

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For each spatial location i, we define its local spatial proxy as: ri (N() EjENTH) hy. where (i) denotes the set of immediate neighbors of spatial location h, is the embedding of neighboring spatial location j. The pair (44, forms a positive pair, reflecting spatial proximity and biological similarity. To create negative examples, we generate shuffled embedding matrix H' by randomly permuting the rows of H, destroying spatial coherence. For each i, let Ny be the shuffled embedding and ry its corresponding shuffled proxy, forming negative pair (N4, Finally, we train discriminator & via binary cross-entropy loss to distinguish these positive from negative pairs, The slice-specific
contrastive loss is: SECL- - 1 Σi log D(hni, rks) + log(1 (1- - P(haar rk)) for 1, 2. The
overall contrastive loss is LSCI. = LScr. + L..
2.4 Final Loss Function
In summary, the training objective of JADE comprises three components:
ESCL + A2 + AaLmaintain + Aa + Cy
Throughout the paper, set 22 10, x 0.1, Às 1. We use data-driven method to select À from 0.2 to 2.0 depending on calculated similarity score between slices. If two slices are similar, we use a larger λ encourage information sharing; otherwise, we use a smaller À to prevent negative transfer. A comprehensive description of hyperparameter tuning procedures is provided in Appendix E Furthermore, the contribution of each individual component in JADE is evaluated through systematic ablation studies, as detailed in Appendix [F] Results show that performance deteriorates markedly when any loss term is omitted, demonstrating that both the misalignment and mismaintain losses are crucial for optimal embedding and alignment quality.
Downstream analysis. After training, we obtained two sets of oiw-dimeniional embeddings. We normalized the length of each embedding vector and applied the mclust algorithm independently, specifying the cluster number based prior knowledge. Following [8] we set the cluster number from through 7 for the DLPFC dataset, and following [20], from 16 through 17 for the axolotl brain dataset, with each cluster corresponding a distinct cell type. We then leveraged the inferred domains to conduct differential expression analysis. For the batch-effect correction evaluation, we projected the embeddings into 2-dimensional space using UMAP, visualized their spatial distribution, and computed the local Simpson diversity index to quantify how well the embeddings from different slices intermingled. To assess alignment quality, we visualized and quantified the correspondences in the alignment matrix within each ground-truth domain, explicitly marking correct and incorrect matches, and computed accuracy scores measure alignment performance.
Fast Computation for JADE
A major challenge for SRT alignment methods is their high computational cost, scaling quadratically with the number of spatial locations. Methods such as PASTE (79) and our JADE algorithm require computing similarity matrices between all location pairs, resulting in prohibitive runtime and memory usage for high-resolution datasets. The primary computational bottleneck in JADE is the cross- attention step, which calculates pairwise similarities and scales (nnnddd). To accelerate this, introduce an approach that aligns at a coarser resolution using aggregated spatial units ("hyperspots"), significantly reducing computational complexity. Despite this approximation, Fast-JADE achieves performance comparable to JADE on the DLPFC dataset (see Appendix for detailed comparison).
Hyperspot embedding construction. For each tissue slice, we apply K K-means clustering to group spatial locations into fewer, coarser spatial units, resulting my & n, and m2 < 722 hyperspots respectively. The number of hyperspots is set to approximately 10-20% of the original number of spatial locations for each slice. Each hyperspot embedding is computed by averaging embeddings of the spatial locations within the cluster, resulting in compact representations.
Compute artes-attention between hyperspots. We compute the cross-attention weights and align- ment matrix the hyperspot level. Specifically, Chyper = Softmax (- (-HAbypet:T M M H/yper /Vd) similar to I]. Using these hyperspot-level attention weights, we then compute the alignment and maintenance losses, Lmmaittai and Lalign at the hyperspot level.
From hyperspot-level to spatial location-level Alignment. After training, we transfer the learned alignment back to the full resoluteolt space. Specifically, we reuse the same projection head M com-
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pute the fine- ahee-griind spatial location-wist wise attention weights: C Softmax (-HTMM" (LMMMMH//// H2/va).
where H1 E I xd and H2 E Rx are the original spatial location embeddings. This ensures consistency between coarse and fine levels and avoids retraining at full resolution. The resulting matrix C' is then passed through the Sinkhorn- Knopp algorithm to obtain an alignment matrix II with uniform marginals.
4
Experiments
We benchmarked JADE against six representative baseline models, selected for their relevance to either spatial alignment or embedding tasks in spatial transcriptomics, For alignment accuracy, we compared with PASTE [79), Seurat [57]. and STAligner [81], three widely used methods that align SRT slices based on transcriptomic similarity and spatial proximity. For evaluating the learned embeddings through spatial domain detection, we included GraphST (7),, STAGATE [15], and STAligner, which incorporate spatial or graph-based information to enhance domain identification.
To provide a unified assessment, we used a comprehensive alignment metric that accounts for both correctly aligned and unaligned locations (Appendix BB. Embedding quality was quantified using the Adjusted Rand Index (ARI) for biological domain recovery. the integrated local inverse Simpson's s index (iLISI) [54] for cross-slice integration, and UMAP visualizations for qualitative evaluation of coherence and batch correction. For biological interpretability, we conducted differential expression analysis to identify domain-specifie marker genes and validated them against known anatomical annotations and literature, confirming that the learned embeddings capture biologically meaningful spatial structures and gene associations.
We also tested JADE on two additional datasets in Appendix H the MERFISH dataset [1] and the Breast-Cancer Visium/Xenium dataset (26). previously used SLAT 711. As summarized in TI JADE consistently outperforms or matches state-of-the-art baselines, including SLAT, STAI- igner and SpotScape(500 in both domain-detection accuracy (ARI) and alignment accuracy (ACC). These results demonstrate JADE's ' robustness and adaptability across distinct spatial transcriptomics platforms (MERFISH, Visium, Xenium) and tissue types (brain and breast).
4.1 Joint Spatial Alignment and Representation Learning Across Human DLPFC Slices
Dataset description. We evaluated our proposed method on the Human Dorsolateral Prefrontal Cortex (DLPFC) dataset generated with the 10x Visium platform [56]. standard benchmark in spatial transcriptomics. The dataset comprises 12 serial tissue sections, including four sequential slices (A-D) from each of three donors (I-III), with expression profiles of 33,538 genes measured at 47,681 spatial spots. Within each individual, slices A-B and C-D are adjacent pairs separated by 10 μm, while slices B and C have larger separation of 300 yam Differences across individuals are primarily attributed to batch effects arising from technical variations in sample processing, sequencing, or tissue handling. Each slice was annotated with seven spatial domains, corresponding to six cortical layers and the white matter [45). These expert-providde annotations served as the ground truth for spatial domain detection analysis. Following preprocessing in Appendix B the two selected slices retained about 1500 shared highly variable genes for each pair.
Improved clustering accuracy. Figure (AA provides a visual comparison of the predicted spatial domains from each method against the ground truth for both Slice A and Slice B of Sample III. Visually, JADE demonstrates the highest accuracy recovering the annotated cortical structure, across slices A and B with clear, smooth boundaries. In contrast, other methods yield noisier and less coherent spatial domains. Quantitatively, JADE achieves median ART values of approximately 0.61 and 0.65 for Slices A and B, for Sample III as shown in Figure B). This represents statistically significant improvement over GraphST (0.59 and 0.58), STAligner (0.56 and 0.59), and STAGATE (0.52 and 0.53). The top row of Figure C further visualizes the learned low- dimensional embeddings produced by each method using UMAP, colored by their true biological cluster annotation. JADE consistently demonstrates superior performance, yielding highly distinct and well separateed biological layers that form cohesive clusters with minimal overlap. Appendix C shows additional results for other samples and other adjacent slices.
JADE effectively mitigates batch effects in multi-slice integration. The bottom row of Figure P
illustrates the effectiveness of batch effect removal across different methods by visualizing UMAP embeddings colored by slice identity (slice A: blue, slice B: red). Effective integration is reflected by

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Figure 2: (A) Predicted spatial domains for slices A and (Sample III) using five methods. (B) ARI for slices and B of Sample III in DLPFC. p-values are calculated by Wilcoxon-rank sum test, where ** p < 1%, *tpp < 0.1% and **** p < 0.01% (C) UMAP of embeddings colored by predicted clusters (top) and slice (bottom). (D) Alignment accuracy across adjacent slice pairs (AB, CD, BC). (E) Spatial expression of marker genes confirms biologically relevant domain structures. (F) Visual comparison of alignment accuracy for Layer I Sample III (Slice A vs. Slice B). True alignments represented in blue; wrong
shown in yellow.
the intermixing of spatial locations from different slices, indicating successful alignment in shared latent space. JADE achieves the highest inter-slice mixing, suggesting excellent batch correction performance. In contrast, GraphST, STAligner and STAGATE display limited alignment: the two slices remain largely separated within the UMAP space, suggesting poor batch removal efficacy, JADE also attained the highest iLISI score of 1.98, outperforming GraphST (1.52), STAligner (1.64), and STAGATE (1.61), confirming its superior performance in integrating SRT data across slices while correcting for batch effects.
Superior alignment performance. Figure 2)D presents a comprehensive quantitative assessment of alignment accuracy across adjacent slice pairs (AB, BC, CD) for three distinct samples, comparing JADE against existing methods including PASTE, STAligner, and Seurat. Among these, the B-C pairs represent the most challenging alignment scenario due their larger inter-slice distance (300)m)) compared to the 10pm separation in A-B and C-D pairs. Across all samples and slice combinations, JADE consistently demonstrates superior alignment accuracy, particularly in challenging scenarios. While PASTE achieves comparable performance to JADE in easier settings (AB and CD pairs), exhibits substantial performance degradation when confronted with the more challenging BC aligmments. Notably, for BC pairs in samples I and II, JADE surpasses PASTE by margins exceeding 50%. STAligner shows moderate accuracy but is consistently lower than JADE and PASTE across all slice pairs. Seurat performs the poorest in all cases, with particularly low alignment accuracy in the BC pairs. These results highlight JADE's superior alignment performance, particularly in challenging integration settings. In Figure F)), we visualize Layer alignment between Slice A and Slice B in Sample III across four methods. Blue lines indicate correct matches within the same annotated layer, while yellow lines indicate errors. JADE achieves the best outcome, with mostly correct (blue) alignments and very few incorrect (yellow) ones.
Domain-specific differential expression gene analysis. We performed domain-specific differential expression (DE) analysis based on the spatial domains detected by JADE and identified six rep- resentative marker genes (ENCI, NEFL, PCP4, KRT17, MBP, and CRYAB). These genes were selected for their strong domain-leved enrichment and subsequently validated through literature for their well-established region-specific expression patterns in the human cortex. Figure E) displays
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Figure (A) Domain segmentation results for Juvenile and Adult slices comparing ground truth against four methods. (B) ARI scores for four methods. p-values are calculated the same as in Figure 2 (C) UMAP of embeddings colored by predicted clusters (top) and slice (bottom). (D) Alignment accuracy for Juvenile and Adult slices. (F) Spatial expression of marker genes confirms biologically relevant domain structures. (F) Visual comparison of aligmment accuracy for CP cell type between the juvenile and the adult. True alignments are represented by blue lines, while wrong alignments are shown in yellow.
the spatial expression patterns of these genes across two adjacent DLPFC tissue slices (top and bottom rows). ENCI, NEFL, and PCP4 exhibit clear laminar structures consistent with neuronal populations localized to middle and deep cortical layers [45] 70 17]. Their spatial localization is preserved across slices, demonstrating coherent biological structure. KRT17, typically associated with epithelial-like or glial cells, shows more punctate and scattered expression, particularly in the gene, is strongly expressed in the
upper portions of the slices [I] 45). MBP, mnyelination-rllaee lower regions of both slices, likely corresponding to white matter (WM), and the spatial coherence across slices further supports successful alignment astrocyte-assoiiteed marker, exhibits a broader expression domain with intermediate intensity
20 45 25 CRYAB, a reseos-response and
Beyond expression-basse baselines, we further evaluated JADE against GPSA 28 an image- informed alignment model that integrates histological features in Appendix H As summarized in Table TO, JADE achieves higher alignment accuracy across all DLPFC slice pairs while maintaining comparable clustering quality, indicating that reliable alignment can achieved without reliance on histology images.
Joint Learning of Axolotl Brain Dataset Across Different Developmental Stages
We applied our method to the task of jointly learning alignments and embeddings SRT data across distinct developmental stages. This integration is crucial for gaining insights into the dynamic processes of cell proliferation and differentiation. However, achieving such comprehensive integration is inherently challenging due to technical batch effects and fundamental biological shifts, both of which significantly complicate the establishment of accurate underlying alignment.
Dataset description. We evaluated JADE on SRT dataset of the axolotl telencephalon (a region of the brain) generated using the Stereo-seq platform (. This dataset captures gene expression across five developmental stages: three embryonic stages, the juvenile stage, and the adult stage. In this study, we focused our analysis on the last two, which together span a broader range of mature brain architecture. The juvenile stage and adult stage have 17 and 16 distinct cell types respectively. Among them, fourteen are shared between both stages, while the rests from the juvenile stage differentiate or transition into cell types in the adult stage. Following preprocessing, the two selected slices retained 1,000 shared highly variable genes, with 11,698 and 8,243 spatial locations, respectively. To reduce computational time, applied the accelerated JADE method introduced in Section 3 using 1 1,000 hyperspots per slice, corresponding to about 10% of the spatial locations.
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Improved clustering accuracy. FigureBi A) provides a visual comparison of the domains detection results of JADE and baseline methods in Adult (top row) and Juvenile (bottom row) slices. Compared to the ground truth, JADE consistently recovers structurally coherent and anatomically accurate domains in both stages. Notably, the adult brain, JADE is the only method that successfully reconstructs the blue peripheral ring cluster, representing vascular leptomeningeal cells (VLMC) (x] This region is either partially fragmented (in GraphST), blurred and mixed with neighboring domains (in STAGATE, STAligner). In addition, JADE accurately produces a coherent, bilaterally symmetric red region in the telencephalon core, while STAGATE yields considerable color mixing within this region, STAligner only partially recovers it, and GraphST produces overexpanded red region, suggestive of excessive smoothing. These qualitative patterns are supported by the quantitative results in FigureB.B For the Adult stage, JADE achieves the highest median ARI score (approximately 0.53), significantly outperforming STAligner (0.48), STAGATE (0.42), and GraphST (0.43). For the Juvenile stage, JADE also obtains high median ART (approximately 0.37), demonstrating statistically significant improvement over STAGATE (0.35) and GraphST (0.32). While JADE's performance for the Juvenile stage is quantitatively comparable STAligner's by ARI, its qualitative domain recovery remains notably more coherent and anatomically accurate as shown in Figure 3 A). The top row of Figure 3 further visualizes the UMAP for the embedding features, colored by the true cluster annotation. JADE produces well-separated and compact clusters, indicating a clear differentiation of spatial domains in the latent space, while other methods exhibit considerable mixing of domain colors, reflecting ambiguity in domain boundaries.
JADE effectively mitigates batch effects in multi-slice integration. The bottom row of Figure C compares methods via UMAP embeddings colored by slice (Adult: red, Juvenile: blue). JADE shows near-perfect mixing within structured clusters, indicating superior batch-effect removal. In contrast, STAligner, STAGATE, and GraphST display notable batch-induced separation. Quantitatively, JADE achieves the highest LISI score (1.85), surpassing GraphST (1.78), STAligner (1.25), and STAGATE (1.23), highlighting its effectiveness in integrating data across developmental stages.
Superior alignment performance. As shown in the bar plot in Figure B D), JADE achieves the highest alignment accuracy among all methods, substantially outperforming PASTE, STAligner, and Seurat. This result underscores JADE's 's ability to establish precise correspondences between spatial locations across slices, even under the challenging setting of cross developmentaal stage alignment, where substantial morphological and transcriptional variation exists. Figure 3 F) further visualizes the alignment accuracy for cortical plate cell type between the Juvenile slice and the Adult slice, to support this finding. JADE yields the highest proportion of correct (blue) alignments, demonstrating its superior ability to preserve anatomical consistency during cross-slice registration.
Domain-specife gene. Figure B) displays the spatial expression patterns of six canonical marker genes, SCGN, ZIC1, CCK, PENK, SLC1A3, CENPV.L, across Juvenile and Adult slices (top and bottom rows). These genes are known to exhibit region-specific expression within the axolotl brain and thus serve as internal benchmarks for spatial alignment and biological interpretability. Specifically, SCGN and ZICI, for example, are associated with distinct neuronal populations and developmental patterning, and their laminar or domain- across developmental stages, reflecting coherent spatial organization 51 59) CCK and PENK, which are neuropeptide-relate genes, show distinct regional enrichment, highlighting the emergence of functional specialization in the maturing brain [30, 8) SLCIA3, glutamate transporter gene involved in astrocytic function, exhibits broad but domain-enriched expression, consistent with known glial distribution 3 CENPV.L, associated with nuclear and centrosomal processes, displays a sharply localized expression pattern, providing a clear contrast across domains (58). Together, these genes illustrate the biological relevance of the spatial domains identified by JADE, demonstrating its ability to uncover consistent, developmentally regulated gene expression patterns across stages of brain maturation.
expression patterns are preserved
5 Conclusions
In this paper, we address the critical yet understudied challenge of joint spatial alignment and representation learning across multi-slice SRT data. We propose JADE, a unified framework that simultaneously infers spatial correspondences and learns biologically meaningful low-dimensional embeddings. Through comprehensive evaluations on human DLPFC and axolotl brain datasets, JADE demonstrates superior performance in spatial domain detection, alignment accuracy, and batch effect correction compared to state-of-the- methods. This study provides a robust computational tool
9

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for integrating multi-slice SRT data, with the potential to advance 3D tissue reconstruction, cross condition comparison, and spatially informed transcriptomic discovery. However, several limitations remain. First, while JADE performs well across a range of spatial transeriptomics platforms and tissue types, its performance may be affected by extreme sparsity, highly unbalanced slice resolutions, or limited overlap in tissue regions across slices. Second, JADE currently models pairwise slice alignment, which may limit its ability to fully reconstruct larger tissue volumes or resolve global correspondences across long serial sections. Third, the current framework assumes static snapshot of spatial organization and does not account for temporal variation, which is increasingly relevant in developmental or regenerative contexts. Future work will extend JADE handle fully joint alignment across multiple slices, incorporate spatiotemporal transcriptomics data, and integrate additional data modalities such as histological imaging or spatial epigenomies. We also aim improve scalability for serrahhigh-resolutiin sample heterogeneity. To the best of our knowledge, no potential negative impacts resulting from work have been identified.
datasets and explore methods to increase robustness under technical noise or
6 Acknowledgment
This work was supported by the National Science Foundation (NSF) and the National Institute of General Medical Sciences (NIGMS) under award number ROI R015M122114 by the National Institutes of Health (NIH) under award number R35GM160372, and by the NSF under award numbers DBI- 2526948 and IIS-2500960.
References
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Input: Slices (A,, X,) and distance matrices D, for i {1, 2); degree matrices D hyperparameters Ag...... ..... As; epochs T; latent dim d: #Sinkhorn iterations s. Output: Alignment II Rm x embeddings H, R=4xd.
Initialize parameters {Wies die: Wia, bid, M,4)
for epoch 1 to T do
// 1) Salcode-Decode (GCN encoder/decoder
A; 1/-1/2,12220 A,D, 1/2
H; t RcLU,A, bie);
X, - ReLU
A. W baa).
Lrecon f - | Xill + 1 1 X2l1.
1/ 2) Cross-attention & Sinkhorn for alignment
S, f H,M R
// linear projection (attention)
C < Softmaxrows S1S2 /Vd) E R
II + Sinkhorn,(C) (C);
11 doubly-stochastie with marginals ( m²
Emarginal + KL M2
// 3) Spatial-structure maintenance & embedding alignment
Emaintain f 1 D1 - n 1112111111 || + D2 - D,LIIE..
Calign n.
H4 n2I1H221 1 ||2 -Ill Hilp.
// 4) Self solf-supervised graph contrastive loss (per slice) for E (1 do
Fij + [لt. EKEN(H)) ha:: // neighbor average in the spatial graph Form positives (hij, riy) and negatives Tyy) by row permutation of H; (() SCL t 1, E}=
[log ((hs,, riy) + log(1 - D(h/j. r()]]
end
LSCL f- SCL + L.e 1/ 5) Update
Liot &- Lrecom + A2 LSCI. + A3 femaintain da Lalign + À5 mmarginna optimizer. step V Ltot).
end
return II, HH, H2
Algorithm JADE (pairwise training loop)
A Pseudocode of JADE
We summarize the training loop for JADE and its accelerated variant Fast-JADE. The notation matches Sections 2 and] 3 A: the spatial graph, X; the gene-expression matrix, D; the degree matrix of A, and D; the within-slice pairwise distance matrix. JADE alternates between (i) encoding/decoding to refine embeddings and (ii) alignment in the latent space via attention and Sinkhorn normalization. Fast-JADE performs alignment at coarser "hyperspot" level for efficiency, and then recovers full-resolution correspondences using the learned projection head.
B Implementation details for JADE and benchmarks
Data Preprocessing. We followed the standardized preprocessing workflow implemented in the SCANPY package [69] to prepare the input data for our model. For each tissue slice i, raw gene expression counts normalized by library size and tr-arsnffoored. Gene expression values were then sealed to unit variance across spatial locations. The top 3,000 highly variable genes (HVGs) identified independently in each slice, and only the intersection was retained, resulting in shared gene set of size p < 3000 for both datasets (around 1,500 for DLPFC and around 1000 for axolotl brain dataset). This produced two input feature matrices: X1 R xp and X₂ E R2xx where and n2 denote the number of spatial locations in slices 1 and 2, respectively.
Spatial Graph Construction. For each tissue slice i, we construct unweighted spatial graph G = (V, E,) that captures the spatial relationships among spatial locations using spatial information S. Here, V; represents the set of spatial locations, and E, consists of edges connecting neighboring locations based on their spatial proximity. To determine connectivity between spatial locations, we
16

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Input:
Slices (A, X,) and distance matrices D, for i {1, {1, degree matrices Dú hyperspot
counts m,;
assignments N (I); hyperparameters .2...., As; epochs T;
latent dim d; #Sinkhorm iterations
Output: Alignment II 1 x embeddings H; E Rm4xd
Initialize parameters {Wies bie: Wid, bid, M, M) for epoch = 1 to T do
// 1) Sacodde-Dccose
(same Alg. 1
Ag +- D A, 1/2; A,D;;12 H; <- ReLU (A,XWW + bic);
X, ReLU ReLU + bta).
Lrecon < _ | X1 + - ||2 -211.
11 2) Hyperspot embeddings (cluster-level averaging)
H. [1] I EjeN(() hj -1=1,... , mi
1/ 3) Hyperspot-level pross-attenin & Sinkhorn
Shyper Hhwner M E Rm,
((0) t- Soww (S Shyper (5 (shpper) /Va)
(1 + Sinkhorn (CiO))
Emarginal f KL 11 1m
[1(0)
1m2
1/ 4) Hyperspot-leve level maintenance alignment losses
Lmaiitaii
me |D m² II (I D F + | mf (7) T Dhyper (
Lalign mi || my H1 hyper + 1 | m, ( H hyppr ll..
1/ 5) Graph contrastive (spot-level) identical to Alg. 1
Compute LSCL as in Algorithm
11 6) Update
Liot + Lrecon + X2 LSCL + As Lmmintain + X Lalign + Às Emarginal' optimizer wtt.iiiierrrrrpppppcoo L(ot).
end
Recover II: Reuse the trained M to compute C' = Softmax (HH (H2M) /Vd) and
then apply Sinkhorn, to obtain the full-resolution (as in Algorithm return IT, H1, H2 Algorithm 2: Fast-JADE (coarse-to-fine alignment with hyperspots)
compute the Euclidean distances between all pairs of locations using their spatial coordinates, then establish edges based on defined neighborhood size k; where an edge is created between spatial location and spatial location j if is among the k nearest neighbors of i, thereby constructing graph that captures the spatial relationships among spatial locations in the tissue slice. For all real data analyses, we set k to be 3 The resulting graph is mathematically represented by an adjacency matrix A, = (a:;), where ajj- = 1 indicating connection between spatial locations and j. and asj 0 indicating no connection. After this step, we obtain two adjacency matrices of the spatial graph in two slices, A E " xm and A2 E 2222
Evaluation metrics. In this paper, we evaluate both alignment accuracy and representation learning quality across methods. To evaluate spatial alignment, we extend beyond conventional metrics that only consider the proportion of correctly aligned spatial location pairs sharing the same annotation (e.g., layer label) 779 78). While commonly used, these traditional metries can be misleading: they often favor methods that selectively align "easy" spatial location pairs while ignoring harder regions, thereby inflating accuracy at the cost of coverage and interpretability. To address this limitation, we adopt an alignment accuracy metric that incorporates both aligned and unaligned spatial locations,
offering a more robust and informative assessment. Specifically, let x E [o, 1| [ x be the alignment matrix where Tız = 1 if spatial location in slice 1 is mapped to spatial location in slice (or for soft alignment methods like JADE). We normalize each column
to sum up to 1/mg, yielding a matrix ã that retains soft alignments while assigning zero mass to unaligned spots. Our alignment accuracy is then defined as Ace = Σi, 7;y (1, = 1y), where 1, and I, denote the biological annotations (e.g., cell type, tissue layer) for spatial location i and j, respectively. This formulation rewards biologically meaningful alignments-i.e. mappings between spots with consistent tabels-whil penalizing both
17

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misalignments and omissions. When all spatial locations are perfectly aligned within the correct biological regions, Acc = I. Finally, to ensure symmetry, we repeat the entire procedure swapping the roles of slice 1 and slice 2 and report the average of the two scores.
Beyond alignment, we evaluate the quality of the learned representations produced by each method. We use the adjusted Rand Index (ARI) to assess clustering accuracy by comparing predicted domain labels with ground-truth annotations, providing a quantitative measure of how well the representations capture underlying biological structure. To assess batch effect removal, we compute the local inverse Simpson's 's index (iLISI), which quantifies the degree of slice mixing in the embedding space space-hight higher values indicate better integration across slices. We further perform qualitative assessment using Uniform Manifold Approximation and Projection (UMAP): coloring spatial locations by their true domain labels reveals biological coherence, while coloring by slice identity visually demonstrates integration quality and batch correction performance.
Baseline methods We benchmarked our method, JADE, against a set of six representative baseline models, selected for their relevance to either alignment or embedding tasks spatial transcriptomics. For alignment accuracy, we evaluated against PASTE [79]. Seurat [57], and STAligner [81], three widely-used methods designed to align SRT slices based on transcriptomic similarity and spatial proximity. For evaluating the learned embeddings through spatial domain detection, we benchmarked against GraphST [38] STAGATE [15) and STAligner, all of which incorporates spatial or graph- based information to enhance the detection of spatial domains. Below we outline, for each benchmark method, the key preprocessing steps, parameter settings, and clustering or alignment workflows used in our comparisons. All pipelines begin from the same raw count matrices and spatial coordinate annotations.
JADE. For each pairwise alignment task, we first selected the top 3,000 highly variable genes from each slice, then took the intersection of these two sets, yielding approximately 1,500 genes for every pair in DLPFC and 1000 genes for axolotl brain dataset. We then applied log-normalization to the expression matrix, and constructed spot-by-gene feature matrix. For the DLPFC dataset, we normalized each inter-slice distance matrix by the minimum distance between any two distinct spots within the same slice. For the axolotl brain dataset, because the juvenile slice slightly larger physically than the adult slice, we rescaled the coordinates of the adult slice to match that of the juvenile slice. We ended up multiplying the x coordinates of the adult slice by approximately 1.3 to climinate any alignment bias induced by scaling. The data-driven approach of selecting λz-As can be found in Section E. We employed a GCN with a single hidden layer to project the original expression matrix into 64-dimensional latent space. Following Xu et al. (76). set the neighborhood size to = 3, which has been shown to yield strong performance. Before joint training, we pretrained the model obtain an initial estimate of the alignment matrix II, since the embeddings H are essentially uninformative at the start of optimization.
Cpretrain = LSCL + >2Creeon + X3Lmaintain + X2 + AsSmarrginal
Similar the All-Anignment loss Caligas we define
1 ||x 12I1X2l + 1 '1x,2 I Xille. n1
Lalign
m2
Throughout, we fixed X 5.0. We used Adam optimizer with learning rate set 0.002, number of pretraining epochs as be 200 and number of training epochs set as 800.
GraphST. Following the GraphST protocol, we used the same preprocessing steps as JADE and then assembled each spot's neighborhood by integrating within-slice 2D spatial locations. Specifically, we fixed the neighborhood size to A =3 is also recommended by GraphST. All other GraphST hyperparameters were left at their package defaults. After computing the spatially informed graph, we applied the mclust Gaussian mixture model for final cluster assignment, using smoothing radius of 20 spots in the refinement stage, which again mirroring GraphST's recommended default.
3 spots for each query location, which
STAligner.
We subjected the data to our standard HVG filtering and normalization pipeline before invoking STAligner's is built-in neighbor selection routine. For the human DLPFC slices, we set the cutoff radius to spatial units, which yielded on average approximately 5 neighbors per spot; for the axolotl brain slices, increased the cutoff to 50 units to
18

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account for differences in spot density, also achieving roughly 5 neighbors per spot. All other STAligner hyperparameters remained at their defaults. Clustering on the aligned feature space was again performed with melust, allowing direct comparability to GraphST and JADE.
STAGATE. After the shared preprocessing steps, we turned to STAGATE's graph attention framework. We utilized its default neighbor selection within each slice, specifying radius units for DLPFC (approximately 5 neighbor spots) and 50 units for the axolotl data (approximately neighbor spots). This radius-based neighborhood ensures that each spot aggregates information from a consistent local context before passing through the graph attention layers. We retained STAGATE's default training hyperparameters and extracted the learned embeddings for clustering via mclust.
Seurat. We applied the canonical Seurat integration workflow across all four consecutive slices of each sample in DLPFC dataset. We selected the top 3,000 variable genes for integration and computed 15 principal components on the combined expression matrix.
PASTE. Finally,
the original PASTE algorithm with its default settings. Throughout, we set a = 0.1 as recommended. No parameter tuning was performed beyond the defaults supplied by the PASTE package.
Biological applications. To assess the biological interpretability of the learned representations, we performed downstream analysis of Nomaann-seciife gene expression. For each spatial domain identified from the embeddings, we conducted differential expression analysis using the Wilcoxon rank-sum test to identify Nomain-enrichee marker genes. These markers were then validated against known anatomical annotations and litrrature-uurated gene lists. This analysis demonstrates the ability of our method to recover spatially organized, functionally coherent tissue structures and to reveal biologically meaningful gene domain associations.
C Additional results for DLPFC
Sampie
Ano 5
Second Blice
Stice
Second Sice
Second Slice
0.7-
0.5
0.4-
0.3
0.6
0.5
BC
0.4
0.7-
0.6
CD
0.4
0.3
Method JADE
GraphST
STAligner
STAGATE
Figure 4: Adjusted Rand Index (ARI) results for three DLPFC samples (1-III, left to right). illustrating pairwise clustering of adjacent sections. Rows correspond to slice pairs AB, BC, and CD (top to bottom), and each boxplot summarizes ARI scores for both slices over 20 independent replicates.
Complementing Figure 2 F), Figure 4 presents the ARI results for all samples and their adjacent slice pairs in the DLPFC datasct. In nearly every comparison, JADE outperforms the other methods by
19

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substantial margin. Across all three DLPFC samples (I-III) and for each adjacent-slice pairing (AB, BC. and CD), JADE not only achieves the highest median ARI but also exhibits consistently tighter score distributions than the competing methods. For example, in Sample I's AB pair, JADE's median ART is roughly 0.55, compared with about 0.45 for GraphST, 0.50 for STAligner, and 0.40 for STAGATE-an improvement of 0.05-0.15. Similarly, in Sample II's BC pairing. JADE scores near 0.62, while GraphST and STAligner both cluster around 0.60 and STAGATE lags at approximately 0.42. Moreover, JADE exhibits uniformly narrower interquartile ranges, particularly when compared to STAligner in Samples II and III and to STAGATE in Sample This indicates less variability and greater robustness to random initialization of JADE algorithm. Together, Figure 4 and Figure ( highlight the satisfactory improvement achieved by JADE and underscore that joint alignment and embedding delivers more accurate and stable clustering across consccutive tissue sections.
JADE
PASTE
STAligner
Seurat
Layer1
Layerz
Layer
Layer4
Layers
Layer
WM
Figure 5: Illustration of alignment results from fixed layer of Slice A to Slice B for Sample III, comparing four methods; blue lines denote correct correspondences, and yellow lines denote incorrect links.
Complementing Figure D). Figure displays the top 250 spot correspondences between a fixed layer of Slice A and Slice for Sample III. Blue lines indicate correct matches, while yellow lines denote incorrect ones. Overall, JADE delivers superior alignment quality compared to all three other
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benchmarks: it produces markedly smoother, less noisy mappings than STAligner or Seurat across all seven layers. and achieves higher correspondence accuracy than PASTE with only a minimal trade-off in smoothness.
Table 1: Accuracy of top 250 alignment correspondences by domain.
Method
Layerl
Layer2
Layer3
Layer4
Layer5
Layer6
WM
JADE
0.996
0.636
0.908
0.776
0.912
0.752
1.000
PASTE 79
1.000
0,584
0.840
0.724
0.848
0.836
1.000
STAligner 81
0.936
0.648
0.832
0.252
0.752
0.740
0.992
Seurat 57
0.016
0.084
0.136
0,296
0.276
0.344
0.020
Table 2: Fraction of unaligned cells per domain for each alignment method.
Method
Layerl
Layer2
Layer3
Layer4
Layer5
Layer6
WM
JADE
0.000
0.000
0,000
0.000
0,000
0.000
0.000
PASTE
0.000
0.000
0.000
0.000
0.000
0.000
0.000
STAlignne 81
0.739
0.683
0.709
0.818
0.738
0.705
0.790
(57rat(57]
0.953
0.960
0.932
0.862
0.889
0.818
0.984
In Table 1 we report, for each spatial domain within DLPFC, the alignment accuracy achieved by the top 250 correspondence links when matching Slice A Slice B in Sample III. Each entry shows the proportion of correctly paired spots among the first 250 alignments for that domain, providing domain-specific assessment of alignment performance. JADE emerges as the most reliable method, achieving nearly perfect accuracy (1.00) in Layer 1 and WM and maintaining at least 0.63 accuracy in every layer. PASTE also attains perfect matches Layer and WM but shows greater fluctuation in intermediate layers (ranging from 0.584 to 0.848). STAligner also delivers competitive results in early layers, 0.936 in Layer and 0.648 in Layer 2, but its performance drops markedly in deeper regions (as low as 0.252 in Layer 4), although it still nearly reaches perfection in WM (0.992). In contrast, Seurat fails to produce meaningful alignments across all domains, with accuracy scores below 0.35 in every layer (0.016-0.444) Table reports., for each cortical layer (Layers 1-6) and white matter (WM), the fraction of spots left unaligned by each method. Both JADE and PASTE achieve a fully dense correspondence matrix, no spot remains unaligned in any domain. In contrast, STAligner fails to align a substantial fraction of spots (68-82% across layers, and 79% in WM), while Seurat leaves even more spots unmatched 96% in Layers 1-3, tapering 81-829 in Layers 6 and 4-5, and 98% in WM). These results highlight that only JADE and PASTE guarantee ine-grained spot-spot alignment, whereas STAligner and Seurat produce large numbers of unaligned spots.
D Additional results for axolotl brain dataset
Complementing Figure BJ. Figure displays the top spot correspondences between a fixed layer of juvenile slice to adult slice. The umber correspondences is determined by half of the corresponding spots. Blue lines indicate correct matches, while gray lines denote incorrect ones. Similar to DLPFC, JADE delivers superior alignment quality compared to all three other benchmarks overall.
Table compares. for each common cell type between juvenile and adult slices, the accuracy of the top correspondences and the average fraction of spots left unaligned. Across all cell types, JADE attains the highest or near-highest top-link accuracy, with values ranging from 0.105 (sstIN up to 0.766 (nptxEX). PASTE closely follows JADE, in several cases enjoying the highest accuracy for dpEX, but generally trails by 5-10 percentage points. While STAligner exceeds JADE on individual domains (e.g. SegnIN: 0.778 vs. 0.722: sfrpEGC: 0.171 vs. 0.145), JADE remains close to STAligner in some cases (e.g. segnIN, sfrpEGC). However, STAligner's average fraction of unaligned spots 0.724, meaning over 70 % of cells remain unaligned. Seurat performs poorly throughout, with top-link accuracies below 0.10 in every domain and an average of 0.925 unaligned spots. Taken together, these results underscore that although STAligner can rival JADE in top-ranked matches for certain cell types, its high rate of unaligned spots prevents truly fine-graineds cell-to-cell alignment. In contrast, JADE (and PASTE) deliver both high accuracy and cell-cell alignment, ensuring no cell is left unmatched. JADE (and PASTE) combine high top-link accuracy with exhaustive alignment, leaving none of spots unaligned, making them the only methods to guarantee both precision and completeness of correspondences.
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JADE
PASTE
STAligner
Seurat
CMPN
CP
MSN
VLMC
cokIN
dpEX
mpEX
прtxXx
dbDEC
scgnIN
STppEGC
sstlNN
INBLL
WntEGC
Figure Alignment from given cell type in juvenile slice to adult slice, comparing methods (JADE,
PASTE, STAligner, and Scurat). Blue lines denote correct correspondences, while grey lines denote incorrect links.
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Table Alignment accuracy of the top correspondences and average fraction of unaligned spots for each
common cell type between juvenile adult slices. For each cell type, the number of correspondences equals half of its total cells.
Domain
# cells
JADE
PASTE 79
STAligner 81
Scurat 7
CMPN
782
0.357
0.288
0.448
0.012
CP
1500
0.224
0.157
0.121
0.069
MSN
54
0.685
0.704
0.741
0.037
VLMC
523
0.585
0,539
0.772
0.011
cckIN
99
0.211
0.169
0.237
0.019
dpEX
456
0.809
0.568
0.721
0.011
mpEX
464
0.623
0.394
0.591
0.012
npIxEX
840
0.751
0.637
0.744
0.031
ribEGC
187
0.337
0.096
0.690
0.011
segnIN
713
0,421
0,445
0.372
0,059
strpEGC
349
0.630
0.166
0.745
0.011
sstIN
294
0.109
0.075
0.306
0.003
tNBB.
257
0.183
0.105
0.237
0.000
wntEGC
509
0.658
0.326
0.633
0.069
Avg. frac. unaligned
0.000
0.000
0.724
0.925
E Hyperparameter tuning and sensitivity analysis
The training objective of JADE is
ESCL + >22rreoon Aaamaintain + A4Lallinn +
single slice loss
aligmment loss
The overall loss can be decomposed into three terms: the single-slice reconstruction loss, the alignment loss, and regularization term. Throughout, we fix X2 10 and As and choose neighborhood size of k The hyperparameters X3, X4 govern the trade-off between enforcing accurate slice-to-slice alignment and preserving meaningful, slice-specific embeddings. Within the alignment loss, Lmaintain acts as a regularization term or prior belief that encodes our prior belief in the spatial coordinate similarity between the two slices. For the DLPFC dataset, we normalize each inter-slice distance matrix by the minimum distance between any two distinct spots within the same slice. We recommend using \4 0.1 and A3 2.0 by default, except in cases where the slices are a priori less similar- which we set À = 0.2. To quantify slice-to-slice similarity- and thereby define the
and max distance, which measures the average
guide hyperparameter selection feature mismatch between corresponding spots after neighborhood smoothing. Specifically, suppose have slices with nı and n2 spots. We first perform joint PCA and reduce the normalized gene expression matrices into low-dimensional features 7, E R xd and Z₂ E Raaxd Denote the adjacency matrices of these two slices by A₁ and Ag, respectively. We define the mini-max measure as follows:
Mini-max Z2) quantile {min <i5
(A2 15 SiS R1, 0.99]
mcan: (A, mcan, | (AA2))))11
where the inner minimum is taken row-wise over the first slice's smoothed features, quantifying the distance between each spot of the first slice and its closest counterpart on the second slice. The mini-ma max distance is then defined as the largest quantile among these minimal distances. Table reports the mini-max distances for three samples across their adjacent slice pairs (AB, BC,
Table 4: Mini-mal max distances quantifying slice-to slice similarity for three samples.
Sample
AB
BC
CD
Sample I
0.2726
0.5670
0.2609
Sample
0.2958
0.4713
0.2764
Sample III 0.2439
0.2127
0.2368
CD). We note that the BC pairs in Sample I and Sample II have substantially larger distances than
the rest. For these two cases, we set Ag = 0.2. Consequently. for all other cases, we set X3 = 2.0
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to promote joint learning between slices. Figure and Figure 8 present sensitivity analyses for the hyperparameters A and λa, respectively. Both the adjusted Rand index and the alignment score remain stable over wide range of values: A from 0.5 to 2.0 times the default value; A from 0.05 to 0.25, deteriorating only when either hyperparameter set to very low levels.
Although we fixed A2, As throughout the experiment, we extend the sensitivity analysis to X2 and As Table further demonstrate the flexibility of our algorithm.
Average ARI
Average Alionment Score
0.5
07-
0.54
0.52
JADE
JADE D.5
JADE
.AE 1.3
JADE =20
Figure 7: Sensitivity analysis: Varying As where r3 the magnifier of against JADE. Each boxplot
summarizes the outcomes independent replications.
Average ARI
Average Alignment Score
0.8
0.550
076
0.525
JADE A
A 0.05
JADE
0.15
À 0.25
Figure 8: Sensitivity analysis: Varying Au. Each boxplot summarizes the outcomes of 100 independent
replications.
Ablation study
Table Sensitivity analysis of A2 and As for JADE.
Metric
Default
0.5 x Xa
2.0 x A2
2.5 x X2
0.5 As
2.0 x As
2.5 x As
ARI
0.550
0.550
0.564
0.564
0.547 0.801
0.545
0.552
Alignment ACC
0.788
0.797
0.790
0.788
0.773
0.787
Figure 9 compares JADE versions with mismaintain loss (A3 0) and no misalignment loss (A4 0). Results show that performance deteriorates markedly when either loss term is omitted, demonstrating that both the misalignment and mismaintain losses are crucial for optimal embedding and alignment quality. Setting \ = 0 causes the ARI to drop from 0.55 to 0.53 (a 4% decrease) and the alignment score fall from 0.8 to 0.7 (over 10% decrease), underscoring the critical role of the misalignment loss. Setting Àa causes the ARI to drop from 0.55 to 0.525 (a 5% decrease) and the alignment score to fall from 0.8 to 0.62 (about 20% decrease), underscoring the critical role of the mismaintain loss.
G Scalability of Fast-JADE
Table and present the runtime and average ARI for JADE and Fast-JADE, the accelerated version of JADE using hyperspots as introduced in Section 3 We see that as the runtime reduce

---

Average ARI
Average Alignment Score
0.80
0.575
0.75
0.550
0.70
0.85
0525
0.50
0.55
Method
JADE
JADE A
JADE A3 0
Method
JADE
JADE A
JADE A3 0
JADE
JADE
JADE =
Figure 9: Ablation study: each boxplot summarizes the outcomes of 100 independent replications, We calculate
the p-value using the Wilcoxon-rank sum test. **** stands for p-value lower than 0.01 %
Table 6: Runtime comparison of JADE and Fast-JADE (relative run time).
Method
DLPFC
Axolotl Brain
JADE
1.000
1.000
Fast-JADE (with 2000 hyperspots)
0.504
0.640
Fast-JADE (with 1000 hyperspots) 0.200
0.333
significantly when using Fast-JADE instead of the standard version of JADE while the ARI remains almost the same. Table X presents the GPU runtime per epoch for Fast-JADE. As shown in the table, Fast-JADE demonstrates approximately linear scaling with respect to the data size, maintaining efficient performance on large-scale data.
H
Discussion
Direct alignment against transitive alignment. We conducted additional experiments on the DLPFC dataset (Sample III) using slices A, B, and C. Specifically, we first computed pairwise alignments AA (between A and B) and Ic (between B and C) using JADE, and then derived transitive alignment Al = 1lAB x Llcc, followed by Sinkhorn normalization to enforce the doubly stochastic property. We compared this transitive IA with the direct alignment obtained by running JADE on slices A and C. The alignment accuracy for the direct A-C alignment was 0. 0.767, whereas the transitive alignment via A B C achieved an accuracy of 0.749. These results suggest that although transitive alignment using JADE is feasible, accumulates intermediate alignment noise, resulting in slightly lower accuracy than direct pairwise alignment. This finding highlights important point: IADE's pairwise design supports flexible alignment across arbitrary slice pairs and enables indirect mapping when necessary, but direct alignment remains the preferred strategy due to its superior accuracy.
Performance under unbalanced number of spots in two slices. We conducted experiment on the DLPFC dataset (Sample III, slices A and B), where we randomly masked a subset of spots from slice A to simulate scenarios with unequal spot counts. Table reports the results obtained by varying the proportion of removed spots (10% 25%, and 50%) in the DLPFC data.
Table 7: Average ARI comparison of JADE and Fast-JADE in DLPPCC
Method
DLPFC
JADE
0.551 (0.002)
Fast-JADE (with 1000 hyperspots)
0.536 (0.001)
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Table 8: GPU runtime for Fast-JADE (milliseconds per epoch).
Number of spots per slice
10,000
20,000
50,000
100,000
Runtime (ms/epoch)
14.6
32.3
84.8
177
Across all tested levels of spot removal (up to 50%), the Adjusted Rand Index (ARI) for slices A and B, overall alignment accuracy (ACC), and batch-correction metric (iLISI) remain highly stable, showing only minimal fluctuations. This robustness demonstrates that JADE effectively handles situations with substantially different spot counts between slices, making practical for real-world applications where tissue sections vary in size.
Table 9; Performance under unequal number of spots on the DLPFC dataset.
% Spots Removed
ART (Slice A)
ART (Slice B)
ACC
iLISI
0%
0.62
0.65
0.83
1.98
10%
0.60
0.66
0.81
1.97
25%
0.61
0.65
0.82
1.98
50%
0.62
0.67
0.82
1.98
Comparison with image-based alignment methods. To evaluate JADE against image-based align- ment methods, we conducted an experiment with GPSA (28), the only method in the benchmarking study by Hu et al. (24) that integrates both gene expression and histology features. As shown in Table [Ō] JADE consistently outperforms GPSA in alignment accuracy across all slice combinations in the DLPFC dataset.
While incorporating histological images can, in principle, improve alignment, their effectiveness depends heavily on image quality, resolution, and cross-sectional consistency. In practice, H&E images may be noisy, misaligned, or inconsistently stained. Morcover, these images are often obtained from adjacent rather than identical sections, limiting their spatial correspondence with transcriptomic profiles. Such discrepancies can introduce spurious or noisy signals, particularly when histological structures do not clearly delineate molecular domains.
By contrast, JADE relies on gene expression and spatial location information, which are more consis- tently measured across spatial transcriptomics platforms. This design enables JADE to be broadly applicable technologies such as the Stereo-seq platform (as shown Figure where histological imaging is unavailable, and to remain robust when image quality is variable or inconsistent.
Importantly, JADE's framework is modular and can be extended to incorporate image-derived information in future work. For example, histological features could be integrated by modulating the spatial graph (e.g., assigning image informed weights to graph edges) or by combining image embeddings with expression-basee utility in contexts where nighquuaitt image data are available, while preserving its core advantage of joint alignment and representation learning. Unlike alignment-onle methods such as GPSA or PASTE, JADE uniquely supports both spatial alignment and shared fow-dimensional embedding. enabling a broader range of downstream analyses, including clustering, visualization, and trajectory inference.
representations. These extensions could further enhance JADE's
Table 10: Alignment accuracy (ACC) comparison between JADE and GPSA the DLPPC dataset (Samples
I-III: slices A-D).
Sample
Sample II
Sample III
Method
Average
AB
BC
CD
AB
BC
CD
AB
BC
CD
JADE GPSA 28
0.76
0.54
0.81
0.88
0.76
0.84
0.83
0.82
0.79
0.78
0.19
0.20
0.25
0.42
0.34
0.28
0.18
0.17
0.17
0.24
Comparison with new benchmarks. To further evaluate the generalizability and robustness of JADE, we conducted additional experiments on two diverse and challenging datasets: the MERFISH dataset [10] and the breast cancer Visium/Xenium dataset [26]. previously used in SLAT [7]. In the latter, one slice was generated using Visium (approximately 3,500 spots and over 15,000 genes) and the other using Xenium (over 140,000 spots but only about 300 genes). As shown in Table II] JADE consistently outperforms or matches existing methods, SLAT and STAligner, both domain detection
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accuracy (Adjusted Rand Index, ART) and alignment accuracy (ACC). These results demonstrate JADE's robustness across distinct spatial transcriptomics platforms (MERFISH, Visium, Xenium) and tissue types (brain and breast).
We note important caveat regarding the breast cancer dataset. This dataset does provide manually curated one-to-one ground-trute correspondences between the Visium and Xenium slices, The Visium slice includes coarse region-level labels (e.g., immune, invasive), whereas the Xenium slice contains more fine-grained cell-type annotations (e.g., CD8* T Cells, Invasive Tumor). To enable quantitative evaluation, we manually harmonized these label sets based on biological correspondence and naming conventions. Although this approximation enables consistent comparison across methods, introduces some ambiguity into the label-based evaluation. The reported alignment accuracy (ACC) should therefore be interpreted with caution, as it may partially reflect label mismatches rather than true misalignment. more definitive assessment would require expert-annotant alignments, which are currently unavailable for this dataset.
Table 11: Comparison between JADE (Fast-JADE with on the MERFISH and Breast Cancer datasets. Results are averaged over 20 runs.
1000). SLAT, STAligner, and SpotScape
MERFISH 10)
Breast Cancer 26
Method
ARI-1
ARI-2
ACC
ARI-
ARI-2
ACC
JADE
0.504
0.538
0.706
0.433
0.230
0.336
SLI
0.224
0.331
0.386
0.420
0.197
0.294
STAligner 81
0.371
0.487
0.535
0.359
0.186
0.089
SpotScape 50
0.346
0.265
0.690
0.277
0.179
0.312
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Reviews:
[{"review_id": "tf8VkrHlww", "reviewer": "Reviewer_Yzhq", "summary": "In this paper, the authors proposed  a unified computational framework to simultaneously learns spatial alignments and their embeddings across pairs of tissue slices. The spatial information of each slide was initially represented as k-nearest neighbor graph and embedding was generated via graph convolutional networks (GCNs). Graph attention was then employed to obtain alignment using the embeddings. The final objective function includes self-supervised graph contrastive loss to maintain local neighborhood structure, alignment loss, gene expression reconstruction  loss and a regularization term. \n\nThe authors performed extensive experiments using two datasets and compared their performance with existing approaches in terms of alignment accuracy and downstream applications. Results demonstrated its superior performance.", "questions": "1. The approach can only work  on two slices. Can the authors do some experiments, for example, first establish alignments between slices A&B, and B&C, derive alignment between A&C, and compare it with the direct alignment of A&C?", "limitations": "Yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n1. The paper addresses a timely problem in bioinformatics. It is well written and easy to follow. \n2. The idea of performing alignment and learning the embedding simultaneously is novel. \n3. The results are convincing. \n\nWeaknesses\n1. The proposed approach does not differentiate spatial from temporal domain, as showed in the two different datasets, which could be very different in terms of the actual corresponding locations between the two slices. \n2. Using graphs to represent the locations will lose coordinate information. Can the authors access the impact of such a representation?  \n3. It can only work for a pair of slices.", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for the thoughtful and constructive comments. Please see below for our response.\n\n>  ***Comment:** The proposed approach does not differentiate spatial from temporal domain, as showed in the two different datasets, which could be very different in terms of the actual corresponding locations between the two slices.* \n\n**Response:** Thank you for raising this important point. JADE is designed to align spatial transcriptomics (SRT)  datasets across tissue sections without assuming any temporal ordering or anatomical continuity. This design reflects the current structure of most publicly available spatial omics datasets. \n\n\n**Spatiotemporal SRT data are still rare**: While modeling temporal structure can be important for studying dynamic biological processes, spatiotemporal spatial transcriptomics datasets, which capture spatially resolved gene expression over time, are currently limited due to technical challenges. These include difficulties in collecting consistently aligned serial sections across time points, preserving spatial structure, and maintaining high RNA quality throughout the time course.\n\n**Focus on multi-sample integration:** In contrast, multi-sample spatial transcriptomics datasets are much more widely available. These include data collected across individuals, biological replicates, or conditions, typically without consistent spatial or temporal alignment. JADE is specifically designed for this general setting. It learns a shared embedding by leveraging both spatial context and gene expression similarity, without relying on external spatial registration or temporal metadata. This enables robust alignment across diverse datasets such as tissue atlases, cross-sectional disease studies, and multi-region profiling.\n\n**Effectiveness in cross-stage and heterogeneous data:** Importantly, even in datasets spanning different developmental stages, such as the Axolotl Telencephalon Dataset from Stereo-seq (as shown in Figure 3 in our original submission) are drawn from different individuals and contain distinct spatial resolutions and morphologies. Nevertheless, JADE is able to successfully integrate these samples by leveraging both spatial context and gene expression similarity. In our experiments, JADE achieved the highest domain detection accuracy and alignment performance across juvenile and adult axolotl brain slices. It was the only method to reconstruct key anatomical structures (e.g., the peripheral vascular leptomeningeal cell ring and Nptx+ lateral pallium excitatory neuron), yielded the most coherent latent embeddings with strong mixing across slices, and identified biologically meaningful spatial expression patterns for marker genes such as *SCGN*, *ZIC1*, and PENK. These results highlight that even without explicitly modeling temporal structure, JADE can align cross-stage datasets by leveraging gene expression signals that implicitly reflect developmental progression.\n\n**Future extension to temporally resolved data:** While modeling true temporal progression remains an important goal for understanding dynamic biological processes, current spatial transcriptomics technologies do not support dense time-course sampling from the same tissue. As temporally resolved spatial datasets become more accessible, the JADE framework could be extended to model temporal progression by integrating trajectory-informed regularization, time-aware embeddings, or spatiotemporal graph structures. These extensions would enable JADE to explicitly capture both spatial and temporal dependencies in future datasets. We appreciate the reviewer’s suggestion and we will include these discussions in the revised manuscript. \n\n>  ***Comment:** Using graphs to represent the locations will lose coordinate information. Can the authors access the impact of such a representation?* \n\n**Response:** Thank you for your valuable comment. \n\n**Use of spatial graphs in prior work**: Constructing spatial graphs from location coordinates is a standard and well-validated approach in methods for modeling spatial transcriptomics data (e.g., GraphST [1], STAGATE [2], SpaGCN [3]). These methods prioritize capturing local neighborhood relationships, such as spatial proximity and context, over absolute coordinate values, which can be distorted across sections or individuals due to variations in tissue placement or morphology. Thus, spatial graphs provide a robust mechanism to borrow strength from nearby locations while being resilient to global spatial inconsistencies.\n\n**Empirical evaluation**: To directly address the reviewer’s concern, we conducted an additional experiment in which we concatenated the original spatial coordinates ($S$) to the gene expression matrix ($X$), resulting in an augmented feature matrix $X' \\in \\mathbb{R}^{n \\times (p+2)}$ as the new input for each spatial location.  We set the adjacency matrix $A$ to the identity matrix, thereby removing all graph-based connectivity and relying solely on the absolute spatial positions. We then ran JADE on this modified input (We refer to this procedure as **JADE-concat**). As shown in **Table R1**, this brute-force inclusion of absolute coordinates performs worse than our original JADE framework, which leverages the spatial graph, across all evaluation metrics, including Adjusted Rand Index (ARI), Alignment Accuracy (ACC), and integrated local inverse Simpson’s index (iLISI). This shows the effectiveness of using spatial graph. \n\nTable R1: Performance comparison between JADE and JADE-concat on the DLPFC dataset (Sample III, slices A and B). Bold values indicate the best performance for each metric.\n\n|                 | **ARI (Slice A)** | **ARI (Slice B)** | **ACC** | **iLISI** |\n| --------------- | :-----------------: | :-----------------: | :--------------------: | :--------------------------: |\n| JADE        |     **0.62**                |     **0.65**                |                 **0.83**       |    **1.98**                          |\n| JADE-concat |     0.58                |       0.51              |               0.66         |  1.91                           |\n\n\n>  ***Comment:** It can only work for a pair of slices. The approach can only work on two slices. Can the authors do some experiments, for example, first establish alignments between slices A&B, and B&C, derive alignment between A&C, and compare it with the direct alignment of A&C?* \n\n**Response:** Thank you for this insightful comment. Following your suggestions, we conducted additional experiments on the DLPFC dataset (Sample III) using slices A, B, and C. Specifically, we first computed pairwise alignments $\\Pi_{AB}$ (between A and B) and $\\Pi_{BC}$ (between B and C) using JADE, then derived a transitive alignment $\\Pi_{AC} \\propto \\Pi_{AB} \\times \\Pi_{BC}$ (followed by Sinkhorn normalization to enforce doubly-stochastic properties). We compared this transitive $\\Pi_{AC}$ against the direct alignment obtained by running JADE on A and C. We found that the alignment accuracy for the direct A–C alignment was **0.767**, whereas the transitive alignment via A–B–C yielded an accuracy of **0.749**. This result suggests that although transitive alignment using JADE is feasible, it tends to accumulate intermediate alignment noise, leading to slightly lower accuracy than direct pairwise alignment. We appreciate the reviewer’s suggestion, which highlights an important point: JADE's pairwise design supports flexible alignment across arbitrary slice pairs and enables indirect mapping when needed. However, direct alignment remains the preferred strategy due to its superior accuracy, as demonstrated in our experiments. We will include this discussion and analysis in the revised manuscript.\n\n[1] Yahui Long et al. GraphST: Spatially informed clustering, integration, and deconvolution of spatial transcriptomics. Nat. Commun. 14, 1155 (2023).\n\n[2] Kangning Dong and Shihua Zhang. Adaptive graph attention auto-encoder for spatial domain detection in transcriptomics. Nat. Commun. 13, 1739 (2022).\n\n[3] Jian Hu et al. SpaGCN: Integrating gene expression, spatial location, and histology via graph convolutional networks. Nat. Methods 18, 1342–1351 (2021)."}, {"review_id": "pKVn0DfXln", "reviewer": "Reviewer_D17F", "summary": "Authors introduce JADE for simultaneous alignment and representation learning of ST spots across multiple paired slices. The objective uses a combination of recon, OT-alignment loss and contrastive loss and is benchmarked against 6 other baselines (either alignment or embedding) on 2 datasets, showing improvement in alignment accuracy and domain segmentation.", "questions": "Given the availability of paired H&E image with visium and the long standing literature in image-based registration. How does the authors' approach compared against a computer vision-based baseline of image registration, both in terms of performance and runtime?", "limitations": "Yes.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\nMethod is intuitive with good performance. Authors also provide a computationally-efficient approximation.\n\nWeaknesses\nDoes not take into account H&E images associated with Visium data / lack of comparison with methods that perform image-based alignment.", "was_revised": true, "final_justification": "I thank the authors for an exceptionally thorough and convincing rebuttal. They have fully addressed my primary concern regarding the lack of comparison to methods that use H&E histology images.", "rebuttal": ">  ***Comment:** Does not take into account H&E images associated with Visium data / lack of comparison with methods that perform image-based alignment.* \n\n**Response:** We thank the reviewer for this thoughtful comment. \n\n**JADE is designed as a joint alignment and embedding framework**: We would like to respectfully clarify that JADE is not solely an alignment method. Instead, it is designed as a unified framework that simultaneously performs cross-slice spatial alignment and shared low-dimensional representation learning. This joint optimization is central to JADE's design and enables a range of downstream analyses such as spatial domain detection, trajectory inference, and spatially variable gene detection analysis that go beyond alignment-only methods can support. To our knowledge, JADE is the first method to offer this capability within a single framework.\n\n**Rationale for benchmarking choices:** In our original submission, we selected strong and representative alignment methods as baselines. In particular, PASTE was included because of its demonstrated accuracy in alignment tasks, as supported by the recent large-scale benchmarking study by Hu et al. (Genome Biology, 2024). Among the five alignment methods assessed in that study, PASTE was consistently among the top performers.\n\n**New benchmarking comparison with method incorporating H&E images:** We appreciate the reviewer’s suggestion to compare JADE with methods that utilize H&E images. To this end, we have conducted a new benchmarking experiment with GPSA (Jones et al., Nature Methods, 2023), which, to our knowledge, is the only method mentioned in the Hu et al. benchmarking paper that supports the incorporation of both gene expression and histology features for alignment. As shown in Table R2, JADE consistently outperforms GPSA in alignment accuracy across all slice combinations in the DLPFC dataset. These results suggest that JADE is able to achieve strong performance even without directly incorporating image data.\n\n**Advantages and broader applicability of JADE:** While image-based features can in some cases aid alignment, their utility depends heavily on the quality, resolution, and consistency of the imaging data. In practice, H&E images may be noisy, poorly aligned across slices, or contain staining artifacts, and are often collected from adjacent rather than identical tissue sections, limiting their spatial correspondence with the transcriptomic data. Incorporating such features directly into computational models can introduce spurious signals or additional noise, particularly when the image modality does not clearly delineate anatomical structures relevant for molecular alignment. By contrast, JADE is designed to model on gene expression and spatial location information, which are more consistently measured across spatial transcriptomics platforms. This enable JADE to be broadly applicable to a wide range of technologies, such as the Stereo-seq platform (as we shown in Figure 3), where histological imaging is unavailable, and to maintain robustness in settings where image quality is variable or inconsistent. \n\n**Future directions:** Importantly, the JADE framework is modular and can be extended to incorporate image-derived information in future work. For example, histological features could be integrated by modulating the spatial graph, such as assigning image-informed weights to graph edges, or by combining image embeddings with expression-based representations. These extensions could further enhance JADE's utility in settings where high-quality image data are available, while preserving its core advantage of joint alignment and representation learning. Unlike alignment-only methods such as GPSA or PASTE, JADE uniquely supports both spatial alignment and shared low-dimensional embeddings, enabling a broader range of downstream analyses, including clustering, visualization, and trajectory inference.\n\nTable R2: Performance comparison between JADE and GSPA on the DLPFC dataset (Sample I, II, III, slices A, B, C, and D). Bold values indicate the best performance for each metric.\n\n| Sample  | Case | JADE | GSPA |\n|:------:|:----:|:----:|:----:|\n| Sample I | AB   |  **0.76**    |  0.19    |\n|        | BC   |  **0.54**    |  0.20    |\n|        | CD   |  **0.81**    |  0.25    |\n| Sample II | AB   |  **0.88**    |  0.42    |\n|        | BC   |  **0.76**    |  0.34    |\n|        | CD   |  **0.84**    |  0.28    |\n| Sample III | AB   |  **0.83**    |  0.18    |\n|        | BC   |  **0.82**    |  0.17   |\n|        | CD   |  **0.79**    |  0.17    |\n| Average|      |  **0.78**        |   0.24       |\n\n>  ***Comment:** Given the availability of paired H&E image with visium and the long standing literature in image-based registration. How does the authors' approach compared against a computer vision-based baseline of image registration, both in terms of performance and runtime?* \n\n**Response:** We thank the reviewer for this thoughtful comment. We would like to clarify the distinction between our method and conventional image registration approaches, and explain why such baselines are not well suited for the problem that JADE is designed to solve.\n\n**Limitations of histology-based registration in practice:** (1) The feasibility of using H&E image-based registration depends strongly on the spatial transcriptomics workflow. In the original 10x Visium protocol, the H&E image is often obtained from an adjacent tissue section, not the same one used for RNA capture. This is because H&E staining can compromise RNA quality, and separate serial sections are used to preserve transcriptomic integrity. As a result, aligning the transcriptomic data with the corresponding H&E image already requires an additional registration step, and introduces unavoidable discrepancies between the molecular and histological data. (2) Recently, the Visium CytAssist workflow enables H&E imaging and transcript capture from the same tissue section. This allows for more precise correspondence between image and gene expression data at the spot level. However, even under this setup, a standard image registration pipeline has several important limitations when applied to the task of multi-sample spatial transcriptomics integration. As mentioned in our previous response, even when histological information is incorporated into the alignment process, as is the case with GPSA, the resulting performance is substantially worse than that of JADE. This might suggest that approaches relying exclusively on histological images are even less likely to succeed. Moreover, many spatial transcriptomics platforms, including the Stereo-seq technology used in Figure 3 of our manuscript, do not provide histological images. These considerations highlight JADE’s broader applicability and robustness across different spatial transcriptomics technologies. \n\n**Image registration is insufficient for molecular alignment:** (1) Image registration methods rely exclusively on histological features and ignore gene expression profiles entirely. They are therefore sensitive to variations in staining intensity, tissue processing, and imaging conditions, which can differ across experiments and reduce registration accuracy. (2) Image-based alignment cannot be applied to cross-platform or cross-modality settings, where histology images may not exist or may not be comparable. (3) Image registration does not address the core challenge of transcriptomic alignment, which involves learning a biologically meaningful correspondence between spatially resolved molecular profiles across samples. \n\n**JADE provides embeddings for integrated molecular analysis:** Most importantly, image registration methods do not generate any molecular embedding for the spatial transcriptomics data. They simply return a spatial transformation that aligns two tissue sections at the image level, without learning a latent representation of gene expression. In contrast, JADE jointly aligns multiple tissue sections and learns a low-dimensional embedding that reflects shared transcriptional and spatial structure across samples. These embeddings are directly useful for downstream analyses such as clustering, visualization, and trajectory inference, and provide a richer representation than spatial alignment alone.\n\nWe hope this clarifies the distinct goals and advantages of JADE relative to conventional image registration."}, {"review_id": "bMXucwolUk", "reviewer": "Reviewer_TnAY", "summary": "This paper introduces JADE, a computational framework that simultaneously learns spatial alignments and low-dimensional embeddings for multi-slice spatial transcriptomics data. The method combines graph autoencoders, attention-based OT for alignment, and contrastive learning for embedding refinement. The authors evaluate JADE on human dorsolateral prefrontal cortex (DLPFC) and axolotl brain datasets, claiming superior performance over existing methods in spatial domain detection, alignment accuracy, and batch effect correction.", "questions": "1. Have the authors considered extending the framework to handle more than two slices simultaneously using multi-marginal optimal transport?\n2. How does the method perform when slices have significantly different numbers of spots or coverage areas?", "limitations": "Limitations are partially discussed in the Discussion section. More limitations are discussed in the weakness review above", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "- Strength\n  1. The problem of joint optimization of alignment and representation learning is well-motivated. JADE addresses this important problem while other existing methods handle it separately.\n  2. The roundtrip loss objective that alternates between alignment and embedding refinement is interesting. \n  3. The paper is well written and the experiments are detailed and comprehensive. \n\n- Weakness\n  1. JADE assumes full correspondence which might not hold. By enforcing a doubly stochastic alignment matrix with uniform marginals, JADE essentially assumes every location in slice A maps to something in slice B. This is a strong assumption that breaks down if slices aren’t perfectly overlapping or equal sized. Methods like PASTE2[1] handle this by allowing unassigned mass and JADE currently cannot. This is a significant weakness for scalability to larger or diverse datasets\n  2. Despite the loss being interesting, JADE’s loss function is complex and combines five functions with their own hyperparameters. The performance is highly sensitive to these hyperparameter choices, and likely requires dataset-specific tuning (Supp section D). I'm concerned about the method's robustness and practical usability\n\nminor typo: line 9, embedding representation of each slice -> embedding representation of each spot\n\n[1] Liu, Xinhao, Ron Zeira, and Benjamin J. Raphael. \"PASTE2: partial alignment of multi-slice spatially resolved transcriptomics data.\" bioRxiv (2023).", "was_revised": true, "final_justification": "- The rebuttal clarified key concerns, particularly around the unequal number of spots across slices\n- I agree with other reviewers that the novelty of the method is limited", "rebuttal": ">  ***Comment:** JADE assumes full correspondence* \n\n**Response:** Thank you for this valuable comment. We acknowledge that JADE's assumption of full alignment, a limitation noted in our Conclusions section. However, full alignment remains a relevant and effective approach in many spatial transcriptomics integration contexts. JADE is designed to exploit this assumption through a principled and scalable framework, and we provide the following clarifications and justifications.\n\n1. **Full alignment remains appropriate in many practical scenarios**: The assumption of full correspondence is supported by how spatial transcriptomics data are typically generated. In many studies, especially those involving serial or adjacent tissue sections from the same block, standardized protocols and spatial orientation preserve anatomical continuity. This setup, common with platforms such as 10x Visium, Slide-seqV2, HDST, or Stereo-seq, is widely used in applications such as brain mapping, tumor profiling, and developmental tissue analysis [1]. In these contexts, full alignment facilitates accurate reconstruction of tissue structure and is often preferable to under-aligned or sparsity-enforced approaches. Even when integrating data across individuals or datasets, alignment is typically applied to anatomically matched regions (e.g., the same cortical layer or tumor zone), where substantial structural overlap supports biologically meaningful comparison.\n2. **Full alignment is preferred over partial alignment when overlap is high**: In cases of substantial or complete overlap, full alignment offers advantages over partial matching by avoiding under-alignment. Recent methods such as GPSA [2] and BiGATAE [3], assuming full alignment, demonstrate superior performance in tasks such as multi-slice spatial domain detection and 3D tissue reconstruction. **In contrast**, partial alignment methods, such as PASTE2, are designed to handle substantial missing regions or non-overlapping areas but may underperform or over-regularize when full correspondence is present. Additionally, these methods require tuning a hyperparameter (overlap percentage between the two slices to align), which is challenging and demands significant prior knowledge, often unavailable in practice.\n3. **JADE can handle imperfect overlaps and unequal size data in practice:** While JADE assumes full alignment, it has demonstrated robustness in real datasets where slices are not perfectly overlapping or equally sized. For example, in the experiments where we evaluated JADE's performance on the DLPFC datasets when the number of spatial locations are unequal across slices (details see **Table R3**), we found that JADE **remains highly stable**. This suggests that JADE is tolerant to moderate mismatch. \n4. **Fast-JADE supports scalability to large and diverse datasets:** In our paper, we have developed Fast-JADE, a computationally optimized variant. In our benchmarks, Fast-JADE achieves a runtime of 0.015 seconds/epoch for 10,000 spots, scaling linearly to 0.177 seconds/epoch for 100,000 spots, demonstrating strong efficiency for integration at scale. \n5. **JADE is more than just an alignment tool:** Unlike PASTE or PASTE2, which focus on alignment without embeddings, JADE jointly optimizes alignment and representation in a shared latent space via a roundtrip framework, enhancing both tasks mutually. This enables broader downstream tasks like cell state mapping, spatial domain detection, and trajectory inference.\n6. **Future directions: relaxing the full correspondence assumption:** We agree that extending to partial alignment would enhance JADE's flexibility. A promising direction is relaxing the doubly stochastic constraint using unbalanced optimal transport, allowing partial matching or unassigned mass. We view this as a valuable extension and will include this discussion in the revised manuscript.\n\n[1] Khan, M., Arslanturk, S., & Draghici, S. (2025). A comprehensive review of spatial transcriptomics data alignment and integration. Nucleic Acids Research, 53(12), gkaf536. \n\n[2] Jones, A., Townes, F. W., Li, D., & Engelhardt, B. E. (2023). Alignment of spatial genomics data using deep Gaussian processes. Nature methods, 20(9), 1379-1387.\n\n[3] Tao, Y., Sun, X., & Wang, F. (2024). BiGATAE: a bipartite graph attention auto-encoder enhancing spatial domain identification from single-slice to multi-slices. Briefings in Bioinformatics, 25(2), bbae045.\n\n>  ***Comment:** Hyperparameters of JADE’s loss. Robustness of JADE* \n\n**Response:**  Thank you for this constructive comment. \n\nTo clarify, while there are four hyperparameters ($\\lambda_{2}-\\lambda_5$) in our loss function, three are fixed across datasets: $\\lambda_2$=10 (reconstruction, following GraphST [1]), $\\lambda_4$=0.1 (alignment), and $\\lambda_5$=1 (marginal), based on empirical validation during development. Only $\\lambda_3$ (maintenance) requires tuning (from 0.2 to 2.0), and we employ a **data-driven approach**: if two slices are similar, we use a larger $\\lambda_3=2$ to encourage information sharing; otherwise, we use a smaller $\\lambda_3=0.2$ to prevent negative transfer. **So the only hyperparameter that needs to be selected is $\\lambda_3$.**\n\nImportantly, as shown in Figure 4 (Appendix), JADE’s performance is robust across a broad range of $\\lambda_3$ values. Both the average ARI and alignment score show stable results over different $\\lambda_3 \\in [0.2, 2]$, with only marginal variation. This indicates that the method is not highly sensitive to the precise choice of $\\lambda_3$, thus reducing the burden of hyperparameter tuning in practice.\n\nIn addition, to further demonstrate the robustness and practical utility of our method, we evaluated JADE on **two additional datasets**: the MERFISH dataset and the Breast Cancer dataset. Please see **Table R5** in our response to Reviewer c7f2 for detailed results. In summary, JADE continues to outperform competing methods on both datasets, **further supporting the robustness and generalizability of our approach**.\n\n[1] Yahui, L., Kok, A., & Jinmiao, C. (2023). Spatially informed clustering, integration, and deconvolution of spatial transcriptomics with graphst. Nature Communications, 14(1):115\n\n>  ***Comment:** minor typo: line 9*\n \n**Response:** Thank you for pointing this out. We will correct this typo in the revised manuscript. \n\n>  ***Comment:** Have the authors considered extending the framework to handle more than two slices simultaneously using multi-marginal optimal transport (MMOT)?*\n\n**Response:**  Thank you for this insightful suggestion. We agree that while we have focused the current version of JADE on the pairwise setting for conceptual clarity and computational efficiency, extending JADE to handle joint alignment of more than two slices is a **natural and promising direction**. We are actively exploring this direction for future extensions of the framework, however, incorporating MMOT into JADE introduces several nontrivial **challenges**. \n\n1. **Curse of dimensionality:** The coupling tensor $\\Gamma \\in \\mathbb{R}^{n_1 \\times n_2 \\times \\cdots \\times n_m}$ grows rapidly with $m$ and the number of points per slice ($n_t$). For example, even with only three slices and $100$ spatial locations per slice, the tensor has $10^6$ entries; for four slices, this rises to $10^8$. This rapid growth poses memory and storage challenges for real datasets with thousands or hundreds of thousands of spatial locations per slice.\n2. **Expensive computational complexity:** The computational cost of standard MMOT is $\\textbf{polynomial in}$ $n^m$ (e.g., $(n^m)^{2}$). Even with efficient variants such as entropic-regularized MMOT using Sinkhorn-based methods, the cost remains approximately linear in $n^m$. \n3. **Requires careful design of cost function**: In the pairwise setting, cost functions such as Euclidean distance or feature similarity are well-established and straightforward to implement. However, in the multi-slice framework, defining a multi-way cost function that effectively encodes geometric and biological relationships across all slices presents a significant challenge. Conducting pairwise comparisons between every two slices becomes computationally prohibitive as the number of slices increases, necessitating a more efficient approach. One potential strategy is to compute a barycenter (a central representative measure) and map all slices to this barycenter, which could reduce complexity. However, this requires careful design to ensure the barycenter accurately reflects the shared structure and biological context across slices. We leave this for future directions. \n\nWe will add these discussions to the revised manuscript. \n\n>  ***Comment:** How does the method perform when slices have significantly different numbers of spots or coverage areas?*\n\n**Response:**  Thank you for this insightful question.  To address this, we conducted additional experiments using the DLPFC dataset (Sample III, slices A and B), where we randomly mask a subset of spots from slice A to simulate scenarios with unequal spot counts. **Table R3** shows the results of varying the proportion of removed spots (e.g., 10%, 25%, 50%) for DLPFC data. \n\nAs we can see, across all tested levels of spot removal (up to 50%), both ARI (for Slice A and B), overall alignment accuracy (ACC), and batch correction (iLISI) **remain highly stable**, with only minimal fluctuations. This robustness indicates that JADE effectively handles scenarios with significantly different spot counts between slices, making it practical for real-world applications where tissue sections may have varying sizes.\n\nTable R3: Performance of unequal number of spots on DLPFC dataset. \n\n| % Spots Removed (Slice A)  | ARI (Slice A) | ARI (Slice B) | ACC  | iLISI |\n|:---------------:|:------:|:-------------:|:-----:|:-----:|\n|0%|0.62|0.65|0.83|1.98|\n|10%|0.60|0.66|0.81|1.97|\n|25%|0.61|0.65|0.82|1.98|\n|50%|0.62|0.67|0.82|1.98|"}, {"review_id": "hrCWhhnV1X", "reviewer": "Reviewer_c7f2", "summary": "To address the limitations of existing methods that focus solely on either spatial alignment or representation learning, the authors propose JADE, a framework that jointly learns spatial location-wise alignments and shared low-dimensional embeddings across tissue slices. Specifically, JADE computes a cross-slice alignment matrix using the Sinkhorn-Knopp algorithm applied to cross-attention weights, and refines it using a combination of spatial structure preservation loss and embedding alignment loss. In parallel, the model learns low-dimensional embeddings via graph contrastive learning, following a strategy similar to that used in GraphST.", "questions": "1) Please respond to the comments in the 'Weaknesses' section.\n\n2) In highly heterogeneous settings, such as cancer tissue, there is concern that the assumption behind the embedding alignment loss—i.e., that aligned embeddings should be close to each other—may not hold. How does the proposed embedding alignment loss account for such heterogeneity? Please provide a detailed discussion and support it with experiments on a heterogeneous dataset, such as the Breast Cancer data used in prior works (e.g., SLAT).\n\n3) The authors state that the fast version of JADE, which utilizes hyperspots, can reduce computational time. However, it remains unclear whether this approach can scale effectively to very large datasets, which are increasingly common and may contain over 100,000 spots. Please clarify the scalability of Fast-JADE by providing a runtime analysis on such large-scale data.", "limitations": "yes", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 1, "strengths_and_weaknesses": "* Strengths\nThe authors propose a unified framework, JADE, that goes beyond single-task specific methods by performing multiple tasks through jointly learned alignments and representations. Notably, the inclusion of domain-specific gene (marker gene) detection demonstrates that the learned representations can carry biologically meaningful insights. This highlights the potential of JADE for downstream biological interpretation.\n\n* Weaknesses\n1) The main motivation of the paper is that existing methods do not jointly learn spatial location-wise alignments and shared low-dimensional embeddings across tissue slices. However, recent methods such as SLAT [1] and CAST [2] already address both aspects. The key difference lies in their two-stage pipelines (first learn embeddings, then perform alignment), whereas JADE integrates both steps into a unified process. To justify the claimed advantage of this one-step design, the authors should include direct comparisons with SLAT and CAST, both in methodology and empirical performance.\n\n2) There are concerns regarding the novelty of the proposed framework. The components of the proposed method closely resemble existing work. The contrastive learning strategy for representation learning is similar to that used in GraphST, and the alignment component shares conceptual similarities with PASTE, differing mainly in that JADE uses learned embeddings rather than raw gene expression profiles. The authors should clarify the methodological distinctions and contributions of JADE relative to these prior works.\n\n3) The experiments are limited to the DLPFC and Axolotl Brain datasets. However, spatial transcriptomics data vary significantly depending on the platform (e.g., Visium, MERFISH, Slide-seq) and tissue type. To demonstrate robustness and generalizability, the authors should evaluate JADE on additional datasets, such as the MERFISH dataset used in STAligner or the breast cancer data used in SLAT.\n\n[1] Spatial-linked alignment tool (SLAT) for aligning heterogenous slices. Nature communications   \n[2] Probabilistic embedding, clustering, and alignment for integrating spatial transcriptomics data with PRECAST. Nature communications", "was_revised": true, "final_justification": "I have concerns regarding the novelty of the proposed method; however, the paper demonstrates its effectiveness across multiple datasets and tasks, and the authors added important experiments during the rebuttal period.", "rebuttal": "We thank the reviewer for constructive comments. We will add the following discussions, additional experiments, and references to the revised manuscript.\n\n>  ***Comment:** direct comparisons with SLAT and PRECAST (CAST).*\n\n**Response:** Thank you for this valuable comment. \n\n**Methodological Distinction:** SLAT and PRECAST employ a two-stage approach, first learning low-dimensional embeddings independently per slice, then aligning based on these, which can yield suboptimal embeddings as they cannot adapt to alignment insights, and vice versa. **In contrast**, JADE simultaneously optimizes alignment and embeddings through a unified roundtrip process. This joint optimization is advantageous, as alignment and embedding are **inherently interdependent**: accurate alignments rely on embeddings capturing shared transcriptomic patterns, while robust embeddings benefit from alignments resolving spatial correspondences and reducing distortions or batch effects.\n\nBeyond architectural differences, SLAT and PRECAST have methodological limitations: (1) SLAT’s initial SVD-based decomposition assumes a dominant low-rank structure, limiting its flexibility in capturing complex or heterogeneous spatial domains. In contrast, JADE’s end-to-end embedding learning with alignment adapts to diverse biological variations without such assumptions. (2) The embedding of PRECAST highly depends on pre-specifying spatial domain numbers (with BIC for selection); JADE avoids this by learning flexible embeddings compatible with any downstream clustering or domain detection method.\n\n**Empirical Comparison:** As suggested, we implemented experiments to directly compare JADE, SLAT, and PRECAST on two benchmark datasets: DLPFC (sample III, slice A and B) and Axolotl Brain datasets. Table R4 shows that JADE consistently achieves both better domain detection accuracy (higher ARI) and alignment accuracy (higher ACC). This highlights the advantage of jointly training alignment and embeddings. \n\nTable R4: Comparison between JADE, SLAT, and PRECAST on DLPFC  and Axolotl Brain datasets. Bold values indicate the best performance for each metric.\n\n| **Dataset** | **ARI (Slice A)** |   |  | **ARI (Slice B)** |   |  | **ACC** |   |  |\n| ----------- | :---------------: | :---: | :--: | :---------------: | :---: | :--: | :-----: | :---: | :--: |\n|             |        JADE       |  SLAT | PRECAST |        JADE       |  SLAT | PRECAST |   JADE  |  SLAT | PRECAST |\n| DLPFC       |       **0.551**       | 0.323 |  0.400    |       **0.550**       | 0.329 |   0.440   |  **0.799**  | 0.780 |  0.399    |\n| Axolotl     |       **0.375**       | 0.367 |   0.361   |       **0.532**       | 0.466 |  0.416    |  **0.421**  | 0.273 |  0.401    |\n\n>  ***Comment:** methodological distinctions and contributions of JADE relative to these prior works.*\n\n**Response:** Thank you for this thoughtful comment and the opportunity to clarify the methodological contributions of JADE in relation to prior work, particularly GraphST and PASTE. While JADE draws inspiration from these methods, its **core innovation** lies in unifying these into a joint, iterative framework that mutually refines alignments and embeddings, addressing the limitations of prior two-stage or isolated approaches. Below, we outline the key distinctions.\n\n1. **Methodological distinction from GraphST:** GraphST does not explicitly model spatial location-level alignments across slices, treating integration as a secondary step without iterative feedback. JADE builds on contrastive learning but integrates it within a roundtrip framework, where embeddings are refined alongside alignments using attention-based OT, ensuring spatial correspondences directly inform feature learning (and vice versa). This joint optimization prevents inconsistencies, such as misaligned homologous regions leading to noisy embeddings, which GraphST may overlook. \n2. **Methodological distinction from PASTE:** PASTE uses fused Gromov-Wasserstein OT on raw profiles for alignment, excelling in 3D reconstruction but not learning embeddings, limiting downstream utility. JADE applies OT to learned embeddings with attention weighting to focus on relevant features while suppressing noise, and its roundtrip iteration allows joint optimization of alignments and embeddings.\n3. **Key Innovations and Contributions of JADE:** By jointly optimizing alignment and representation learning in a shared latent space, it creates a feedback loop where alignments guide embeddings to better capture cross-slice consistencies, and embeddings enhance alignments by providing denoised, biologically meaningful features. This is particularly beneficial in noisy SRT data, where raw profiles (as in PASTE) can be sparse and batch-affected, or independent embeddings (as in GraphST) may fail to resolve distortions. To our knowledge, **JADE is the first framework to jointly optimize for spatial alignment and shared low-dimensional embedding in an end-to-end manner.** Empirically, the above Table R4 further illsutrate our advanatge when compared  with two-stages methods: SLAT and PRECAST.\n\n>  ***Comment:** The experiments are limited to the DLPFC and Axolotl Brain datasets.*\n\n**Response:** Thank you for your thoughtful suggestion. Following your advice, we have expanded our experimental evaluation to include two additional and diverse datasets: the MERFISH dataset and the breast cancer Visium/Xenium dataset (as used in SLAT), where one slice was generated using Visium (~3,500 spots with >15,000 genes) and the other using Xenium (>140,000 spots but ~300 genes). Results from these datasets are presented in Table R5, showing that JADE consistently outperforms or matches prior methods in both domain detection (ARI) and alignment accuracy (ACC). These findings further support JADE’s robustness across different platforms (MERFISH, Visium, Xenium) and tissue types (brain and breast).\n\nWe would like to note one important caveat regarding the breast cancer dataset: it lacks manually curated one-to-one ground truth correspondences between the Visium and Xenium slices. The Visium data provides coarse region-level labels (e.g., \"immune\", \"invasive\"), while the Xenium data [1] provides fine-grained cell type labels (e.g., \"CD8+_T_Cells\", \"Invasive_Tumor\"). For evaluation, we manually harmonized labels based on biological correspondence and naming conventions. However, this mismatch introduces ambiguity into the label-based evaluation metric. Establishing accurate ground truth alignment would require expert annotation by biologists, which is not currently available for this dataset. As a result, the reported alignment accuracy (ACC) should be interpreted with caution, as it may be influenced by label bias rather than true misalignment. Nevertheless, the evaluation provides a consistent basis for comparison, as all methods are assessed using the same approximate label mapping.\n\nTable R5: Comparison between JADE (Using Fast-JADE with $m_1=m_2=1000$), SLAT, and STAligner on MERFISH  and Breast Cancer datasets. Bold values indicate the best performance for each metric.\n\n| **Dataset**         | **ARI (Slice 1)** |      |      | **ARI (Slice 2)** |      |      | **ACC** |      |      |\n| ------------------- | :---------------: | :--: | :--: | :---------------: | :--: | :--: | :-----: | :--: | :--: |\n|                     |        JADE       | SLAT | STAligner |        JADE       | SLAT | STAligner |   JADE  | SLAT | STAligner |\n| MERFISH  |        **0.504**           |  0.224    |  0.371    |     **0.538**              |  0.331    |  0.487   |   **0.706**      | 0.386     |  0.535   |\n| Breast Cancer       |   **0.433**                |  0.420    |   0.359   |   **0.230**                |  0.197    |   0.186   |   **0.336**      |  0.294    |  0.089    |\n\n[1] Janesick, A., Shelansky, R., & Sarah E. B. T. (2023). High resolution mapping of the tumor microenvironment using integrated single-cell, spatial and in situ analysis. Nature Communications, 14, 8353.\n\n>  ***Comment:** experiments on a heterogeneous dataset, such as the Breast Cancer data used in prior works (e.g., SLAT).*\n\nThank you for this constructive comment. JADE addresses cross-slice heterogeneity by combining two key strategies: (1) it employs seperate encoders and decoders for each slice, allowing the model to capture platform-specific variations such as gene coverage, resolution, and batch-specific scaling effects. (2) Embeddings from both slices are mapped into a shared latent spcae, and alignment is enforces via the misalignment loss, which encourages biologically meaningful spatial correspondence across datasets. Moreover, in settings such as the breast cancer study—where one slice is generated by Visium (~3500 spots but >15,000 genes) and the other by Xenium (>140,000 spots but only ~300 genes)—Fast-JADE clusters spots into hyperspots and aligns the slices at the hyperspot level, thereby mitigating heterogeneity. As demonstrated in the previous results, Fast-JADE outperforms SLAT and STAligner, highlighting its potential for heterogeneous datasets.\n\n\n>  ***Comment:** Please clarify the scalability of Fast-JADE by providing a runtime analysis on large-scale data.*\n\nThank you for the insightful comment. To assess runtime performance, we conducted GPU-based runtime profiling using varying numbers of spatial locations while fixing the number of hyperspots per slice to \\($m_1$ = $m_2$ = 1000\\). As shown in the table below, Fast-JADE demonstrates linear scaling behavior with respect to input size, maintaining efficient performance even on large-scale data:\n\n| Number of spots                   | 10,000 | 20,000 | 50,000 | 100,000 |\n|:------------------------:|:------:|:------:|:------:|:-------:|\n| Runtime (ms/epoch)       |   14.6     |   32.3     |   84.8   |    177     |\n\nIn future work, we plan to incorporate mini-batch training and sparse OT approximations to further improve scalability for ultra-large datasets."}]

Author rebuttal:

Meta-review: This paper introduces JADE, a framework that jointly learns spatial alignments and shared embeddings across tissue slices using graph neural networks, attention-based OT, and contrastive learning. Evaluations on DLPFC and Axolotl datasets, with additional rebuttal experiments, show consistent improvements over existing methods.

### Strengths
- Addresses an important and timely problem in spatial transcriptomics.
- Joint optimization of alignment and embedding is a well-motivated and practically useful idea.
- Clear writing and thorough experiments, including new analyses in rebuttal (heterogeneous datasets, runtime scaling, comparisons with image-based and graph-based baselines).
- Demonstrates strong and robust performance across multiple datasets and tasks.

### Weaknesses
- Methodological novelty is incremental, drawing on existing ideas from GraphST and PASTE.
- Assumption of full correspondence may limit applicability in some scenarios.
- Evaluation breadth, while expanded in rebuttal, could still be more comprehensive.

Despite some limitations in novelty and scope, the paper makes a solid and practically impactful contribution, with convincing results and thoughtful rebuttal clarifications. I recommend acceptance.
Decision: Accept (poster)