Predicting Functional Brain Connectivity with Context-Aware Deep Neural Networks
Authors: Alexander Ratzan
Sidharth Goel
Junhao Wen
Christos Davatzikos
Erdem Varol
Venue: NeurIPS 2025 poster ()
Keywords: neuroscience
connectomics
transcriptomics
transformers
fMRI
Primary area: neuroscience_and_cognitive_science
TL;DR: We apply context-aware deep neural networks to predict functional connectivity from gene expression in human datasets.

Abstract: Spatial location and molecular interactions have long been linked to the connectivity
patterns of neural circuits. Yet, at the macroscale of human brain networks,
the interplay between spatial position, gene expression, and connectivity remains
incompletely understood. Recent efforts to map the human transcriptome and
connectome have yielded spatially resolved brain atlases, however modeling the
relationship between high-dimensional transcriptomic data and connectivity while
accounting for inherent spatial confounds presents a significant challenge. In this
paper, we present the first deep learning approaches for predicting whole-brain
functional connectivity from gene expression and regional spatial coordinates, including
our proposed Spatiomolecular Transformer (SMT). SMT explicitly models
biological context by tokenizing genes based on their transcription start site (TSS)
order to capture multi-scale genomic organization, and incorporating regional
3D spatial location via a dedicated context [CLS] token within its multi-head
self-attention mechanism. We rigorously benchmark context-aware neural networks,
including SMT and a single-gene resolution Multilayer-Perceptron (MLP),
to established rules-based and bilinear methods. Crucially, to ensure that learned
relationships in any model are not mere artifacts of spatial proximity, we introduce
novel spatiomolecular null maps preserving key transcriptomic autocorrelation
structure. Context-aware neural networks outperform linear methods, significantly
exceed our stringent null map estimates, and generalize across diverse connectomic
datasets and parcellation resolutions. Together, these findings demonstrate a
strong, predictable link between the spatial distributions of gene expression and
functional brain network architecture, and establish a rigorously validated deep
learning framework for decoding this relationship. Code to reproduce our results is
available at: github.com/neuroinfolab/GeneEx2Conn.

Predicting Functional Brain Connectivity with Context-Aware Deep Neural Networks
Alexander Ratzan 1 Sidharth Goel', Junhao Wen Christos Davatzikos', Erdem Varol 1.2
Department of Computer Science, New York University
2 Neuroscience Institute, Grossman School of Medicine, New York University
DDeparmennt of Radiology, Columbia University
*Department Radiology, University of Pennsylvania
*Correspondence: asr6550nyu. edu, ev22408nyu. edu
Abstract
Spatial location and molecular interactions have long been linked to the connec- tivity patterns of neural circuits. Yet, at the macroscale of human brain networks, the interplay between spatial position, gene expression, and connectivity remains incompletely understood. Recent efforts to map the human transcriptome and connectome have yielded spatially resolved brain atlases, however modeling the relationship between dighesiinniional transcriptomic data and connectivity while accounting for inherent spatial confounds presents a significant challenge. In this paper, we present the first deep learning approaches for predicting whole-brain functional connectivity from gene expression and regional spatial coordinates, in- cluding proposed Spatiomolecular Transformer (SMT). SMT explicitly models biological context by tokenizing genes based on their transcription start site (TSS) order capture multi-scale genomic organization, and incorporating regional 3D spatial location via dedicated context [CLS] token within its multi-head self-attention mechanism. We rigorously benehmark context-aware neural net- works, including SMT and single-ge genge- resolution Multilayer- Pereeeerrr-rrrerron (MLP), established rules-based and bilinear methods. Crucially, to ensure that learned relationships in any model are not mere artifacts of spatial proximity, we introduce novel spatiomolecular null maps preserving key transcriptomic autocorrelation structure. Context-aware neural networks outperform linear methods, significantly exceed our stringent null map estimates, and generalize across diverse connec- tomic datasets and parcellation resolutions. Together, these findings demonstrate a strong. predictable link between the spatial distributions of gene expression and functional brain network architecture, and establish rigorously validated deep learning framework for decoding this relationship. Code to reproduce our results is available at: github..... com/ www.nnnfwlaaa/aaoaa/ Exeeeaeeeeeeeeeeeom
Introduction
Throughout development and into adulthood, the coordinated expression thousands of genes shapes the molecular and structural scaffold of the brain (1.2]. Functional brain networks emerge from this scaffold through the synchronous activity of multiscale neural components [3] This emergent organization is central cognition, supporting processes such vision, language, and memory with disruptions to these networks linked to range of neuropsychiatric and neurodegenerative disorders 4.. Understanding the spatiomolecular landscape that gives rise to functional brain networks is critical step towards uncovering the genetic basis of brain function and dysfunction. Thus, we set
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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out to address the fundamental hypothesis that the biological richness of gene expression is highly predictive of functional connectivity [
Recent advances in brain-wide gene expression atlases and large neuroimaging datasets have made possible connect spatial variations in gene expression with the organization of functional brain networks [9] [0]. However, the path to robust predictive models has several key obstacles. First, the scale of transcriptomic data, involving thousands of genes with complex co-expression patterns, demands models with high expressive capacity. Conventional approaches, often favoring bilinear factor models for their perceived explainability, may not adequately capture inherent non- non-linearities [1 12 13 7 Second, major confound in neurogenomic studies is spatial autocorrelation: nearby brain regions often share similar gene expression and connectivity patterss due shared developmental trajectories, vascularization, or signal bleed, potentially inflating statistical associations not rigorously controlled [66 17 Third, obtaining directly paired brain-wide gene expression and in-vivo functional connectivity data from the same human individual is challenging due to postmortem collection of gene expression, motivating the use of carefully aggregated population atlases from multiple data sources. Lastly, effectively integrating biological context- such as the genomic organization of genes or the precise 3D spatial embedding of brain regions- intoo predictive models in meaningful way beyond simple feature engineering, remains open question.
To address these challenges, we introduce context-award neural network architectures including the Spatiomolecular Transformer (SMT) designed specifically for predicting functional connectivity from regional gene expression and spatial coordinates (Figure I evaluated through rigorous experimental setup. Inspired by single-cell approaches such as spaC. [88 and scBERT [19 that use multimodal contextual information to improve performance on downstream tasks, SMT derives brain region embeddings from gene expression sequences tokenized based on reference genome position (transcription start site, TSS) and incorporates regional spatial location information via dedicated [CLS] token. Critically, SMT utilizes Attention with Linear Biases (ALiBi) (20 in its bidirectional multi-head self-attention mechanism to encourage hierarchical transcriptomic representations of the input sequence. Furthermore, to counteract the limited sample size of human gene expression data [22 24 through
(1I, we leverage the large corpus of individual connectomes in our fMRI datasets
distributional target-side augmentation approach during training (25). All methods are evaluated under brain-wide wide and spatially constrained train-test splits alongside a novel spatiomolccular null mapping technique to assess if performance is inflated by spatial autocorrelation.
As such, we claim the following main contributions in this paper:
We introduce the first deep learning approaches for predicting functional connectivity from regional gene expression in humans, featuring an attention- based architecture (SMT) with biologically-informee components for targeted hypothesis testing.
We introduce and validate a novel spatiomolecular null mapping evaluation technique that generates surrogate gene expression maps preserving not only spatial autocorrelation but also key transcriptomic correlation structures, providing a highly stringent benchmark for assessing genuine predictive signal.
Context-aware neural networks, including SMT and single-gene resolution Multilayer- Perceptron, achieve significant performance gains in predicting functional connectivity as compared to bales-based and bilinear methods. Crucially, this performance significantly exceeds that of our rigorous null models and shown to generalize across multiple connec- tomic datasets (UK Biobank [22), Human Connectome Project [23] MPI-LEMON (4 and parcellation resolutions.
Our findings highlight that the complex, multimodal architecture of functional brain networks can be predicted from spatiomolecular features using context-aware neural networks, well beyond what chance or spatial proximity would dictate. Context-aware neural networks thus offer robust framework for multimodal modeling of brain function in health and disease.
2 Preliminaries
RNA- see-sseuenninngg (RNA-seq) provides snapshot of transcriptomic activity across single-cell or bulk tissue samples, typically summarized a gene expression matrix as in Figure Gene expression has recently been integrated with noninvasive neuroimaging to uncover molecular correlates of brain

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Gene Expression
(s,y,a)
Spatiomolecular Transtormer
Functional Connectivity
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Figure Spatiomolecular context-aware deep modeling for connectivity prediction. Gene expression from the Allen Human Brain Atlas is sampled across the entire brain. The Spatiomolecular Transformer (SMT) uses a reference genome based tokenization strategy and multi-head self attention (MHSA) to encode gene expression profiles for region-of-interd token, initialized based on 3D coordinates of sampled ROIs, is optionally passed as token to the SMT. Concatenated embeddings used to decode population average connectivity, Alternatively, fully connected Multilayer-Percepeee Perceptron can be trained using concatenated gene expression vectors.
(ROI) and j. A learnable [CLS]
Resting-state functional MRI (fMRI, collected during task-fre free windows, characterizes intrinsic brain activity by computing functional connectivity the Pearson correlation of BOLD
organization 26 27
signals between brain regions [4]. Letting X E T represent a population-average transcriptome and Y R symmetric connectome, the goal is to learn a predictive mapping f: X + Y, or equivalently f() = Yij, testing the fundamental hypothesis that the biological richness of gene expression is predictive of whole brain functional connectivity at the atlas-level. Our study leverages high resolution brain maps carefully aggregated from population datasets learn predictive mapping between the transcriptome and connectome.
2.1 Datasets
Allen Human Brain Atlas (AHBA). With approximately 500 spatial locations sampled in each hemisphere across the cortex, subcortex, and cerebellum, the Allen Human Brain Atlas is the most spatially-resolved human gene expression dataset date. Microarray data was collected from six neurotypical donors (mean age=42.5, sex ratio=5:1 (M:F)) using whole gellegeemmm Agilent microarrays 77 Data processed using recommendations from the abagen package ensuring stable measurements through a differential stability threshold, filtering genes based on background noise and consistent inter-regional coexpression patterns across donors. Since we are relating gene expression across the most stringent differential stability threshold retaining final set of 7,380 genes averaged per region across donors 21]. Detailed processing steps are outlined in Section A. Raw data is available at https::/portal.brannnnm
populations,
UK Biobank (UKBB). The primary connectivity dataset in our study is subset of n 1814
healthy participants from the UK Biobank (mean age=63.3 years; age range=45-82; 55% female) with available resting state functional MRI (rs-fMRI) (22). Scanning protocols and preprocessing steps are outlined in Section A.I Functional timeseries were extracted using the 7-network Schaefer 400 parcel cortical atlas (28). extended to 456 regions with the inclusion of the Tian subcortical atlas 29 ($456 parcellation). Pairwise Pearson correlation of parcel-level BOLD signals was used to compute functional connectivity matrices. The population averaged 456 region UKBB dataset yields 103,7 740 edge-level targets and corresponding region-pair inputs from AHBA for model optimization (see Figure A))
3

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Alongside UKBB, the Human-Connectome Connectome-Projeet Doung-Adull (HCP- YA) (3 and Max Planck Institute Leipzig Mind- -eeee-rrri-nooee Dataset (MPI-LEMON) 24 are used as validation connectomic datasets. Despite substantial age shift between these datasets and UKBB, we observe consistent backbone connectivity structure in the population average functional connectomes across datasets (Figure 4 Processing details for HCP-Y. YA and MPI-LEMON are outlined in Section A.1
2.2 Baselines and related works
To rigorously evaluate context-aware deep neural networks, compare them against three classes of established models from the neuroimaging and connectomics literature.
Rules-based methods. We first include simple, interpretable models that test foundational hy- potheses of brain organization. These include an exponential decay model [17 30). assuming connectivity strength decreases with Euclidean distance. A related model uses a Gaussian kernel, which decays symmetrically with squared distance. We also include a Corre- lated Gene Expression (CGE) model, computed by correlating PCA-reduced gene expression profiles between pairs of regions, effectively predicting connectivity based on molecular similarity 4 31] While interpretable, these methods are constrained by their fixed forms and feature sets.
= =xp-=xp(-
Connectome Model. Second, we implement learned bilinear models prominent connectomics 11 12]. The Connectome Model (CM), introduced by Kovács et al. [I, instead formulates synaptic connectivity prediction as learned bilinear regression problem, modeling the connectome as Y = XOXT where X is single neuron gene expression matrix and O is unknown gene-gene interaction matrix. Qiao [12] extends the Connectome Model by introducing Bilinear Low-rank decomposition of O. Implementation details for the Connectome Model and its low-rank counterpart can be found in Section A.3
Partial Least Squares Regression. Finally, we include Partial Least Squares (PLS) regression, the predominant multivariate method imaging transcriptomics for linking multiple data modalities PLS identifies latent variables that maximize the covariance between gene expression and connectivity profiles. To adapt PLS for our edge-wist prediction task, we reformulate it into an encoder-decodeer model: we use its learned shared projections to create region-level embeddings and then predict connection strength via a bilinear decoder. Details can be found Section A..3
5
2 3 9].
This comprehensive suite of baselines allows us to benchmark the performance gains offered by our more expressive, non-linear architectures.
3 Methods
Spatiomolecular Transformer (SMT). Transformers have been adapted for numerous biological tasks due the sequential nature of gene expression data [32) with notable advances in single-cell perturbation modeling, disease classification, and cell type annotation [9 33 [A]. Similar methods remain largely unexplored for understanding the spatiomolecular foundations of brain connectivity. architecture for
Motivated by successes in single-cell modeling, we formulate a transformer- prediction task. Despite the scarcity of spatially human brain gene expression data, we leverage the abundant amount of connectomics data to train a context-aware transformer end-to-end.
the canseriptome-connecte
Here, we adopt a BERT-style multi-head self-attention (MHSA) based transformer architecture [35), requiring tokenization of the gene expression input. Given the dimensionality of the gene space, = 7380, we partition the gene expression vector of each region I; E IR into contiguous non- overlapping bins of k genes sorted by transcription start site (TSS)
the human reference genome (see Section A.2 for details). Setting k = 60 genes yields = g/k: k: = 123 tokens per region, each represented length-k: scalar vector. These are projected into an embedding space via learned linear map. forming input E f with embedding dimension d 128. This value projection encoding strategy is effectively leveraged by models like TOSICA 33 and scBERT (19].
Each token embedding sequence is passed through up to 4 layers of MHSA with 2-4 attention heads, where the input X is linearly projected into queries, keys, and values as Q XWQ. K = XWw, and V XWy, with Wo. WK, Wy E mdxd, and dn, d/h. To incorporate positional priors

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PCA Correlated Expression
Bilinear Lowrank
Multi-Layer Perceptron
SMT [CLS]
DMN
Prediction from True Brain
r=0.34
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r=0.75 75
r=0.82
0=0.85
eval
Vis
Prediction from Null Brain
-=034
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r=0332 0=0299
0
Figure 2: Population connectome reconstruction. [A] Average population connectome, Y. with delineated subnetworks of Schaefer 7-newwork 400 region parcellation (28) (LH=left hemisphere, RH=right hemisphere, SCTX=subcortex). KDEs are plotted for a subset of cortical regions with vertical blue lines representing the mean. Connectivity values are probabilistically sampled during training from the underlying population (e.g. UK Biobank, 1=1814) under our target augmentation protocol. [B] Connectomes are stratified into 10 four-fold train-test splits based random or spatial split strategy. Edges connecting train and test sets are omitted. [C] For each split, models are trained using both the true brain and spatiomolecular null brain. Reconstructed Ytest for select models are displayed with comparison to null reconstructions for an example random split.
without learned embeddings. we add ALiBi (Attention with Linear Biases) slopes 20 the attention logits, implemented using FlashAttention [36] to enable scaling to hundreds of tokens (and thus thousands of genes) per region. The fixed head-specific penalties bias each head toward different ranges of token interactions:
(QKT + Vonn
Attention K, V) = softmax
Vdh
where encodes relative-position biases. Steep slopes prioritize local interactions while shallow slopes attend globally. This inductive bias allows the model to co-embed genes at multiple genomic motivs-mt by the bidirectional organization of functional gene groups within and across chromosomes (37, (8)) Given that genomic interactions may be coarse at the macroscale of whole- brain networks, ALiBi over k gene tokens encodes genomic proximity as a soft prior, while value projection-based tokenization preserves single-gene-level signal relevant connectivity prediction. Furthermore, chromosomally organized tokens can be compared post-hoc with known functional gene groups or Genome-Wide Association Studies for deeper biological insight 39
Following transformer layers, the final output is flattened and linearly projected to form a region embedding 24 IR, where L dout and dout 10. For given region pair, the concatenated 3-layer MLP decoder to predict connectivity Y.j-
embedding [2; 2y] is passed through
Single-gene resolution Multilayer Perceptron (MLP). parallel, we implement fully connected
multilayer perceptron (MLP) with to four hidden layers. The input to the model is the concatenated single-gene resolution gene expression vector from pair of regions, of dimensionality 2 x 7380 genes. Architecture and optimization details for SMT and MLP can be found in Section A.3
5

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Incorporating spatial context awareness, Spatial position is another form of biological context that can be introduced our non- non-linear models, with well documented links connectivity strength 7 17 Here, we extend the input sequence with spatial information by concatenation of MNI (Montreal Neurological Institute) 3D coordinates for the MI.,, and for the SMT through dedicated [CLS] token initialized by the coordinates of each brain region. This token is linearly projected into the same embedding dimension as the gene expression tokens and participates fully in multi-head self-altention in Temporal Fusion Transformer [4]] Unlike BERT, the full sequence including the [CLS] token is used as the output representation of the sequence, instead of using the [CLS] token exclusively. For both the MLP and SMT, we interpret spatial coordinates context carriers that condition the encoding of molecular information based on anatomical location in the brain.
27
Distributional target-side augmentation. To improve model robustness and generalization beyond the population-averagel connectome, we introduce a distributional target-side augmentation strategy. Rather than training exclusively the mean connectivity matrix Y Rexr we leverage the full distribution individual-leve connectomes Y' E R X Inspired by curriculum learning principles [42] and imbalanced data sampling 443. expose the model to subset of subject-specific targets at different stages of training. By replacing static supervision with a set of n-r dynamic targets, this strategy injects meaningful variance into the loss landscape without altering evaluation, which remains hased on mean squared error against Y. We use a decaying schedule augmentation strategy for the SMT model across all datasets an effort to improve test-set generalization. Algorithmic details and scheduling strategy experiments are outlined in Algorithm 2 and Section A.5
4 Evaluation
Train-test split. To rigorously evaluate model performance, we employ two train-test split protocols: random and spatial. Each protocol is repeated across 10 rounds of 4-fold cross- volsdvvaii,t,nn, resulting in 40 total splits per model. For both settings, model specific hyperparameters are tuned using a nested cross-validation procedure on mean-squared error described in Section A.3
For each random split, 75% of brain regions used for training and 25% for testing, with models trained on the ("(zi) graining-region edges and evaluated on the disjoint ("rr) test edges (Figure 23). This split tests model's ability to generalize across regions that may be sampled from the same underlying distribution, allowing it to leverage the full diversity of functional connections across the brain. To more stringently test spatially invariant generalization, we implement spatial split protocol adapted from Hansen et al. [ For each fold, we select source region and define the test set as the 25% of brain regions that are spatially closest based on Euclidean distance in Montreal Neurological Institute (MNI) space. The remaining 75% of regions comprise the training set. This repeated across four folds, ensuring full brain coverage. This more challenging protocol tests model's ability to generalize to regions that are both unseen and spatially distinct from those in training. Both splits are visualized Figure
Cone Gote Gore birrosion
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150
Disaance (mm)
150
Distance (mm)
101
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Low-error null spin
High-error null spin
Random null
Figure 3: Spatiomolecular null brain maps. Example null brain maps generated from Algorithm
I Parcel color represents the second principal component score of gene expression matrix, X, at each ROI. Polynomial and exponential decay curves fit using 5mm bins to model correlated gene-cxpression vs. distance. Curve parameters are compared between true and null brains to measure how well each null brain map preserves realistic transcriptomic autocorrelation.

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Spatiomolecular null mapping. Our trst split setup evaluates generalization to unseen brain regions by using common splits across all models, but it does not fully account for critical confound in neurogenomic data spatial autocorrelation. Adjacent brain regions often share similar gene expression and connectivity patterns, which can inflate statistical associations [16]. To disentangle these effects, we implement spatially constrained null models that preserve realistic autocorrelation structure between brain regions while shuffling expression-to-regue assignments.
We adopt the procedure of Váša et al. 44,, performing 10,000 spatial rotations, or "spins', of the gene expression matrix and selecting null brains that best match the empirical correlated gene expression (CGE) vs. distance curve (for details see A.4 and Algorithm []. Traditional spin tests preserve geometric features like distance decay but do not account for transcriptomic structure [45]: our CGE-matched nulls address both. This approach aligns with recent trends using null brain map rejection sampling to minimize false positive inflation [46]. Figure 3 shows the second principal component of the gene expression matrix projected onto the cortical surface for the true brain and three possible null brain maps. The low-error null spin highlights the global smoothness preserved by null brain matching the true CGE vs. distance relationship. Conversely, naive randomly shuffled brain map completely destroys the CGE vs. distance trend.
For each four-fold train-test split, models are retrained and evaluated using one of 10 lowest error spatially shuffled gene expression inputs while keeping the original connectome target the same. This enables us to test whether models trained on true data are capturing genuine biological transcrip- cone-conee patterns rather than relying on mere spatial autocorrelation or genetic similarity.
Performance metrics. True and null model performance is evaluated using a range of global metrics including Pearson correlation, R², mean squared error (MSE), and geodesic distance computed on the Riemannian manifold of symmetric positive semidefinite correlation matrices [47]. Geodesic distance serves as a complementary measure of similarity in global correlation structure, potentially capturing topological properties missed by elementwise metrics. We also report stratified correlations: (i) by connection distance using uniform bins up 180 mm, (ii) by subnetwork, based whether
test connection is, for example, intra- or Visual (ii) by edge strength where |r > 0.3 Tables
2 and Figure S present a subset of these metrics; the full 32 metric sets for all experiments are
available in our repository, github. www.eeur/oooeeeeeeeee http//eeroonnooooc http:///eeee.eo/o/oooooooo//////
5 Results
Overall performance. A primary finding of our study is that non-linear architectures class consistently outperform linear and rules-based methods. Both the SMT and MLP, trained only on gene expression, achieve the highest global performance for both random and spatial train-test splits (Table D] Performance gains are especially pronounced under the stringent spatial split, with improvement gains exceeding 0.08 Pearson-r for long-range and strong positive connections (>0.3) as compared to the best linear method (Table
Table 1: Global metric test-set performance on UKBB dataset for random and spatial splits (mean#SI) over 10 four-fold splits. Best metric-wiss performance per section is bolded)
Random Split
Spatial Split
Model
Pearson-r (Trle/Null)
MSR
Geodesic
Pearson-r (True/Null)
MSE
Geodesic
CGE (PCA)
.3+ .174.04
158:.011
15.1
.31 ..2+.07
.114.002
13.5+2.4
Dist. Gauss, Kernel
.300 /--
.31+.002
18.3+1.7
.41:005/ 114:05/-----
.39+.009
14.4+1.9
Dist. Exp. Decay
.3+.033 ---
.000.0033
15.7+0.7
.44t.06/
.036+0099
14.0+
Bilinear CM (PCA)
.11:04 / .32+.06
.025+.003
15.3+0.6
42t.15/.25t..
.080..110
16.3+2.1
Bilinear CM
62+.10 .21..08
.030+.012
16.1
44t.25/.154.
.076+.077
16.842.3
Bilinear CM (PLS)
72+.08 / .33+.08
.016.004
12.0+1.9
.8t.17 /.2
.029.0100
14,5+4.1
Bilinear Low-rank
.77+.03 / 42+.07
0144.001
11.2+1.1
66t.13
134..13
.055.0099
12.9+2.2
MI.P
.78+.03 / .294.09
.014.0011
10.3+1.1
.72+.13
1.4.133..24..11 12
.023+0112
10.5+
SMT
.79+.03 / .344.09
.013+.001
10.2+1.0
.72+.13 130
.022+.010
10.8+1.7
MI.P w/ coords
83+.03 / 48+.09
.0110.001
9.640.8
.74h.13 74tt13/.424.11 122..11
.021..011
10.3+2.1
SMT [CLS]
84+.0 / .73+.05
.010+.001
9.8+1.0
.7t. 194.13
.0254.012
11.1+2.0
Null reflects model performance when trained spatiomolecularry shuffled brains. Models sectioned by rules- based, learning- -aased with gene expression, learning based with gene expression and spatial information.
learning-based
7

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Table 2: Stratified metric test-set performance on UKBB dataset for random and spatial splits (mean#SD over 10 four-fold splits, Best metric-wise performance per section is bolded)
Random Split
Spatial Split
Model
Short-r
Long-r
Inter-hemi-r
Strong-pos-r
Short-r
Long-r
Inter-hemi-r
Strong-pos-
CGE (PCA)
252.04
194.08
202.04
.32.05
.31.088
.07.226
.31.. 12
.0t.08
Dist. Gauss, Kerel
40z.04
.77
.17
.32.00
.3+.06
.11.088
.292.10
.35=009
Dist. Exp. Decay
04
.00.07
.4
.34..0
.45+.06
.01+.13
.374.13
.6+.09
Bilinear CM (PCA)
.57.00
.35.07
.00.04
.31.088
.424.17
.20..24
.391.18
.22..12
Bilinear CM
63a.12
.55..09
S8s.11
12
.43..77
.25
.27.224
11a.19
Bilinear (PLS)
755.08
.63+.11
.72+.08
137..10
.01..88
.381.25
52t..99
.324.10
Bilincar Low-runk
03=.03
.70=006
.77
.40
.67..15
202.28
.57.166
.352.10
MLP
03+
67+.06
.77+:03
.8+.088
.73+.14
.50+.26
.62+.17
A3+.11
SMT
.8=.03
.69.07
.78=.03
.8t+.07
.72
.92.27
.62+.17
40+.11
MLP w/ coords
85+.03
75+.06
.3
.3d.077
.74+.15
.58..22
.664. 16
16+.12
SMT w/ [CLS]
.62..0
.781.06
.84
.551.06
.701.13
.531.26
.624.20
.11.13
Figure 5 quantifies non-linear gains across functional subnetworks, with the strongest improvements observed in unimodal cortex (e.g.. Somatomotor, Visual). In complement, Figure 2 shows that linear models underperform in reconstructing distributed, strong positive connections within the Visual system and Default Mode Network. These patterns suggest that non-linear architectures better equipped capture the inherent complexity of such connections. Notably, the low-rank bilinear model from Qiao [12] performs competitively and offers greater robustness than the standard PCA-reduced inputs, suggesting may be optimal to learn embeddings in supervised fashion (e.g. PLS, low-rank projection) for linear methods.
Connectome Model, regardless of single-gent
Performance above spatiomolecular null shuffle. Crucially, both linear and non-linear models significantly outperform their respective spatiomolecular null evaluations, indicating that learned representations capture molecular interactions beyond spatial autocorrelation and gene co-expression. Null performance varies moderately across models, generally falling in the range of methods (r 0.3-0.4), which explicitly model properties of spatial and molecular similarity.
Spatial context effects. A performance boost is observed when spatial context is introduced to non-linear methods in the random split setting. This gain is less pronounced under the spatial split, where the SMT with [CLS] token exhibits stronger overfitting effects than the MLP. This is accompanied by high null performance (r = 0.73) highlighting that spatial coordinates alone are powerful predictors of connectivity, a signal the SMT with [CLS] architecture effectively leverages (Figure B3.). However, our stringent spatial split evaluation decisively shows that the model learns more than just this spatial signal. In that setting, the null model performance drops substantially while the true model's performance remains high, doubling the performance gap over the null and confirming the capture of genuine, spatially generalizable molecular information. Future architectural modifications could consider gating or regularization strategies to optimally leverage spatial context.
UKBB
HCP-YA
MPI-LEMON
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age
monr age
Figure 4: Cross-dataset population connectome reconstruction. [A] Multi-resolution population average connectomes sorted by posterior-anterior axis. [B] Chord plot representing Pearson-r reconstruction when training SMT w/ [CLS] models on a full source dataset and predicting on full target dataset. coarser resolution generalizes to higher resolution (c.g. 391->729). See Section for experimental details on cross-datase, generalization experiments.
arrows are visualized when exceeding the null, and within-datase if a

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Multi-dataset replication. SMT results are replicated using the HCP- YA and MPI-LEMON datasets by repeating the same random and spatial split protocols used in Table Results are shown in Tables 5 Performance trends are consistent across datasets and parcellation resolutions, with all models exceeding their respective spatiomolecular null baselines. The SMT tends to produce more accurate predictions at higher resolutions, which may be byproduct of increased pairwise training data at higher resolutions. Overall performance is somewhat attenuated in these datasets, particularly for MPI-LEMON, likely due to differences in preprocessing rather than biological ignal-supported by similar cohort demographics between the validation datasets but differing ranges connectivity strength.
Cross-dataset generalization. To test whether ceancriptomee-conccttooo mappings generalize across datasets, we evaluate whether model trained on one dataset can predict another dataset's s connectome above a spatiomolecular null brain map. For each connectomic dataset, we train the SMT with [CLS] using both true and null brain at its native resolution. We then assess, for example, whether an SMT model trained on UKBB can predict the MPI-LEMON 183 connectome better than a null model trained on spatially shuffled gene expression in the native MPI-LEMON 183 resolution. This approach isolates generalizable cross-dataset transcriptomic patterns beyond spatial autocorrelation and the influence of spatial coordinates. As shown in Figure 4 SMT with [CLS] models trained on UKBB and HCP significantly outperform nulls when predicting MPI-LEMON 183 (r 0.78, 0.73 respectively). and MPI-LEMON 391 generalizes strongly to the finer MPI-729 resolution (r = 0.86). Full experimental details are provided in Section
Embedding evaluation. The SMT's dedicated encoder enables direct visualization of learned region-level embeddings across the brain (Figure 5) Each region of interest (ROI) is represented by an embedding matrix of dimensionality 123 x 10 for 60 gene bins, obtained from model trained on the full UKBB dataset using default hyperparameters. Evaluating embeddings by UMAP reveals a structured representation of the Visual system by the SMT, which, unlike the bifurcated organization observed in raw gene expression UMAP, forms a coherent transcriptomic subspace clustered by strong functional connectivity patterns. This suggests that the SMT captures connectivity- transcriptomic variation that may be distinct from purely transcriptomic gradients. Other systems, such as the Somatomotor and Default Mode networks, also exhibit densely clustered, anatomically consistent embeddings. The bilinear low-rank model also produces hub-like clusters that appear aligned with connectivity, but this relative clustering is less aligned with cortical anatomy.
axis of
A
Sagittal View
Raw Gene Expression
Bilinear Low-rank Embeddings
SMT Embeddings
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UMAP1
UMAP1
UMAP1
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B
Spat Spiit Performanc Sair of SMT Blinsar Low rank
Spacial Spilt Performance cematlle Parameters
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Figure 5: Model embeddings, non-linear gain, and parameter count analysis. [A] Anatomical coordinates visualized alongside raw gene expression, Bilinear Low-rank and SMT embeddings using UMAP (subcortex and cerebellum omitted). [B] Gain in Pearson-r for subnetwork specific test metries for SMT vs. Bilinear Low-rank model. [C] Spatial split test performance plotted as a function of parameter count (log-10 10 scale) for select linear and non-linear methods.

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Ablation and hyperparameter experiments. Validation set hyperparameter experiments and post-hoc ablations of the SMT architecture are detailed in |ection[A.3] These analyses reveal that SMT performance is broadly robust to the choice of tokenization strategy, however, the addition of ALiBi positional slopes consistently improves performance across tokenization variants. We also evaluate eight target augmentation protocols and find that introducing distributional batches of population-Ievel edges during vrining-particularts those with strong positive or negative edge largets-enhance generalization under both random and spatial splits, with gains of up to Pearson-r 0.05 in strong connectivity ranges (Figure TÖp. Sorting strategies and alternate target augmentation protocols are core areas of future development, which may support further performance gains of the SMT over MLP despite SMT's 's reduced parameter count.
Parameter count analysis. Figure depicts test set generalization performance under the spatial split protocol as a function of the total number of learnable parameters. Increasing model capacity generally yields log-linear monotonic improvement in performance, with a plateau observed among non-linear architectures at approximately 10" parameters. Notably, the binning strategy employed by the SMT reduces the parameter count from roughly 7M in the MLP baseline to about 2M with 60 gene bins. At just 80K parameters, the bilinear low-rank model remains competitive, suggesting a potential intermediate regime for compact non-linear transformer-based architectures with preserved performance. In contrast, the bilinear CM model trained on the full gene set contains approximately 55M parameters with massively reduced accuracy, indicating that performance not solely attributable to parameter count scaling.
6
Discussion
central finding of this work is the significant performance leap achieved by non-linear models (both MLP and SMT) over traditional linear approaches for the genomics-to-comeee to-conecctooi decoding problem. While the absolute performance difference between SMT and MLP is modest, we present them not competitors but exemplars of two distinct deep learning strategies for this novel problem. The MLP establishes a powerful, high-performance baseline, confirming the value of non-linear modeling. The SMT, in contrast, serves as biologically-inforeed framework whose modular architecture offers unique advantages for scientific inquiry. Its sequential design allows for direct hypothesis testing of biological priors, such genomic organization via TSS- Finally, SMT's architecture is naturally suited for future integration with large-scale genomic foundation offering a clear path for advancing the field.
models 32 48 19],
While this work establishes new framework, we acknowledge several key limitations. First, the AHBA dataset, despite being the field's gold standard, is derived from only six donors, which may not fully capture population-level transcriptomic diversity. Second, while our non-linear models significantly outperform linear baselines, the modest performance gap between the MLP and SMT highlights that further architectural innovation is needed to fully leverage biological priors. Our qualitative analysis of SMT's embeddings (Fig(5) and attention weights (Fig 13) offers a promising but preliminary step toward interpretability; a systematic validation of these learned gene-set contri- butions is critical future direction. Looking ahead, this framework opens several exciting avenues: applying these models to larger and more diverse transcriptomic datasets, integrating individual genetic variations such as polygenic risk scores [49, and extending the models to predict patient- specific connectome alterations [50] 39, 51. Ultimately, moving from population-leve mapping to individualized prediction [52] will be the key unlocking the clinical potential of this approach for understanding the molecular basis of brain disorders.
Acknowledgements. This work was supported by NIH grant RO0MN128772 to E.V. and the DOD National Defense Science and Engineering Graduate fellowship. We thank Dhivya Srinivasan, M.S., Theodore D. Satterthwaite, MD, Tien Tong, Ph.D., and Matthew Cieslak, Ph.D., for providing insightful scientific feedback on the study design as well data access and pre-processing assistance. BioRender software was used for figure creation.
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A Technical Appendices and Supplementary Material
A.1 Dataset Processing
Allen Human Brain Atlas. Transeriptomic data is preprocessed from the Allen Human Brain Atlas (AHBA) using the abagen toolbox [53], following set of best- hest-practice steps standardize expression across donors and reduce noise from technical and biological sources. Unless otherwise specified, all processing steps follow established workflows [26 3 21).
Within-Donor Normalization. Gene expression values for all tissue samples are normalized within each donor to account for individual differences in signal scale distribution. A scaled robust sigmoid transformation is applied to each gene expression vector zg, defined across regions for a given donor:
Darm
2. median(z,)
1 + exp
(QI((())
This transformation preserves rank while being robust outliers. A subsequent min-max rescaling step standardizes the values to the unit interval:
Tnorm min (nom)
Escaled
max(Xnomm min (Tnom)
This two-step procedure is distribution-fiee and avoids assumptions of normality, unlike traditional z-scoring.
Sample-to-Regee -Re-ion Assignment. Tissue samples are assigned to regions in a reference parcellation using their MNI coordinates, constrained by hemisphere and cortical/subcortical classification. Expression values for samples mapping to the same region are averaged, resulting in a subject-specific region-by- gene matrix of shape r g.
Gene Selection and Filtering. To reduce noise and retain biologically informative genes, we follow a multi-stage filtering process. First, genes expressed below background noise are excluded. Next, quantify spatial reproducibility via differential stability, defined as:
As(g)
1
Σ
Σ r(B.(g), By()) j=1+1
where (g)g) is the regional expression profile of gene for donor i, and N = 6 is the number of AHBA donors. Genes with high Ag(g) show consistent regional variation across brains. We use the strictest threshold recommended for the Schaefer-400 parcellation, retaining a final set of 7,380 genes per region.
Cross-Donon Aggregation. After normalization and filtering, gene expression values are averaged across donors produce population-level matrix. To address incomplete sampling across hemi- spheres, we employ abagen's mirror-and-inee iiiroo-and-inteppolatee strategy: missing regions are imputed using their contralateral counterparts and smoothed via weighted averaging over the 10 nearest neighbors in the source hemisphere. This yields a complete x matrix aligned to the target parcellation, suitable for downstream modeling.
See 53 for licensing.
UK Biobank. rs- rs-fMRI scans were acquired on Siemens Skyra 3T scanner (TR 735 ms. TE 39 ms, multiband factor 8,, 2.4 mm isotropic resolution, sean duration 6:10 min) 22 Preprocessing followed the UKBB minimal pipeline (22) and was further refined using XCP-D 54 implemented in
Nipype (55). This included the removal of non-stcady-state volumes, notch filtering of motion regres- sors, global signal regression, despiking via 3dDespike, and bandpass filtering (0.01-0.1 Hz) applicd to both data and confounds [56, 57]. Population averaging followed the parcellation of individual rs- Is-fMRI scans into connectivity matrices. The $456 atlas used be found at htttps://gitth hotp//eam..Ic//aaaaaaa/c//////// fsLR f
atlas moclas-44455 www.44555555el.e.. larepaarrlss_se_..__ dssg. json
Human-Connectome-PPie Young Adult (HCP-YA). The HCP-YA dataset contains rs-fMRI data processed identically to the UKBB dataset in the $456 parcellation. Despite substantial de- mographic shift (n=1065; mean age = 29; age range 22-35; 54% female) between cohorts,
18

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observe a stable backbone connectivity structure in the population average connectomes between UKBB and HCP (Pearson-r 0.90, Figure Further details for the HCP- YA cohort can be found at
23 58, 59
Max Planck Institut Leipzig Mind-Brain-Bode Dataset (MPI-LEMON), MPI-LEMON is comprehensive neuroimaging dataset (n 136; age range 20-30; 72% male). The MPI dataset uses an unsupervised voxel-level clustering approach to generate parcellations at various scales including 183, 391, and 729 region resolutions from which functional connectivity can be computed. MPI- LEMON comes with paired, minimally processed AHBA gene expression data at each resolution. Processing was done with the recommended abagen 53 parameters. Bi-hemispheric imputation was not done for missing regions in this dataset, which differs from the paired AHBA dataset used for UKBB. See Jimenez-Marin et al. [24 for further details, licensing, and data access.
A.2 Experimental Details
Human reference genome ordering. Genes are sorted by their transcription start site (TSS) in the SMT tokenization procedure. For each protein-coding gene, the earliest TSS is selected across all tran- scripts, regardless of strand orientation. Genes are then ordered globally-fire first across chromosomes, then within each harrmosome-yyeldding a biologically grounded input sequence. This ordering is intended enhance interpretability and biological plausibility for SMT. The reference genome used is available at jncpi.nnmmmm.. www.amm..iih.goo..mmeee waahhgooo/daattset//geommeeeee LCCGGCCCCOOOCCCOC1111C00CC 000000405 40. Implementation details are provided in GeneEx2Conn/dann enigma/ genaa www.lllsstssaaaa refgenome, Bareeeoom__RDMMM.e_._
Parcel centroids. Spatial coordinates for brain regions are used throughout our analyses. For each parcellation, we determine the centroid of each anatomical region using provided metadata files. Coordinates are defined in the Montreal Neurological Institute (MNI) stan- dard space. For the MPI-LEMON dataset, these centroids are available via the original release 224] For the UKBB dataset, we provide a reformatted metadata file directly at /data/UKBB/ TaLiBB/atlas-ae atlas-44456Parcels htaprParrcel__see___eeeeeeeeeeee ceaeeeerrefrmmmttee.em csv. Centroids for this custom par- cellation were computed using mwlearnnnnnnn plotting....ni......mo.....o f wwtdddiannedlliiieee www.rrellaaionnctuccooooooa
Stratified metrics ranges. Brain region centroids serve two main purposes in our analyses: (1) as input features for models incorporating spatial information, such as the SMT with [CLS] token, and (2) to stratify model performance by inter-regional distance. We define short-, mid-, and long-range Pearson correlations by dividing the brain's 'sinss maximum inter-regional distance (180 mm) into three equal intervals: short-range (< mm), mid-range (60-120 mm), and long-range (120-180 mm). In addition to these distance-stratified metrics, we also compute performance over connection strength categories: strong positive (r > 0.3), strong negative (r -0.3), and weak connections
(-0.3 < r < 0.3).
A.3 Model Optimization
Hyperparameter selection. To select the optimal hyperparameter configurations for each model in Table [ and Table 2] we perform nested inner cross-validation using random sampling from a hyperparameter grid defined from wider grid searches and manual fine-tuning. For each model, 3-6 hyperparameter combinations are sampled, with the exact number depending on the model's complex- ity and the size of the grid. Each model also contains a best default parameters configuration, which is guaranteed to be sampled in addition to the randomly sampled configurations. The combination yielding the lowest validation loss on a dedicated subset of validation nodes, then used for full training and performance evaluation on the test set. Full hyperparameter grids for all models are available in our repo at //GeneExxConn//oooeaa conf igs] All experiments are run on 100 or H100 NVIDIA GPUs on a high-performance compute cluster, taking no more than hour per fold.
Optimization details. All gradient- based models, including both linear baselines and MLP archi- tectures, are trained using the AdamW optimizer. The mean squared error (MSE) between predicted and ground-truth connectivity values are used as the training loss. We perform model selection based on validation-set performance across cross-validation folds. All model architectures and hyperparam- eter configurations can be found in our repo, github. http:///eeerrrrtoooooaeeeeeeeeee /models/ configs.
under
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Rules-based baselines. We adopt several simple rules-based baselines for predicting inter-regional connectivity Yi from spatiomolecular properties. The exponential decay model assumes decay of connectivity strength with Fuclidean distance dij. given by Vi, SA + (1-SA, SA exp(-di//SAA)
where ae and S control the asymptotic offset and decay rate 17
Bilinear Connectome Model. Optimizing gene-gene interaction weights O is challenging due to its quadratic scaling with the number genes and the large combinatorial space it spans. Kovács et al. [1I restrict their analysis to subset of 19 innexin genes and estimate O by minimizing [[vee((Y) (X @ vev (O)(O)]l + ail [ellve(())] We adopt more scalable formulation that minimizes mino || XOX I | + X OI using closed-form solution described in Section A.4, enabling efficient learning of interaction matrices on the full gene set or on dimensionality -eaeeeeeeanttt-eeeeedddddee reducedd features.
Bilinear Low-rank model. To reduce parameter count and enforce symmetry in the predicted connectome, we further simplify the bilinear model by exploiting the symmetry of Y. and optimizing shared projection matrix E ddd This yields the objective min ş which preserves representational power while significantly lowering computational complexity.
x || + A|] E p
Partial Least Squares (PLS). PLS simultaneously learns projections for inputs X and outputs Y to maximize covariance in a shared latent space, providing a powerful framework for decomposing high-dimensional, collinear data into low-dimensional latent components [60) The general form of the PLS model can be written as X = TPT + and Y = UQ' + E, where P E 18ak and Q E ig** are projection matrices, T, U E gr*k are the corresponding score matrices, and E, F are error terms. Each latent component & of P and Q is learned by maximizing maxp.a (Xp)) (Yq), followed by solving the regression T3 = U. yielding the overall model Y = XPT 3Q
PLS-based encoder-decoder adaptation. To adapt PLS for our edge-wise prediction task, we reformulate it into an encoder-decoder framework. We first use its learned projections to create region-level embeddings t, XPP from P learned on training set (Xuinn Ymain). Connection strength is then predicted via a bilinear decoder by minimizing the mean squared error between predicted and observed connectivities, mino 3 Ei (Yr, t Ot,)². The latent dimensionality k and regularization parameter À are selected via vross-validation.
Multilayer Perceptron. The input to the fully-connected MLP is of shape x 7380 with 2-4 hidden layers. Each hidden layer includes batch normalization, dropout, and ReLU activations. The model trained using the AdamW optimizer with weight decay for regularization. All hyperparameters, including network depth, hidden layer size, dropout rate, and learning rate, are selected via cross- validation to mitigate overfitting given the high-dimensional input and large parameter space.
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A.4 Spatiomolecular Null Shuffle Details
Implementation. Null brain maps were developed to address inflated false- cosee-positive rates that arise when comparing spatially structured brain data. Instead of naive permutations, spatially informed spin methods generate surrogate maps that preserve spatial autocorrelation while disrupting correspondence with true data, enabling statistical null distributions that isolate the contribution of spatial structure.
We adopt the spin-based procedure of Váša et al. which projects cortical parcel centroids onto a sphere, applies random rotation, and reassigns each parcel's data the region lands on. This method preserves intes-hemispheric contiguity and has been shown to be robust across parcellation resolutions [6]] For subcortical structures, we instead apply the spin (more formally shuffle) directly in coordinate space for the subcortex and cerebellum, ensuring bilateral symmetry, overcome the spherical topology of the subcortex.
Even with modifications for subcortical structures, a naive spatial spin, though preserving distance- based spatial autocorrelation, may disrupt the genetic autocorrelation structure of the transcriptome. Genetic autocorrelation reflects the principle that regions with similar gene expression profiles tend exhibit stronger functional connectivity. This pattern partially overlaps with spatial proximity, but may include more complex distance-based molecular relationships.
To quantify transcriptomic autocorrelation, examine how correlated gene expression (CGE) decays with distance. We bin region pairs into 5mm intervals based on Euclidean distances and compute the mean CGE within each bin, yielding a
decay curve. The canonical curve observed in human data [6]] and across species [6] typically follows an exponential decline. Notably, we observe secondary rise in CGE around 120mm, likely driven by -aagg associations between cytoarchitectonically similar regions. Negative CGE values at larger distances often correspond to cortico-subcortical interactions (21).
Algorithm CGE-Matched Spatial Null Brain Map Generation
1: Input: True transcriptome Xime Rrx9, region coordinates C R2x
number of spins N,
number of top spins to return
2: Define: Exponential CGE curve (d) SA Je
3: Define: 3rd-order polynomial CGE curve g(d) aaid #zz + a3d 04
4: Compute true CGE vs. distance parameters (SA SA lnue que ...., a from X and
5: for i = 1 to N do
6: (a) Cortical Spin: Project cortical coordinates Cax to the unit sphere 7: Generate rotation matrix R, SO(3) and compute C R,
8: Construct bijective mapping क. (l,..., Fax) + {l...., Fexx based on Váša et al. [44]:
Initialize unassigned set U [l,...,,ex]
While u + 0:
1. Select the most distant pair (). Eu
2. Assign new index: nT.x = arg min, ||C y] Cax Lill2, likewise for
3. Remove p. from 24
9:
(b) Subcortical Spin: Define Tith by applying symmetric shuffle on subcortical coordinates
10:
Construct null matrix: X = concat(X.,, [TīiN] ".rih,,X,n Xxub (uuh(
11:
Compute CGE vs. distance from X and C
12:
Fit fe(d) to extract (SA), SALO)
Fit (d) to obtain (a a2, az. a1)
14:
Compute total reassignment cost C, E/e [[Cau[]]] - (i)ll2
15: end for
Standardize each CGE parameter and across null spins using z-scores 17: Compute total standardized error for each spin i:
(=(AA}) = =(SAX") +|=(SA()) = =SAAte))
Σ [((a)) =(ujuee +|/////(/))) =ue
Rank spins by ascending e, 19: Return: Top K lowest-crror null transcriptomes {Xxmull
x ((K)
21

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Connectome Model Null Distribution (10k Spins)
Partial-Least Squares Null Distribution (10k Spins)
1500
1500
Empirical (n)
Empirical (n=0.77)
-600
Count
Top 10 mean (r=0.38)
Count
1000
Top 10 mean (r-0.64)
1000
-4000
500
500
2000
0
0.25
0.35
0.45
0.55
Pearson correlation
Pearson correlation
Figure 6: Null distributions of Connectome Model and Partial Least Squares. Each histogram shows the distribution of Pearson correlation between predicted and observed connectomes across 10,000 spatially spun/shuffled gene expression matrices. Left: Connectome Model (CM). Right: Partial Least Squares (PLS). Bars are colored by the average mean error rank across 25 bins (darker better rank). Red dashed lines mark empirical performance on the true gene expression matrix; blue dashed lines indicate the mean performance using the 10 lowest error nulls.
Figure illustrates that spin-based nulls generated by Algorithm produce highly variable CGE dis-aastance curves, ranging from biologically realistic exponential decays distorted, spatially disordered profiles. To address this, we implement a rejection sampling procedure that selects null transcriptomes best preserving both spatial and transcriptomic autocorrelation, enabling stringent null testing without requiring full null distributions. The left panel of Figure 3 shows the empirical CGE decay from the true brain, while representative outcomes of our procedure are labeled as "Low-error null spin" and "High-error null spin". "
In experiments, we N 10,000 spatial spins and select the top K 10 based Al- gorithm 1. The full implementation is provided our repository at /sim/nul1. py within the generate papaatee__lll___ saill_spins(( () function. The procedure for fitting the exponential decay and polynomial parameters are also outlined in this Python file.
Effect of mean error rank. Despite the mismatch between features and targets introduced by spatial spinning, we hypothesize that gene expression inputs preserving realistic spatial and genetic structure will yield more realistic connectome predictions. If autocorrelation indeed predictive of connectivity, null brain transcriptome datasets with more realistic CGE profiles should result in predictions closer to the true value.
We test this by fitting two linear models-the Connectome Model (CM) and Partial Least Squares (PLS)-using 10,000 spatiomolecular null spun/shuffled brains. For each spin, we fit the models using the null gene expression matrix X' and evaluate the Pearson correlation between predicted and observed Y. For PLS, we use 10 latent components (selected via grid search over 0-25 dimensions selecting the elbow point based on Pearson r); for CM, we use PCA-reduced gene expression with 27 components (capturing 95% of the variance), enabling efficient training via the closed-form solution outlined below. We train and test on the full dataset as is standard for generating null distributions under null spin tests [16].
Figure indeed confirms that model performance across spins is sensitive to the quality of the CGE profile. Histograms of prediction accuracy (Pearson-r) reveal that the top 10 most CGE-consistent nulls produce better fits than the bulk of nulls. This effect is consistent across both models, and supports the idea that realistic gene-distance relationships are critical determinant of null predictive accuracy.
Closed form solution for the Connectome Model. We solve the ridge-regularized bilinear regression problem:
min IY - XOX 1 + Il
where X E Ruxd Y E Rxx O dd and À > À set following Kovács et al.
Using
|| Tr(A A), we expand the objective:
((0) TY - 2T<(OX YX) TT(O X XOX (oxTx)+ATI +))AT(OTT).
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Letting A - X X and M = XX,,, we simplify:
[()) = const (TOr + Tr(O" АOA) +
OT).
Taking the gradient with respect to 0 gives:
VoL = -2 + 240A 220.
Setting the gradient to zero and rearranging:
40A+ XO = M.
Assuming A is symmetric and positive definite (e.g,, after PCA), we pre- and post-multiply by (A + A to obtain:
o = (A+
or equivalently.
This formulation enables vast speedups over Kovács et al. 11 original Kronecker formulation, enabling fitting of the Connectome Model for many iterations and for larger dimension, d.
Train-fest split with spatiomolecular null comparison. As described in 4 each model in Table i is tested across 10 random or spatial four-fold splits. For each split, a corresponding unique spatiomolecular null gene expression matrix (from the top 10 out of 10,000) is used to refit the model and predict held out test set. This results in 40 test performance metrics for the true gene expression and 40 test performance metrics for the null gene expression. Aggregate metries are computed to compare the true vs null model performance. This procedure circumvents the need to refit the model thousands of times using many, potentially suboptimal, null spins.
MLP/SMT performance with coordinates & null gene expression. In Table we observe substantial true vs. null gap in Pearson-r, however, this gap is markedly smaller for the SMT w/ [CLS] under the random split. We posit that this trend is due the fact that the MLP w/ coords and the SMT w/ [CLS] have access to the true coordinates in both the true and null case. Thus, Euclidean coordinates alone might be predictive of connectivity even without molecular information. To deduce the effect of spatial position alone, we fit several variations of null models in Table 3
Table 3: Null model performance comparison with varying feature access on UKBB dataset (mean and standard deviation over 10 random 4-fold splits)
Model
Features
Pearson-r
Short
Midr
Long
R²
MSE
Geodesic
MLP
coords
.72 2 06
.76 06
.67 00
.63 s 1.1
.52 00
.016 .003
13.12 1.01
MLP
permuted + coords
.29 + .07
.28 + 08
.20 + 06
.66 + 09
.05 #111
.035 + .004
16.45 + 80
MLP
SM + coords
.47 1 08
48 .08
.39
361.11
.11
.030 .005
14.31 : 1.2
SMT w/ CLS
permuted coords
.68 06
2.07.07
644.000
1.11
.41
.020 0004
1..79
SMT w/ CLS
SM + coords
.71 + .05
-73+.00 00
.67 + .05
.65 # 08
.7 .09
.018 0003
11.52 + 84
SM indicates gene expression has been permuuted under the spatiomolecular null procedure. Permuted indicates the gene expression is purely random permutation reassignmentt
The MLP trained with coordinates alone demonstrates that spatial position is strong predictor of functional connectivity, achieving Pearson-r > 0.7. This likely accounts for the similarly high performance of the SMT w/ [CLS] model under the random split spatiomolecular null. Aside from architectural differences, the only distinction between these models is that the SMT receives additional (but spatially spun) gene expression input. Still, the SMT w/ [CLS] matches the performance of MI. w/ coords across all metries. The difference observed between the permuted gene expression and spun gene expression highlights the stringency of the spatiomolecular null as argued in A.4 Overall, an MLP trained just on coordinates is effective at connectome reconstruction.
These results reinforce that any model exceeding the SMT with [CLS] null reflects learning of true transcriptomic patterns, rather than spatially autocorrelated structure. Notably, the SMT w/ [CLS] architecture appears to leverage spatial information more explicitly than the MLP, which has reduced ability to isolate positional cues from the high-dimensional input. Attention heads in Figure 13 support strong emphasis of the [CLS] token during learning. In the UKBB dataset, several learned models surpass this stringent null baseline (see Table I. underscoring their capacity to extract meaningful molecular information beyond what is encoded by Euclidean distance.
23

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A.5 Additional Experiments
Hyperparameter experiments. To isolate the effect of key design choices in the SMT architecture, we conduct series of hyperparameter experiments using 10 fixed inner cross-validation splits with the UKBB dataset under our random train-test split. These experiments alter each hyperparameter independently while fixing the default SMT configuration. Figure summarizes the effects of four components: token encoder dimension, token encoder output dimension (number of genes per token), ALiBI slopes, and target augmentation probability. Table Sable44ding displays the hyperparameter grid for the Spatiomolecular Transformer with default parameters bolded.
Inner-CV Experiments
Table 4: Hyperparameter search space for the Spa- tiomolecular Transformer. Default values in bold.
Token encoder dimension performs best 60, grouping larger gene chunks into fewer tokens. This improves speed (reducing quadratic atten- tion cost) with minimal performance trade-off. Advances in efficient attention may eventually allow single-gene tokenization at scale.
Hyperparameter
fisen_enccoee d_model
[20, 60, 180]
[64. 128)
encoder outpol_cim
[S. 10)
use alibi
False]
nhead num, layers
[2. 4]
[2. 2)
deep bidden, dims
(2256,128). ($12,256,181]
uansformr dropout
[0.1,
Fixing the token encoder dimension to 60 di- mension gene chunk bins and varying the output dimensionality after the transformer shows rel- ative stability up to an output dimensionality of 3 per token. A token encoder output dimension- ality of 10 is optimal on the validation set.
dropoutrate rale
0.3]
lewming niee
00.0000,,, 0.0001]
weight decay
[0,0001, 0.001]
batch. sice
[512, 1024]
sug prob
[Hinesr decay, linear pesk, curricalum swap constinn.
mng styl
curriculam swap. sww.._linarr Jineaarddearr decay]
epochs
[90, 110)
workers
[2]
prefetch__aaeer
ALiBi slopes show simple and clear trend im- proving both Pearson-r and MSE when incorporated into the MHSA mechanism, pointing towards the utility of multi-head representations of the input sequence. In the next section we explore the effect of alternate sorting strategies under the random and spatial split. Modest amounts of target augmentation probability 0.1-0.3 are optimal over more aggressive strategies. This is tested for the standard linear decay setting. We explore target-side augmentation strategies further in the subsequent sections.
In general is worth noting that differences between hyperparameters are nominal indicating nuanced effects of each on overall learning, as well as potential combinatorial effects.
Tokenization strategy
0.75
To evaluate the effect of our TSS based tokenization strategy we con-
ponaa
Sq Enta
Commantiis
0.74
00110
0017
2.012
duct post-hoc experiment, where all
1000
hyperparameters are fixed to default.
Lo0G
30325
We then systematically vary the gene bin ordering and the size of the bins. For each gene bin size, k, genes are either binned together randomly, by TSS, or by mean global expression patterns. The mean expression based setup may facilitate the co-embedding of genes based on coexpression and is commonly used in single-cell trans- former based methods (32]. Figure shows changes in performance when varying the token size and tokeniza- tion strategy. The first notable effect that the SMT performs best on both splits with gene groups of 60. There is no clear added benefit to smaller gene bins, which aligns with the inner-C'V experiments in Figure 7 Even when genes are sorted and binned completely randomly, with no biological prior information, SMT performance does not drop. Performance only drops when ALiBi slopes is removed from the model. This points towards a robustness of the value projection transformer style model and that there may be alternate architectural modifications that would introduce more useful biological priors into the SMT. ALiBi
20300
Takoo Focade Dimeeiiio
Token Eruader Output mension
0745
0.35
2018
0.50
2007
0.25
0713
0330
3.000
2008
0.723
1. Augieeitation Pobso Bry
17
AUSI
Figure 7: Validation set hyperparameter experiments for SMT. Performance varies with token dimensionalities, ALiBi slopes, and augmentation probabilities.
24

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A
Fandom Split Pearson Tokenizatoon Stretegy
B
Spatal Spitt Pearson-t by Tekenizatin Strategy
Dortsee
0.750
Coresran
fandam
0.775
Pandomnn
Peamor
0.70
0.700
0.77
0.675
0.650
0.76
0.625
0.75
9,600
dim
cim
Bendom Split Mean-Squared Eiror by Inkenization Stratagy
Scatial Split Mean-Squared Erior by lakenization Strateg
0.0225
Expccson
Erer
0.0150
0.8100
Randemrn Also
0.0145-
8.0275
0.0140
0.0135
9.0200
0.01
Figure 8: Test set tokenization strategy analysis. TSS-based, mean global expression based, and randomly sorted tokenization with and without AL.Bi slopes are evaluated on the test set.
slopes, however, seems to have a positive effect on model performance likely due to its encouraged hierarchical representation of the gene expression sequence agnostic of tokenization sorting strategy.
Target-side augmentation strategy
Given the data-scarce domain of population- troduce distributional target-side augmentation strategy improve generalization. Our approach combines ideas from curriculum learning [42] (25) and synthetic minority oversampling techniques modifying training batches throughout the learning process by injecting signal from the full population distribution.
prediction, we in-
43
Algorithm 2 outlines this procedure, which defines three possible augmentation paths: (i) using targets from the population-averat connectome Y (i.e., no augmentation). (ii) randomly replacing targets in the current batch with individual-level targets from the population, and (iii) replacing targets only if their original population value satisfies lyl > 0, where we fix 0 = 0.3. This threshold ensures that only strong positive negative connections overrepresented during training corennpoooorrriinnngggggo to minority class in typical connectome distributions (see the density function in the bottom right of Fig.
Algorithm 2 Distributional Target-Side Augmentation Protocol
Require: Current mini-batch B {(X,, We epoch total epochs E, augmentation style aug_ aug_style, probability schedule p(e), population matrix Dpop
1: Draw ~ 1)
2: i < p(e) then
3:
if aug_style curriculum_ swap then Identify indices in Dunin where |y| > Sample new batch B from strong edges
4:
5:
6:
Replace all ys in B with subject-level values from Ppop
7:
else
8:
for each target in B do
9:
Replace y/8 with subject-level value from Ppop
10:
end for
end if
12:
else
No augmentation is applied: original batch used
14: end if
Compute loss: LMSE 1 EE (l,) vell
25

---

The augmentation schedule p(e) determines the probability of performing target-side augmen- tation at epoch e. Various scheduling strate- gies-such as linear increase, decrease, constant, and peak-are are visualized in Fig. | This mecha- nism allows us to inject task-relevant population signal at different stages of training. In our main experiments, we select the augmentation strategy using voos-valliation, and Fig. [00 analyzes per- formance differences across augmentation proto- cols. For all styles, the maximum augmentation probability is fixed at = 0.3, based on inner cross-validation results using linear decay.
Target-Sice Sidet Augmentation Schedules
Augmentation Probability ple
0.30
0.25
0.20
None
Decrease
Linea Peak
Linear Increase
0.10
Constant
0.05
0.00
Epoch
Figure 9: Augmentation schedules defining p(e) over training epochs.
Nearly augmentation strategies improve model performance with respect to Pearson correlation and mean squared error (MSE). Gains are especially pronounced when evaluating Pearson-r restricted to strong positive edges (y 0.3), where both constant and linearly decaying augmentation schedules yield an improvement of ~0.05 This effect intuitive, as minority class oversampling emphasizes edges with strong signal, which otherwise underrepresented. Although global metric gains moderate, consistent gains suggest that curriculum guided target-side augmentation improves model robustness across both random and spatial data splits, and should be considered general-purpose regularization strategy in transcriptome-coneeca connectoee modeling tasks in future work.
A
Random
B
Spatial
Eascline HNs Aug
Liear
Succing Poo fug]
Unee Park
0,80
Contait:
Liear
Curtiuluu Centart
Centlntt
Carruuuree Suruuuunneee Linaa Detey
0.74
Carszet:
Curiuluu Swep Uner Docay
0.77
0.78
0.68
0.00
0.76
0.62
Spli Squared
Spetiel Split test Meen Squared Error
0.0155
heat
0.050
Noee
Contuciun Sver Unoer horeas
None
Curroukee Uneer
0.0150
0.0325
Lncel Douay
Curouken Seur Demsunt
Squared Enner
0.0455
Uneer Inceuse
Centive
Curtica
Neen-Squeee Squared Ener
0.0300
Dolay
0.0250
0.0225
0.0300
0.0200
04125
Random Solit Strang Edge Pearsonet
Spatial Split
Strong Edge Rearsonv
Enseliea
Duseine
Uneer
Neee
Curricutee teap Leear semnee
0.46
Newe
Cuerocio Swap Unner trmmese
Contart
Curiicluus Liner Decay
0.44
Contaet
Curticlum Swea Uneer
0.45
Lneer Sureue
Lawa Suroee
Pos. Edge
Box. Edge
0.40
0.38
0.44
0.34
0.62
0.32
0.60
dim
60
Figure 10: Distributional farget-side augmentation analysis. Augmentation style test-set perfor- mance for Pearson-r, MSE, and strong-positiv positive Pearson-7 (>0.3) for [A] random split and [B] spatial split.
26

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A.6 Replication Analysis
Intra-resolution replication analysis. For all resolutions of the MPI-LEMON and HCP dataset, the SMT exceeds its corresponding null estimate (Table 7) under both the random and spatial split setting. The raw performance values are lower than those reported for UKBB, which could be attributed to a variety of fundamental differences between the datasets such as data quality, processing steps, parcellation style, or weaker signal between the AHBA population and the HCP and MPI- LEMON populations. Alternatively, despite using cross-validated hyperparameter searching strategy. more optimal search space may exist for the MPI-LEMON dataset as compared UKBB. Another primary difference between the datasets is that the MPI-LEME dataset contains more positively skewed values whereas UKBB contains strong signal in both the positive and negative direction.
Tables O and Table 8 similarly illustrate performance above the spatiomolecular null but at smaller margin for MPI-LEMON. Strong spatial effects are present at all resolutions in the null setting. This gap is in line with our SMT w/ [CLS] results from I which shows much smaller gap when true coordinates are introduced to the null model. In sum, Tables through confirm robust relationship between gene expression and functional connectivity in the HCP-YA and MPI-LEMON dataset, but there may be more weakly aligned genetic signal in the MPI-LEMON dataset or additional noise introduced by technical artifacts.
Cross-dataset and cross-resolution analysis. We use a full dataset framework to test cross-dataset and cross-resolution generalization simultaneously. Here, we train an SMT w/ [CLS] model source rlsoutoonesolutton pair (e-g.. UKBB $456) and reconstruct the full connectome of a different dataset-resolution pair (c.g.. MPI-LEMON 729). To evaluate whether performance exceeds chance, we benchmark against an SMT model trained on one of the top spatiomolecular spins for the source dataset, keeping spatial coordinates fixed. This model represents the baseline explained by spatial proximity and transcriptomic autocorrelation.
For example, we first train the SMT w/ [CLS] model on the true data and top K null spin of the UKBB S456. If model trained on MPI-LEMON 729 reconstructs the UKBB S456 connectome more accurately than the UKBB-based null model, it implies generalization beyond spatial and genetic autocorrelation. Default model hyperparameters are selected prior to application on the target dataset.
27

---

Table 5: Multi-resolution test set performance for SMT with random CV on MPI-LEMON and
HCP-YZ YA dataset (mean and standard deviation over 10 4-fold splits). (null) indicates model trained
on 10 lowest-error spatiomolecular null brain maps at each resolution.
Model
Resolution
Pearson-r
Short r
Mid r
Long
R²
MSE
Geodesic
SMT (mull)
183
0.26 0.10
0.16
0.17 0.10
0.11
0.22
0.030
0.000
6.02 +
SMT
183
0.50 1: 0.09
0.43 1: 0.11
0.41 = 0.11
0.43 0.09
0.17 = 0.16
0.022 1 0.005
5.62 1: 0.98
SMT (mult)
0.28
0.06
0.20
-0.06 0.07
0.002
0.63
SMT
391
0.57 + 0.05
0.56 +.06
0.49 - 0.06
0.48-+0.08
0.28 0.08
0.017 + 0.002
8.17 0.992
SMT (mult)
729
0.30 0.05
0.25
-0.08 0.08
0.002
11,90 0.77
SMT
729
0.54 0.04
0.53 0.00
0.45 0.04
0.45
0.23 0.06
0.016 + 0.001
10.67 0.77
SMT (mil))
HCP
0.27 0.07
0.28
- 0.08
0.21 = 0.07
0.20
-0.22
0.030 = 0.001
14.41 0.87
SMT
HCP
0.71 0.04
0.75 0.01
0.68
0.01
0.58 0.08
0.47 0.05
0,013 + 0.002
10.89 0.77
Table 6: Multi-resolution test set performance for SMT w/ [CLS] on random split (mean and standard deviation over 10 4-fold splits).
Resolution
Pearson-r
Mid
Long
R2
Geodesic
SMI w/ CLS (mul))
183
0.50 = 0.00
0.44
0.39 +
0.46 + 0.12
0.01 = 0.18
0.026 0.004
6.18 = 0.93
SMT w/
0.57
0.50 0.11
0.12
1 0.12
0,007
SMT w/ CLS (mul))
391
0.61 0.06
0.00 0.006
0.54 0.06
0.54
0.30 0.10
0.016:00.002
7.76 = 0.80
SMT w/ CLS
391
0.68 0.04
0.68 +0004
0.61 +.0.
0.61
0.06
0.42 0.07
0.013
7.61 0.81
SMT w/ CLS (mull)
729
0.66 0.04
0.65 0.04
0.59 0.05
0.59
0.006
0.38 1 0.07
0.013
0.0022
9.63 0.71
SMT w/ CLS
729
0,70 = 0.04
0.70 0.03
0.03 0.03
0.64 0.06
0.45 0.07
0.011
+.000
9.07 1.03
SMT w/ (mulf)
HCP
0.50
0.63 0.05
0.06
0.53
0.10
0.26
0.003
12.50 0.72
SMT w/ CLS
HCP
0,74 = 0.06
0.77 1 0.04
0.70 1 0.05
0.66
1: 0.10
0.52 : 0.08
0,012 1: 0.002
11.27 0.81
Table 7: Multi-rcsolution test set performance for SMT on spatial split (mean and standard deviation
over 10 4-fold splits).
Model
Resolution
Sbort
Mid
Long
R
Geodesic
SMT (mull)
183
0.13
0.10
0.00
1 0.08
0.08
0.10
0.11
1 0.14
-0.25
0.41
0.041 0.013
7.02 1 0.54
183
0.38 0.15
0.35
0.31
0.27
0.02
0.28
0.032 0.008
SMT (mulf)
391
0.19
0.15
0.11=000
201=00
0.08 0.16
-0.15
0.034 0.006
9.31 0.99
SMT
391
0.10
0.17
0.36=0.00 0.09
0.28
0.18
0.021
5.09
SMT (mulf)
729
0,22
0.18
0.00= 0.07
0.10
00.1
0.031 0.005
11.98 0.78
SMT
729
0.48 0.09
0.45
0.31 0.09
0.28
0.17
0.022 0.001
10.73 0.83
SMT (mudf)
HCP
0.25 0.09
0.25 0.10
0.15
0.08
0.09
0.100
-0,20
0.18
0.038 0.011
13.91
1.18
SMT
HCP
0.63
0.15
0.63 + 0.17
0.14 0.55
0.44 + 0.22
0.20
0.81
0.024 0.014
11.13
1.80
Table multi-resolution test set performance for SMT w/ [CLS] on spatial split (mean and standard deviation over 10 4-fold splits).
Model
Resolution
Pearson-r
Short
Mid
Long
MSE
Geodosic
SMT w/ CLS (mull)
183
0.29
0.13
0:24
0.13
0.14
0.14
0.22
0.13
00.35
006=0:0 0.50
0.044
0.019
7.28
2:47
SMT w/ CL.S
183
0.32 4 0.12
0.27 + 0.14
0.19
4 0.14
0.34 + 0.16
0.28
0.39
0.042
: 0.015
7.01 + 1.43
SMT CLS (mall)
391
0.10
0.10
0.13
0.15
0.00
0.030 0.000
8
SMT w/ CL.S
391
0.50 0.09
0.48++0.1
0.34+ 0.10
0.35 0.17
0.15+
0.024 + 0.008
7.95++ 0.83
SMT w/ CLS (mud))
729
0.11
0.10
0:25 0.122
0.23 0
-0.08
0.028 0.007
10.19 0,72
SMT w/
729
0.52 0.09
0.36+0..12
0.31
0.08+00.2
0.025 0.007
9.97
0.88
SMT w/ CLS (mul))
HCP
0.37 0.11
0.37
0.12
0.21 0.12
0.18
-0.27 = 0.58
0.010
2 0.017
13.14 1.56
SMT CL.S
HCP
0.37 0.13
0.57 0.14
0.46
0.47
0.30
0.026 0.012
12.05
2.21
Random split
Spatial split
Train regions
Train regionns Test regions
Test regions
Example Random Fold
Example Spatial Fold
Train
Train
36
(rosteroo Aiterior)
(Laderal)
Test
RRitte for wor-enaaeenn Antersa
(Lateral)
Test
Figure 11: Example connectome train-test folds for random and spatial splits. Weighted target edges are visualized in red between test nodes thresholded r 2 0.3 sparsify the number edges.
28

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Predicted NCP
Predicted UKBB (S456)
Predicted
Predicted
Predicted
30
14
-10
-4A
1...0.99.0076.
050.00 (0.7g)
F. 0,73 (0.59.
== 0.68 (0.82)
0-0062 (0.70)
-0.
000
-044
1.-0.66 (0.76)
(0.78)
0.78 (0.58)
1-0.77 (0.82)
-.-0.70 (0.78)
-00
1.0.53 (0.76)
F. 0.55 (0.78)
FS 0.80 (0.59)
1= 1=0.71
F. 0.69 (0.79)
C- 0.69 (0.76)
F- 0.72 (0.78)
0.92 (0.59)
0.98 (0.82)
0.85 (0.79)
0.6
-04
000
r= 0.72 (0.76)
-08
Figure 12: Cross-dataset generalization of SMT with CLS. The diagonal shows population- aveerage functional connectomes from UK Biobank (S456), Human Connectome Project (S456), and MPI- LEMON (183, 391, 729 resolutions). Connectomes are sorted by the anterior-posterior axis across datasets and resolutions. Each row shows reconstructions from SMT [CLS] models trained on source dataset (highlighted with blue border) and tested external datasets resolutions. Pearson correlation between predicted and true connectomes is shown below each matrix, with the source datasct's 's spatiomoleculaa null performance estimate in parentheses. Null performance is based on SMT w/ [CLS] models fit on a low-error spatiomolccular null gene expression matrix with true coordinates. Connectomes highlighted with green border indicate generalization above native SMT [CLS] null chance. (Non-parenthesine Pearson correlations along the diagonal correspond to training fit and thus do not indicate significance over the null. See intra-resolution effects in Tables
As shown in Figure 12, across all experiments observe consistently high reconstruction perfor- mance and a backbone connectome structure at all resolutions. Meaningful generalization above the null observed in few cases. Both the UKBB and HCP trained models able to predict MPI-LEMON 183 beyond the spatiomolecular null baseline, suggesting a possible conserved molec- ular-connectomic relationship across adult populations. Notably, UKBB participants are older average than those in MPI-LEMON (see Section A.J. supporting the hypothesis that shared tran- scriptomic gradients contribute functional brain organization across the adult lifespan. This is further supported by the fact that the HCP trained model significantly predicts MPI-LEMON 183, at a value slightly worse than UKBB, despite more closely aligned demographies between HCP and
29

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MPI-LEMON. HCP to UKBB generalization exceeds null chance, which is expected given the targets of UKBB are highly similar.
We observe that while UKBB and HCP connectomes contain both positive and negative values, MPI-LEMON matrices strictly positive. This discrepancy may limit the model's ability to capture absolute connectivity values across datasets (as reflected in MSE), though relative connection strengths remain well preserved (as reflected in Pearson-r). Parcellation differences likely also play a role: the UKBB parcellation is functionally defined based on resting-state networks, whereas the MPI-LEMON atlas is derived from unsupervised voxel-level clustering.
Within the MPI-LEMON dataset, we find strong generalization across parcellation resolutions. Five cross-resolution reconstructions exceed the null baseline, including one case where model trained at lower resolution (391) generalizes successfully to higher resolution (729). These results suggest that while spatial position explains much of the variance, gene expression captures complementary structure. As resolution increases and more training data becomes available, models are better able to learn complex molecular-connectmii relationships.
Our cross-dataset generalization analysis demonstrates that predictive accuracy on UKBB not an artifact of the particular dataset's properties. There are common spatiomolecular relationships that the SMT effectively learns despite differences datasets, demographics, imaging acquisition parameters, and parcellation resolutions.
30

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A.7 Attention Weights Analysis
To interpret how the SMT attends gene tokens, we extract and average attention weights from the final layer of the trained transformer encoder. For a given region, the input is sequence of tokenized gene expression values E R where is the number of tokens and d is the embedding dimension. In each layer, X is linearly projected to queries, keys, and values: Q X K = XWK, V XWv, where Wq. WK. Wy E IRdxda, and d, d/h is the head dimension for heads. Each head computes scaled dot-pre not-product attention with ALiBi biases B:
[QKT B
Attention K, V) = softmax
V,
Vdh
where softmax
[QKTBB +B vdd.
E ext defines the attention weights.
After model training (on the full dataset using the default hyperparameters identified via cross- validation), we pass in the full training data to compute these attention weights. For each sample, we extract the self-attention matrix from the final transformer layer for each head. We can average these matrices across all samples and all heads to obtain global attention score matrix:
A
A
bN
where AL E Reex is the attention matrix for the j-th head on the n-th region, and N the total number of regions.
For subnetwork- level analysis, we instead compute attention weights restricted samples belonging to canonical functional subnetworks defined by our UK Biobank 456 region, 9 network parcellation.
We compute the attention weights for each network E (1......)) 9} by passing in regions to the encoder individually. These attention matrices are aggregated in the same way, producing network-specific average attention map Ag. This procedure allows us to characterize how attention distributed over gene tokens in general, and emphasize distinct transcriptomic features attended to for different brain networks.
Figure 13/ shows that, in the absence of the [CLS] token, self-attention patterns differ across heads, with specific gene tokens receiving higher attention in some heads exhibit different spatial frequencies, possibly reflecting local versus global transcriptomic interactions. Such diversity may encouraged by the ALiBi slope mechanism.
than others. These variations also
Figure 13B presents the mean attention scores for the SMT w/ [CLS] model. The first token (expanded for visibility) is the [CLS] token, which consistently receives the highest attention across all heads, indicating strong influence from spatial coordinates. Interestingly, the 54th gene token (located chromosome receives relatively high attention scores in all heads, suggesting that despite the strong emphasis on spatial position, some gene modules such as those related to white matter microstructure, neurodevelopment, or metabolic activity, may selectively co-embed with spatial information to improve prediction. The stability and significance of these attention heads must be further validated to link the gene sets highlighted by the SMT with biologically relevant processes.
Figure 13C shows average attention distributions when regions from specific functional subnetworks separately input into the SMT. Across subset of six functional networks, we observe the subcortex and cerebellum show similar profiles to each other as compared to cortical networks. Certain gene tokens consistently receive elevated attention across all subnetworks. Further analysis of global and subnetwork-speccn attention patterns may help determine whether distinct transcriptomic modules underlie functional connectivity across the brain.
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A
Head
Head
Head
Head
13
14
Query
188
103
I00
100
H
R 08:00 GRER
2 22085555 1363
Key
B
Head
Head
Head
Head 4
Query
101
100
22 252000 2002
Key
C
Network Attention Maps
Cont
SomMot
Defoult
0008
0..00.0 0.00
1.2
-33
(0.00
ac
Bi
62.6
800000 20.K
05.5
6.2
000
Quany
Querry
622
Query
000
000
2042
Key
TSS Ref Genome sorted
TSS Ref Genome sorted
TSS Ref Genome sorted
Figure 13: SMT multi-head self-attention weights. [A] Attention scores for the Spatiomolecular Transformer. Tick marks both Query and Key axes denote token positions at chromosome boundaries. [B] Attention scores for SMT with [CLS] token. The [CLS] token key column is artificially expanded for visualization. [C] Subnetwork-specffic attention weights for SMT, averaged over all heads for subset of six functional subnetworks.
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Table Author contributions.
AR
SG
JW
CD
EV
Study concept or design
Data acquisition or processing
Data analysis or interpretation
Drafting/revision of manuscript for content
Funding acquisition
Note: Bolded initials indicate the primary contributor, Black cells indicate a documented contribution to corresponding activity.
33

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NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
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Justification: The abstract and introduction lay out the context of the problem and list the contributions made to solve the problem in the results section.
2. Limitations
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Does the paper discuss the limitations the work performed by the authors?
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The assumptions and limitations of the described method are described in the discussion section.
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3. Theory assumptions and proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
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Justification: The work is mostly empirical, not theoretical, building pre-existing methods.
4. Experimental result reproducibility
Question: Does the paper fully disclose all the information needed to reproduce the main ex- perimental results the paper to the extent that affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
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The paper provides details on the datasets, preprocessing pipelines, train/test
split methodology. model architecture, and evaluation metrics. These are sufficient to reproduce the claims even without code provided, however our code will be made publicly available.
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Justification: The AHBA and MPI-LEMON datasets are publicly available described in the datasets section. The HCP-YA YA and UK Biobank dataset are available through application. We will provide anonymized code zip file in supplementary materials and publicly release code.
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Justification: The paper covers statistical significance of the experiments the sections describing the null model method, covered in the results and technical appendix.
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8. Experiments compute resources
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These details are covered in the supplementary material.
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Answer: [NA]
This paper relies on previously collected, public neuroimaging and transcrip- tomic datasets. No new data gathering conducted. Approval licenses can be made available upon publication.
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16. Declaration of LLM usage
Does the paper describe the usage of LLMs if is an important, original, or non-standard component of the core methods in this research? Note that if the LLM is used only for writing, editing, formatting purposes and does not impact the core methodology, scientific rigorousness, or originality of the research, declaration is not required.
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Justification: The method described in this paper does not involve LLMs any capacity.
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Reviews:
[{"review_id": "9BNef7uets", "reviewer": "Reviewer_Jt3G", "summary": "This paper proposes a method for predicting population functional connectivity from transcriptomic data. The method, a spatiomolecular transformer (SMT), predicts from gene expression data ordered by their transcription start site and brain regional spatial coordinates in a self-attention mechanism, the embeddings of which are then passed to an MLP for functional connectivity prediction. The method is compared against baselines and results using spatiomolecular null maps in experiments using the Allen brain atlas for the genetic data and UKBiobank and MPI-lemon for the functional connectivity data.", "questions": "1. Please see the questions/concerns in the weaknesses described above. I expand upon a few below.\n\n2. I am not so sure of the validity of the conceptual idea of predicting the functional connectome from gene expression data for a small number of subjects, from a different dataset, at the population level - I welcome further discussion from the authors on this.\n\n3. For the experiments, I would like to better understand the significance of presented results - how the small difference between the proposed method's performance and null model compared to baseline approaches might mean, variation in the runs.", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths: \n1. The motivation of the paper is to understand the link between functional connectivity and gene expression data. Such understanding would make a large impact in neuroscience.\n2. The approach of tokenizing the gene expression data by TSS makes sense in terms of keeping physically contiguous data together. \n3. The experimental approach includes analysis of spatiomolecular null maps to give a sense of whether the correlations learned by the model are meaningful. \n4. The experiments include some generalization experiments of model performance across atlas resolutions and datasets. \n\nWeaknesses: \n1. Concern regarding generalizability of trained models:  \nThe Allen brain atlas includes data from 6 donors - I think it is difficult to accept that a model learned from such a small number of subjects would be generalizability to the greater population. Also, the UK biobank is generally older subjects, and the MPI dataset are young adults - I am not sure it makes sense to build a model to predict between these datasets. \n2. Limited technical novelty:  \nThe novelty in this work may lie in the use of established / other methods (transformer style model, ALiBI biases, use of [CLS] token, etc) for the specific task of predicting functional connectome from gene expression data.\n3. Questions/concerns regarding experimental setup:  \n- The experimental setup involves reserving 75% of functional connections for training, and using 25% for testing, in prediction of a population functional connectome from population gene expression data. However, one may imagine that the connections in nearby or homologous regions may have similar relationships to the genetics - therefore, there may be some inadvertent leaking of information, making the training and testing sets not independent, and thus the results may be inflated. \n- The authors perform 10 random 4-fold splits for validation - I am not sure if this means 10 x 4-fold CV, or just 10 random splits where 25% was reserved for testing. \n4. Questions/concerns regarding significance of results:  \n- The authors perform multiple runs for the experiments which is great, but then only report the means. Reporting some sense of the variance across runs would be informative in understanding of there is really a difference in results.\n- While the authors do report some statistical testing results, it is for one-sided t-test, which is not best practice, unless there is a strong reason to not consider two-sided (which I am not seeing here). \n- The authors run a nice experiment to compute the correlation for a null model. While most compared approaches had a null r of 0.3-0.4 range, the proposed method had a null r of 0.71, yet the results of the proposed method with the real data are at similar to slightly higher levels than competing approaches (around 0.7-0.8). Thus, to me this suggests that the proposed approach suffers from more overfitting as it was able to create a model from the perturbed input data with very high correlation compared to baselines, yet the proposed model on the real data has similar predictive strength as other models. \n- The ablation experiments show very small nominal differences in performance which are likely with in standard deviation (unsure if that is what the sigmas refer to in the figure).\n5. Proofreading needed:  \nThe paper would benefit from additional proofreading to polish the language (edit for grammar, redundant words, etc). Also please check reporting of results in lines 324-326 (seems to be repeat of experiment setup but then reported different performance).", "was_revised": true, "final_justification": "Please see longer response to rebuttal below. In summary, I have increased my score from 2 to 4, given the authors' clarifications, the new experiments with the more challenging ROI split, and the inclusion of standard deviations in the reporting of results address many of my questions, but I still have some remaining concerns regarding novelty/effectiveness of the proposed approach compared to simpler deep learning models and the clarity of presentation of the paper itself.", "rebuttal": "We sincerely thank reviewer Jt3G for their thoughtful and constructive feedback. We agree with the reviewer on several key points: the conceptual validity of modeling population-level data requires careful justification, and that the experimental train/test splits must be robust to spatial leakage confounds. We address the concerns about data validity by discussing a set of recent papers and pipelines that have shown the transcriptomic stability of the AHBA dataset. Furthermore, we have performed two major new sets of experiments that demonstrate the generalization phenomena of our models despite the pervasive autocorrelation present in the datasets. First, to bolster our generalizability claims, we have replicated our cross-dataset analysis using the HCP-young-adults (YA) dataset, showing a stable adult connectome and consistent predictive performance.\n\nSecond, we have implemented a more challenging spatial train-test split, which confirms that our models generalize to spatially distinct regions well above our stringent null model baseline. Together, these new results and clarifications strengthen our central claim: we have developed a novel and rigorous platform for predicting functional connectivity from gene expression using deep non-linear models that learns genuine biological signal beyond spatial autocorrelation. We address the major comments of the reviewer below in further detail and we state our plans to revise the manuscript accordingly with the findings from our new experiments.\n\n## Conceptual validity\nWe thank R1 for raising the point on the validity of using the AHBA transcriptome (from 6 subjects) to predict the connectivity strength in UKBB and MPI connectomes (two age divergent cohorts). Our work models the canonical, population-level relationship between the transcriptome and connectome, a link supported by prior work [1][2]. To ensure our data reflects this stable adult architecture, we took two key steps to ensure that the input transcriptome and output connectomes reflect stable values.\n\n### *Stable Transcriptome:* \nWe used the abagen toolbox to create a robust population-level gene expression map from the 6 AHBA donors. As the gold standard dataset in human neuroscience, ample effort has been dedicated to establishing community standard preprocessing steps [3][4]. This standard practice includes stringent processing to retain only genes with spatially consistent expression patterns across all donors based on a **differential stability threshold explained in a detailed response to a6QV**. As shown by Vogel et al. (2024) [5], the primary gene expression gradients from this 6-donor map are highly correlated (r>0.86) with those from much larger datasets (GTEx, n=121), confirming its validity.\n\n### *Stable Connectome:* \nTo address the age-mismatch concern, we have now replicated the experiment shown in Figure 7 using a new connectome derived from the HCP-YA (Human Connectome Project Young Adult, n=1065) dataset. First, we found the HCP-YA (age 22-35) and UKBB (age 45-82) connectomes to be remarkably similar (r=0.9). Crucially, we found that models trained on either cohort generalize equally well to the younger MPI-LEMON (age 20-30) cohort above null chance, despite age differences. The full results will be added to Fig. 7. This new result confirms our results are robust across cohorts of differing demographics.\n\n| Source      | MPI-183 Target True / Null r |\n|---------------|----------------|\n| UKBB   | 0.78 / 0.59        |\n| HCP-YA | 0.73 / 0.59        |\n\n\n## Train-test split\nThe reviewer raises a valid concern that the random split procedure may leak information due to spatial proximity between training and test regions. This is an excellent point. We recognize that random splits can be susceptible to spatial confounds.\n\nOur initial random-split design (10 rounds of 4-fold CV train/test split) was paired with a novel spatiomolecular null model precisely to quantify and control for this effect (described in sections 3.3. and A.3). The substantial gap between the true and null models (Table 1) provided initial evidence of learning beyond spatial proximity. To provide even stronger evidence, we have now implemented a more challenging spatial split. We do this by selecting a source region and assign the edges from the 25% nearest regions to the test set, with the rest used for training [6]. This is done across 4 folds to cover the whole brain, and repeated 10 times, yielding 40 splits, evaluating generalization to spatially distinct regions. All models are evaluated for the same 40 splits just as was done in the random setting. The results, summarized below, are highly informative:\n\n| Model           | Random Split (True / Null r)        | Spatial Split (True / Null r)       |\n|-----------------|--------------------------------------|--------------------------------------|\n| **SMT w/ [CLS]**   | 0.817 ± 0.028 / 0.713 ± 0.047        | 0.743 ± 0.114 / 0.516 ± 0.111        |\n| **MLP w/ coords** | 0.808 ± 0.031 / 0.466 ± 0.078        | 0.741 ± 0.126 / 0.476 ± 0.098        |\n\nThese new results show that while the null performance of SMT w/ CLS drops by ~0.20 in the harder split (confirming that spatial information is less useful in this regime), the true performance only drops by ~0.08. **This doubles the performance gap between the true and null models**, providing compelling evidence that SMT learns a genuine, spatially generalizable transcriptomic-connectomic mapping. We will add this new train/test split routine to the revised manuscript in a dedicated table. \n\n## Experimental details\n*Standard deviations & statistical testing*. \nTo address reviewer concerns, we will add standard deviations to all our reported results including the ablation experiments. They were initially omitted in the tables due to formatting constraints. They also note our use of a one-sided t-test, which we have replaced with two-sided t-tests. The two sided tests confirm the same patterns that the SMT w/ CLS performs significantly better on long-r (p=0.014) and geodesic distance (p=0.0004) than MLP w/ coords. \n\n## Novelty\nLastly, we acknowledge the reviewer’s observation that some SMT components are adapted from existing techniques. However, we highlight several aspects of novelty in both modeling and experimental design:\n- **First deep learning approach for transcriptome-to-connectome mapping in humans**: Prior work in transcriptome-connectome prediction focuses only on feature-based or bilinear methods citing deep learning approaches as future work [7]; we are the first to apply both MLP and attention-based models in this setting.\n- **Rigorous benchmarking framework**: We systematically compare feature-based, bilinear, and deep models in a unified setting using a spatiomolecular null to isolate biological signal from spatial autocorrelation effects.\n- **Consistent non-linear performance gains**: Nonlinear models, including SMT, outperform existing linear baselines under several split settings. Full spatial split results across all models will be reported in a dedicated table of the final manuscript.\n- **SMT modularity enables testing biologically informed priors**: The transformer architecture allows structured integration of genomic and spatial priors through positional embeddings and contextual tokens, which we find improve performance. This modularity provides a natural foundation for future extensions using [CLS]-like tokens to incorporate additional biological or demographic context. \n- **Interpretability via attention weights**: Building on Supplement Figure 9 (see response to reviewer gLbH), we identified cortical and subcortical specific tokens enriched for gene modules related to dendrite extension and neuronal projection.\n- **Future potential**: While SMT is tested here in a small-scale setting, transformer architectures are particularly well-suited to more data-rich regimes. Having demonstrated its utility and performance above baselines, SMT can be scaled to individualized modeling with larger transcriptomic datasets and extended through integration with pretrained genomic models such as scBERT [8] or Geneformer [9].\n\nReferences\n1. Vértes, P. E. et al. Gene transcription profiles associated with inter-modular hubs and connection distance in human functional magnetic resonance imaging networks. 2016\n2. Anderson, K. M. et al. Gene expression links functional networks across cortex and striatum. 2018\n3. Arnatkeviciūtė, A. et al. A practical guide to linking brain-wide gene expression and neuroimaging data. 2019.\n4. Markello, R. D. et al. Standardizing workflows in imaging transcriptomics with the abagen toolbox. 2025\n5. Vogel, J. W. et al. Deciphering the functional specialization of whole-brain spatiomolecular gradients in the adult brain. 2024\n6. Hansen, J. Y. Mapping gene transcription and neurocognition across human neocortex. 2021\n7. Qiao, M. Deciphering the genetic code of neuronal type connectivity through bilinear modeling. 2024\n8. Yang, F. et al. scBERT as a large-scale pretrained deep language model for cell type annotation of single-cell RNA-seq data. 2022\n9. Cui, Z. et al. Geneformer: Learned gene compression using transformer-based context modeling. 2023"}, {"review_id": "0nI1Oz4oSo", "reviewer": "Reviewer_NCYX", "summary": "This paper introduces the Spatiomolecular Transformer (SMT), an attention-based architecture designed to predict human brain functional connectivity from gene expression data and spatial coordinates. The work addresses a fundamental question in neuroscience: can we predict how brain regions connect based on single-cell spatial transcriptomics. This work does not focus on improving single-cell representation and/or imputation but rather aims at leveraging recent prior works on single-cells and to apply on a real-world application. \n\nThe Spatiomolecular Transformer (SMT) tokenizes genes based on their genomic position (transcription start sites) and uses multi-head self-attention with ALiBi biases to capture both local and global genetic interactions. The authors incorporates 3D brain coordinates through a dedicated [CLS] token that participates in the attention mechanism, allowing spatial information to modulate molecular features. One key experiment in this work is also the Spatiomolecular Null Mapping, to verify that the SMT architecture learn more than simply spatial correlations.", "questions": "- Contributions: are the authors the first ones to apply a Transformer's architecture to predicting functional connectivity ? This could be clearly stated in the contribution as well. \n- TSS ranking: if you do not use the TSS ranking but rather a random split, what is the impact in terms of performance ? It would be interesting to add this in the ablation study.\n- Architecture wise: what is the impact of the learned linear map ? Could it be replaced by 1D convolutions ? What is the impact of the Transformer block vs only 1D convolutions ?\n- Pre-training: what would be the benefits of leveraging a checkpoint pre-trained on dozens of millions of single-cell RNA sequences ? \n- Number of genes: why did the authors limit themselves to 7380 genes ? \n- The loss is not discussed in the main paper nor in the Appendix. I believe could also yield to interesting discussions. I may have missed something but, similarly, I believe different sampling schemes could be discussed for example to ensure balanced representation of short/medium/long-range connections. Do you think this could be useful in your setting ?", "limitations": "One of the two main limitations of this paper, in my opinion, are the following:\n- clearly stating whether it is the first application of Transformers for the task of Brain Connectivity (if not, adding some baselines would greatly improve the comparison).\n- as mentioned the questions above, extending the ablation study would help understand better what elements in this SMT architecture brings performance.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n\n- The problem is extremely relevant: the authors address a fundamental question linking molecular biology to brain function with clear neuroscientific relevance.\n\n- A biologically relevant preprocessing and modeling: \"sorting each region’s expression vector by the genomic position of genes based on their transcription start site\" this is a witty and smart way to rank genes that has biological meaning. It assumes that genes that are physically close on chromosomes often work together or are regulated together. Also, the ALiBi attention slopes incorporate meaningful biological priors about genomic organization. \n\n- Causality: The spatiomolecular null testing is particularly well-designed, addressing a critical confound (spatial autocorrelation) often overlooked in neurogenomics studies. This experiment clearly underlines what the SMT architecture learns apart from spatial correlation. \n\n- Comprehensive Evaluation: Tests across multiple datasets (UK Biobank, MPI-LEMON) and parcellation resolutions, with proper cross-validation and distance-stratified analyses.\n\n\n**Weaknesses**\n\n- Limited Novelty: While well-executed, the transformer application is relatively straightforward. The performance gains over simpler MLP baselines are modest (SMT: 0.79 vs MLP: 0.78 Pearson-r). The authors briefly state that \"the attention mechanism does not substantially outperform comparable non-linear baselines\", this raises questions about the added complexity's value. \"It does enable key design features for qualitative evaluation\": this qualitative study could have been extended, the UMAP projections do not illustrate a qualitatively superior embedding space for SMT. \n- I believe that the SMT architecture could have been studied slightly more, meaning a larger ablation study. What is the impact of the learned linear map ? Could it be replaced by 1D convolutions ? What is the impact of the Transformer block vs only 1D convolutions ?\n- Also, if there is \"a scarcity of human brain gene expression data\", there are hundreds of millions of single-cell data in open public datasets. It could have been interesting to measure the impact of a pre-training on a large non-brain dataset. Beside, there are already some existing pre-trained checkpoints available (scBERT, scGPT, cellPLM, sCT...). \n- It seems that the authors limit themselves to 7380 genes, why is that ? how is the choice done ? could we maybe increase this to reduce the assumptions done ?", "was_revised": false, "final_justification": "", "rebuttal": "We thank reviewer NCYX for their insight and helpful suggestions, which has prompted us to clarify our experimental contributions, expand our ablation study, and evaluate alternative model features. \n\n## Novel contributions\n- To address the reviewer’s first question, to the best of our knowledge, **this study presents the first deep learning approach for predicting functional connectivity from regional gene expression in humans**. Prior work in this space, such as the Connectome Model and its low-rank form [1], has remained limited to bilinear and feature-based methods, with deep learning only proposed as future work. While deep learning has been extensively applied to gene expression and connectomics separately, it has not been applied to this joint prediction problem. Given the relevance of this task, we emphasized careful model benchmarking, cross-dataset validation, and custom null model construction, which are paramount to addressing what the reviewer notes is a fundamental question linking molecular biology to brain function.\n- *A key motivation for using a transformer-based architecture is its flexibility for testing targeted biological hypotheses.* SMT enables systematic integration of structured genomic priors—such as TSS-sorted sequences, positional embeddings, and contextual [CLS] tokens—following trends in models like CellSpliceNet [2]. While MLPs and CNNs can incorporate similar features, **transformers are inherently designed for processing sequential information making such implementations more direct. The reviewer suggests valuable extensions to our ablation studies, including genomic order shuffling and alternative convolutional encoders, which we explore below.\n- Feedback from several reviewers motivated an **extended analysis of Figure 9 to better understand the gene groups relevant to different functional subnetworks (full details in reviewer gLbH response)**. By summing attention weights within each subnetwork, we identified three cortex-specific gene tokens and one subcortical token that consistently received high attention. Gene Ontology analysis revealed distinct modules: **a cortical module enriched for positive regulation of dendrite extension, and a subcortical module enriched for negative regulation of neuron projection development**. This finding is notable because, while functional connectivity is often associated with metabolic or activity-driven pathways, our results suggest a stronger link to developmental wiring mechanisms that persist into adulthood aligning with findings from human developmental literature and mouse studies [3][4].\n\n## SMT architecture\n*Effect of positional information*\nThe reviewer raises an important question regarding the role of positional information in SMT performance, particularly given its biological motivation and architectural contrast with the MLP. To address this, we conducted a focused ablation experiment where we varied only the token dimension (20 vs. 60), gene order (random vs. TSS-sorted), and inclusion of ALiBi positional slopes, holding all other hyperparameters constant. Each configuration was evaluated across the same 40 train-test splits used in Table 1.\n\n**SMT**\n| Configuration | Mean r | Std Dev |\n|--------------------|--------|---------|\n| Token dim 20, random genes, no slopes       | 0.765 | 0.0291 |\n| Token dim 20, random genes, slopes          | 0.763 | 0.0277 |\n| Token dim 20, sorted genes, slopes          | 0.765 | 0.0299 |\n| **Token dim 60, random genes, no slopes**   | **0.777** | **0.0308** |\n| **Token dim 60, random genes, slopes**      | **0.781** | **0.0287** |\n| **Token dim 60, sorted genes, slopes**      | **0.783** | **0.0288** |\n\n**SMT w/ CLS**\n| Configuration | Mean r | Std Dev |\n|--------------------|--------|---------|\n| **Token dim 20, random genes, no slopes**   | **0.815** | **0.0384** |\n| **Token dim 20, random genes, slopes**      | **0.829** | **0.0277** |\n| **Token dim 20, sorted genes, slopes**      | **0.831** | **0.0276** |\n| Token dim 60, random genes, no slopes       | 0.803 | 0.0396 |\n| Token dim 60, random genes, slopes          | 0.818 | 0.0301 |\n| Token dim 60, sorted genes, slopes          | 0.818 | 0.0297 |\n\nThe ablation points towards several trends. First, model performance depends on token dimensionality: the base SMT performs best with token dim 60, whereas SMT w/ CLS favors token dim 20. Second, adding ALiBi slopes generally improves performance, particularly for the SMT w/ CLS even when gene groups are randomly ordered, Third, sorting genes by TSS provides a consistent but modest performance boost across both models, suggesting that the biological sorting may be most useful for interpretability purposes. We will include these experimental results in the section A2 of the supplement.\nWhile the performance margins are modest, they trend consistently in the expected direction, pointing to the potential utility of modeling positional priors, something not directly possible in an MLP. Future work can extend this analysis by grouping genes based on regulatory networks.\n\n### *Convolutions*\nThe learned linear projection in our model follows the standard query-key-value (QKV) attention mechanism, where each token is linearly projected from its original dimension (20–60) into a higher-dimensional space although convolutional strategies may offer advantages for capturing local structure. This design choice aligns with the biological nature of gene expression data, which reflects aggregate signals from multiple mRNA transcripts and isoforms hybridizing to microarray probes. As for long convolutions vs transformer blocks, we opted for transformer blocks due to their sequential design features and attention head interpretability. Recent models like AlphaGenome [5] combine both strategies, and we are eager to explore this hybrid approach in future iterations of SMT. This information will be detailed in the Methods section of the revised manuscript.\n\n### *Incorporating pretrained models*\nWe appreciate the reviewer’s excellent suggestion regarding the use of pretrained gene expression models. We chose to train our model end to end primarily due to the substantial distributional shift between the AHBA bulk microarray data and the single-cell RNA-seq data typically used in large-scale pretrained models like scBERT [6]. Microarray data are normalized to a 0–1 range and often Gaussian distributed, whereas RNA-seq data are typically represented as raw or log-transformed counts, leading to different statistical properties and input dynamics. As noted in a recent benchmarking study, “the underlying data type used in the creation of the embeddings is the most critical factor influencing performance, rather than the specific algorithm or embedding dimension” [7]. That said, we strongly agree that adapting or fine-tuning pretrained models represents a highly compelling future direction.\n\n### *Embedding analysis*\nIn response to the comment on embeddings, we believe future work could apply UMAP or PHATE [8] to edge-level embeddings to potentially reveal more structure than region-level projections. We defer this to future work or the final manuscript since figures are not permitted in the rebuttal phase.\n\n### *Loss functions*\nAll models in our study were trained using mean squared error (MSE) loss, which we will explicitly clarify in the revised manuscript. During early model development, we observed stable learning dynamics using this loss function. We agree that alternative sampling strategies, such as those that ensure balanced representation of short-, medium-, and long-range connections are a valuable extension. This could be especially powerful when paired with a distributional loss function (e.g., negative log-likelihood or KLD), which would allow the model to tune to the full distribution of target values rather than point estimates alone. Our current strategy adopts a simple curriculum-like approach by exposing the model to perturbed targets early in training and gradually shifting to the true targets. However, future iterations could benefit from more targeted or difficulty-aware sampling schemes, which will be stated in the Methods section of the manuscript.\n\n### *Gene selection criteria*\nSince our fundamental goal is to link the transcriptome and connectome at the population-level, we sought to retain genes that are stable across individuals while enabling the model to learn from the high-dimensional feature space. To achieve this, we applied a differential stability filter using the abagen toolbox, which selects genes with consistent regional expression profiles across all AHBA donors (see Eq. 3 in response to reviewer a6QV). This yielded a final set of 7380 genes, balancing dimensionality with cross-donor reliability. While this filtering may omit some potentially informative genes, it avoids injecting individual-level artifacts. We will make the specific steps clear in section A.2. \n\nReferences\n1. Qiao, M. Deciphering the genetic code of neuronal type connectivity through bilinear modeling. 2024.\n2. Afrasiyabi, A. et al. CellSpliceNet: Interpretable multimodal modeling of alternative splicing across neurons in C. elegans. 2025\n3. Vogel, J. W. et al. Deciphering the functional specialization of whole-brain spatiomolecular gradients in the adult brain. 2024\n4. French, L. et al. Large-scale analysis of gene expression and connectivity in the rodent brain: insights through data integration. 2011\n5. Avsec, Ž. et al. AlphaGenome: advancing regulatory variant effect prediction with a unified DNA sequence model. bioRxiv, 2025\n6. Yang, F. et al. scBERT as a large-scale pretrained deep language model for cell type annotation of single-cell RNA-seq data. 2022\n7. Zhong, J., et al.. Benchmarking gene embeddings from sequence, expression, network, and text models for functional prediction tasks. 2025\n8. Moon, K. R. et al. Visualizing structure and transitions in high-dimensional biological data. 2019"}, {"review_id": "76v8XrEjwJ", "reviewer": "Reviewer_gLbH", "summary": "The manuscript entitled \"Predicting Functional Brain Connectivity with a Context-Aware Spatiomolecular Transformer\" presents a transformer-based model (Spatiomolecular Transformer (SMT)) with biologically-grounded data augmentation techniques to map functional brain connectivity with spatial transcriptomic data.\n\nThe model tokenizes gene expression by transcription start site (TSS) to preserve genomic context and includes a spatially initialized [CLS] token to account for brain region location. The proposed SMT model is compared with several linear and non-linear baselines models using datasets from UK Biobank and MPI-LEMON at various parcellation scales. Results demonstrates superior performance of SMT, especially in predicting long-range connections, indicating its capability to capture real biological mechanisms rather than just local similarities.", "questions": "The reviewer is curious why the author formulate the problem only as a \"prediction\", rather than a \"mapping\" task, which has been extensively emphasized but never explained. What will be the limit to do the two-way mapping between functional connectivity and transcriptomic data?", "limitations": "In addition to the more general comments listed above in the \"Summary\", the model’s generalization from UK Biobank to MPI-LEMON (Pearson r = 0.55) is relatively weak given the high-dimensional nature of the input. While some variation is expected due to demographic and methodological differences, the paper doesn't fully account for this or examine other transfer learning strategies to improve robustness.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "The main task of this paper: mapping fMRI-derived functional connectivity from spatial transcriptomics, is an important task to bridge microscope, molecular and macroscope, systems-level neuroscience. However, the authors did not seize this opportunity to investigate deeper neuroscientific insights from the learned mappings. Considering the space limitation of a NIPS submission, the lack of such investigation is understandable, but definitely shall be work on in its future iterations. For example, gene sets contributing to long-range vs. short-range connectivity, or molecular signatures of subnetworks (e.g., default mode vs. visual), are only briefly discussed or left in the appendix. Recent neuroscience works pointed out the utility of spatial transcriptomics for uncovering mechanisms of cortical specialization, which this paper could have explored in more depth.\n\nMethodologically, although the model structure is not that complicated, SMT can advance the field by providing more effective, multimodal integration of gene expression and brain spatial structure, which is much needed in system neuroscience. Additionally, SMT’s architecture allows for interpretable attention maps, which could potentially reveal gene pathways underlying connectivity phenotypes. The development of distributional augmentation sampling subject-level fMRI matrices during training is a creative solution to the low sample size of transcriptomic data. It brings in inter-individual variability from fMRI while maintaining a fixed transcriptome. While the augmentation benefits were modest in ablation studies, this technique is of technical merit and aligns with trends in data-rich domains like genomics. It could serve as a template for integrating population data in low-sample transcriptomic domains in a more general perspective.", "was_revised": true, "final_justification": "The authors provided additional neuroscientific analyses of attention weights that are interesting and help contextualize the results, but these additions were not part of the original manuscript and only partly address the concern that the paper does not sufficiently leverage its method for deeper neuroscientific insight. Methodologically, while the author argued that SMT framework is competently implemented and shows some gains, its performance is only slightly better than a standard MLP and the novelty of the architecture remains limited. For these reasons, I retain my original rating.", "rebuttal": "We thank reviewer gLbH for their supportive comments of our manuscript and appreciate the understanding that given the space limitations, the manuscript is primarily focused on experimental design and modeling results. While we did perform some high-level evaluation of attention weights in Figure 9, we are inspired by the reviewer comments and have extended this analysis further to bring deeper neuroscientific insight to our study. \n\n## Neuroscientific insight\nIn Figure 9C, the average attention weights for 6 of the 9 functional subnetworks are visualized. The tokens are sorted by chromosomal position, with 23 chromosomal boundaries denoted by tick marks on the axes. To gain additional insight from the attention weights, we have performed column-wise sums for each subnetwork resulting in one vector per subnetwork that denotes the total attention ‘paid’ to each token. This set of 9 vectors can be compared by subnetwork to identify token-wise similarities or differences. A visual representation will be included in Figure 9. \n\nAs can be observed in Figure 9C, each functional subnetwork attention matrix tends to have 1-3 tokens with stronger attention weights. Using the summing procedure described above, we **display the top 2 tokens attended to for each functional subnetwork**:\n- Visual: 106, 82\n- Somatomotor: 82, 106\n- Dorsal Attention: 106, 38\n- Salience Ventral Attention: 60, 42\n- Control/Frontoparietal: 60, 106\n- Default: 60, 106\n- Limbic: 60, 112\n- Subcortical: 28, 118\n- Cerebellum: 28, 86\n\nA clear pattern arises. Across the cortex there are 3 common tokens attended to - token 60, 82, and 106. Across the subcortex there is a single common token - token 28. Given the token size of 60 we now have a set of 180 genes for the cortex and 60 for the subcortex to analyze further.\n\nAlthough sorted by TSS, it is possible that some of the genes in these groups are unrelated to the transcriptome-connectome subspace, which may introduce undesirable noise for Gene Ontology analysis. Therefore, we use **HumanBase, which applies tissue specific community detection to find cohesive gene clusters from a provided gene list**. The module detection enables systematic association of gene groups related to specific tissues or processes. Instead of processing the full gene group, resulting modules are tested for functional enrichment of Gene Ontology biological process terms.\n\nOf the 180 genes in the top 3 cortex tokens, three distinct modules are detected. **The first cortex module M1 contains 35 genes enriched for positive regulation of dendrite extension. Of the 60 genes in the subcortex token, the first module M1, contains 15 genes enriched for negative regulation of neuron projection development.** Modules only contain terms passing significance thresholds using one-sided Fisher’s exact tests and Benjamini–Hochberg corrections to correct for multiple tests. HumanBase hyperlinks with full gene lists and enrichment results will be included in the final manuscript as links are not permitted in the rebuttal phase.\n\n### *Interpretation:* \nSince functional connectivity reflects coordinated hemodynamic activity, one may expect enrichment of gene pathways related to neuronal activity and metabolism. Instead, we identified two modules associated with the regulation of selective neuronal wiring patterns - an upregulating module in the cortex and downregulating module in the subcortex. This suggests that the genetic gradients shaping structural wiring during development may also support the maintenance of functional circuits in adulthood. These findings align with Vogel et al.’s [1] observation that developmental transcriptomic gradients persist into adulthood. Moreover, the emergence of neuronal projection modules in the attention weights of the SMT echoes results from several mouse studies , which show that genes linked to neuronal connectivity often correlate with long-range connectivity patterns [2]. These results will be clearly added to our main manuscript and supplement.\n\nWe hope to expand on these findings in future work by generating null distributions of attention weights and evaluating attention across subpopulations as an avenue for deriving imaging-genetics phenotypes. In summary, the inclusion of clearer attention weight visualization, paired with principled Gene Ontology analysis serves to show how the SMT can contribute to neuroscientific insight regarding the transcriptome-connectome relationship. \n\n## Novelty of Target Augmentation\nWe appreciate the comment regarding the novelty of our target-side augmentation protocol and its potential as a template for future work. This strategy leverages a key asymmetry in the field: the scarcity of high-quality gene expression data versus the abundance of connectivity data. One direction we are actively exploring is joint feature-side and target-side augmentation, where each time a new target connectivity value is sampled, the corresponding transcriptomic input is perturbed as well. Specifically, we introduce small amounts of noise to the gene expression vectors, scaled by the variance of each gene across the six AHBA donors. Pairing true connectivity values with realistically perturbed transcriptomic inputs may serve as a form of regularization, potentially improving generalization. We are currently testing this approach along with additional strategies inspired by the reviewers’ suggestions—such as selective sampling, a common technique in imbalanced classification settings. We look forward to reporting these future directions and incorporating them in the next iterations of the SMT.\n\n## Prediction vs Mapping\nWe frame our study as a prediction instead of a mapping task because (1) we have a single population average transcriptomic map and (2) we want to test more complex deep learning based methods on this task. \n\nIf paired transcriptomes and connectomes were available for multiple individuals, the problem could be framed as a true mapping task by holding out entire subject-level pairs for testing. Since we only have population averages here, we instead choose to partition connections of the brain into training and testing sets to evaluate whether learned transcriptome-connectome patterns generalize. If framed as a mapping task using the full population-average data, even a simple MLP with sufficient parameters could trivially overfit the connectome, whereas more constrained models like the Bilinear Connectome Model (see Figure 5) are not expressive enough to fully capture the variance. \n\nWe are excited to explore this problem as a mapping task in future work, potentially with graph-based methods, as more paired imaging-genetics are collected.\n\n## Transfer Learning\nIn most cases the cross-dataset generalization exceeds r>0.7, but the reviewer rightly points out that when trained on MPI 183 resolution, the model only reconstructs UKBB with a pearson-r of 0.55. While we do state that demographic differences may contribute to this result, this outlier result is much more likely due to parcellation differences. The MPI-183 parcellation has ~16k unique connections to train on whereas UKBB-S456 has ~103k. With far fewer samples in a more coarse spatial resolution, it is understandable that the MPI-183 model struggles to generalize across datasets and even within-dataset to more resolved parcellations.\n\nWe agree that additional transfer learning strategies could be further explored. One potential avenue that we are open to discussing with the reviewers, would be to add a metadata token to the model, so that a unified model can be trained across all datasets with awareness to demographics like age, sex, and ethnic background. This could lead to a more robust model and exploration of differences in subpopulations. \n\nReferences\n1. Vogel, J. W. et al. A molecular gradient along the longitudinal axis of the human hippocampus informs large-scale behavioral systems. 2020\n2. French, L. et al. Large-scale analysis of gene expression and connectivity in the rodent brain: insights through data integration. 2011"}, {"review_id": "QUdLD40Kqu", "reviewer": "Reviewer_a6QV", "summary": "This paper proposes using a transformer model SMT to predict brain connectivity from high-dimensional transcriptomic data, incorporating coordinate information to capture each brain region's 3D position. For evaluation, the authors leverage a Spatiomolecular Null Mapping technique to help rigorously control for spatial autocorrelation effects. Across within-dataset tasks on UK Biobank and MPI-LEMON, as well as cross-dataset and cross-resolution tasks, SMT consistently outperforms baseline methods. The interpretability analyses presented in the supplementary material further elucidate the mechanisms by which SMT makes its predictions.", "questions": "1. Why is the UMAP analysis for the MLP not provided in Figure 8?\n\n2. In the supplementary material (line 565), Figure 4 does not seem to include results for SMT w/ [CLS].", "limitations": "The author has adequately discussed the limitations.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n\n- The paper introduces a nonlinear model mapping gene expression to functional connectivity. Comprehensive evaluations on two UKB and MPI-LEMON datasets demonstrate that the proposed nonlinear models can better capture the robust relationship between gene expression and functional connectivity compared to baseline approaches.\n\n- The design of the baselines is great. The analysis based on rigorously defined spatiomolecular null mapping baselines clearly disentangles the respective roles of spatial location and gene expression in predicting functional connectivity. \n\n- The methodology is clearly described, and the overall manuscript is well-structured.\n\n**Weaknesses**\n\n- The major concern is that the proposed SMT does not appear to significantly outperform the MLP model. This raises questions about the necessity of adopting a more complex transformer architecture. The same types of analyses, such as UMAP and activated gene segments, could also potentially be performed using an MLP. The paper does not clearly articulate the specific advantages of SMT or the additional insights gained from using it.\n\n- Other concerns relates to clarity in implementation details:\n\n    1. The process of constructing the population-averaged paired dataset from the Allen Human Brain Atlas and UKB needs to be clearly described. Additionally, details on the amount of data remaining after population-averaging should be provided to improve understanding and reproducibility.\n\n    2. The setting and the impact of $\\alpha_0$ in the Target-Side Distributional Augmentation needs clarification.\n\n    3. In Table 6, how exactly were the Euclidean coordinates projected through fixed layers implemented?\n\n    4. The architecture details of SMT and MLP should be described. Furthermore, the hyperparameter search ranges used in the grid search should be reported to enhance reproducibility.", "was_revised": true, "final_justification": "This paper introduces a nonlinear model that maps gene expression to functional connectivity, with evaluations conducted on two large-scale datasets (UKB and MPI-LEMON). The methodological clarity, well-structured manuscript, and great design of spatiomolecular null mapping baselines and the corresponding analysis are strong aspects of the work. \n\nIn the rebuttal, the authors have addressed several previously raised concerns. Notably:\n\n- They clarified the processing pipelines for the datasets.\n\n- They provided additional details regarding the architectural configuration of SMT and MLP.\n\n- They elaborated on the procedure for projecting Euclidean coordinates using fixed layers.\n\nThese clarifications enhance the clarity and presentation of the paper. However, several important concerns remain unresolved:\n\n**Major concern:**\nThe central issue lies in the unclear benefit of using a Transformer architecture (SMT). The SMT model does not demonstrate a clear performance advantage over the MLP baseline, yet it introduces greater architectural complexity. As currently presented, the use of a Transformer appears unnecessary, and the model lacks architectural improvements that would justify its use in this context. This raises concerns about the clarity of the model’s contribution, and the inclusion of “Transformer” in the title may overstate its relevance.\n\n**Additional unresolved (minor) issues:**\n\n- The rebuttal does not clearly explain the selection or scheduling of the initial augmentation probability.\n\n- The information provided on hyperparameter tuning remains insufficient. The authors mention grid search but do not specify which parameters were tuned and what candidate values were explored. \n\nIn summary, the paper presents an interesting nonlinear modeling framework with comprehensive evaluations. However, the necessity and added value of using a Transformer architecture remain insufficiently justified, which affects the clarity and focus of the paper’s contribution.", "rebuttal": "We thank reviewer a6QV for their helpful and constructive feedback. In response, we have clarified the contributions of our study and expanded on several details, including population-averaging strategies and architecture components. We also thank the reviewer for their appreciation of our baseline and null modeling approach. Many of the baseline models we apply, such as the Connectome Model [1] and its low-rank form [2], have not yet been benchmarked on human data. The reviewer makes an excellent point regarding the comparable performance of SMT and MLP. We view this as a central finding of our study that modern non-linear architectures offer a significant leap in performance over traditional linear models, of which we believe this is the first paper this is studied and observed.\n\nWe hope to present both models not as competitors, but as exemplars of two distinct deep learning approaches in this problem space. The MLP establishes a powerful, general-purpose baseline. In contrast, the SMT provides a modular framework specifically designed to leverage the sequential nature of genomic data and test biologically-informed priors. This architecture enables unique advantages in 3 ways 1) its modularity for incorporating context, 2) its ability to take advantage of pretrained weights from other genomic foundation models, and 3) its interpretability via analyzing attention weights. We have revised the Discussion to articulate this framework and expanded our qualitative analysis to demonstrate the unique scientific insights afforded by the SMT described below:\n1. **Modular components.** The SMT is introduced as a unified model for connectome prediction, with modular components that integrate biological features such as genomic position and spatial context. The transformer architecture is well-suited for modeling structured, semantically rich inputs like genetic sequences, enabling more targeted hypothesis testing—such as evaluating the impact of transcription start site (TSS) ordering on connectivity prediction [3]. It also facilitates richer integration of auxiliary data beyond simple concatenation, using context tokens (e.g., [CLS]/[SEP] in BERT [3]) to encode chromosomal boundaries or functional gene groupings. This modularity makes SMT a strong foundation for future extensions incorporating personalized demographic or genomic information via learned vectors or embeddings.\n2. **Performance.**\nWe believe that incorporating pretrained models with finetuning may yield substantial improvements when paired with components described above. This is supported by findings across genomic foundation models such as HyenaDNA [4] and scBERT [5] citing large performance gains with pretraining. We discussed why this strategy was not yet implemented with reviewer NCYX, but which we will clarify in Future Directions.\n3. **Interpretability.**\nWe present an extension of our Figure 9 results to reviewer gLbH, demonstrating how attention weights can be paired with Gene Ontology tools to further scientific insight. This procedure enabled us to identify two relevant neuron projection gene modules that may be mechanistically related to functional connectivity.\nSMT attention offers a potential mechanistic bridge between GWAS loci and brain connectivity by highlighting not only which genomic regions are important, but also how they interact transcriptionally. For example, 19p13.11, an autism-associated region from Simons Foundation Autism Research Initiative maps to token 106 in our TSS-sorted input, which receives consistently high attention in cortical regions (see reviewer gLbH). The combination of token-level weights and token-token interactions are unique to attention-based models and may be difficult to extract using MLPs.\n\n## Implementation details\nHere, we add further details to be added to Section 2.1 and Supplement A2 to clarify the population averaging steps for the Allen Human Brain Atlas (AHBA), UKBB, and MPI-LEMON datasets. \n\n### Gene expression processing\n1. **Within-Donor Normalization.**\nGene expression values for all tissue samples are normalized within each donor to account for individual differences in signal scale or distribution. This is done using a scaled robust sigmoid transform, which standardizes values while preserving their rank order:\n$$\nx_{\\text{norm}} = \\frac{1}{1 + \\exp\\left( -\\frac{x_g - \\text{median}(x_g)}{\\text{IQR}(x_g)} \\right)}\n$$\nHere, x_g is the expression vector for gene g across all brain regions in a given donor, median(x_g) is its median, and IQR(x_g) is its interquartile range. This transformation is followed by min-max rescaling:\n$$\nx_{\\text{scaled}} = \\frac{x_{\\text{norm}} - \\min(x_{\\text{norm}})}{\\max(x_{\\text{norm}}) - \\min(x_{\\text{norm}})}\n$$\nUnlike z-scoring, this two-step normalization procedure is distribution-free and robust to outliers, allowing expression values to be placed on a comparable scale across donors.\n2. **Sample-to-Region Assignment.**\nFor each subject, tissue samples are assigned to the nearest brain region in the target parcellation using MNI coordinates, with anatomical constraints on hemisphere and cortical vs. subcortical divisions. Expression values are averaged within each region, yielding an r × g matrix (regions × genes) per subject.\n3. *Gene Selection and Filtering.*\nTo ensure that downstream analyses focus on biologically reliable signals, we apply a multi-step gene filtering procedure designed to retain only genes with consistent spatial expression patterns across donors. First, genes with expression below background noise are excluded. Then, we compute the differential stability of each gene g as:\n$$\n\\Delta_S(g) = \\frac{1}{\\binom{N}{2}} \\sum_{i=1}^{N-1} \\sum_{j=i+1}^{N} r(B_i(g), B_j(g))\n$$\nWhere B_i(g) is the regional expression profile of gene g in donor i, and N = 6 is the number of donors. Genes with high Δ_S(g) exhibit stable, reproducible spatial variation. We apply the strictest threshold recommended for the Schaefer-400 parcellation, yielding 7,380 stable genes.\n4. **Cross-Donor Aggregation**\nAfter normalization and filtering, expression values are averaged across donors. Missing regions are filled via bi-hemispheric mirroring and Gaussian smoothing over the 10 nearest neighbors, producing a complete region-by-gene matrix aligned to the target parcellation.\n\n### Functional connectivity processing\nEach subject underwent a resting-state fMRI scan capturing low-frequency BOLD fluctuations across brain regions. Functional connectivity (FC) was computed using Pearson correlation between the BOLD time series of each region pair, yielding an r x r FC matrix per subject. These matrices were then averaged across 1814 UKBB participants to produce a population-level FC matrix representing typical patterns of coordinated brain activity. The UKBB connectome is parcellated into 456 regions (~103k connections). As shown in Fig. 3A, the matrix exhibits canonical subnetwork structure. A similar connectome from 1065 HCP-YA (young adult) subjects (Pearson r = 0.9) suggests a stable population-level architecture across cohorts despite demographic differences.\n\n### Target augmentation\nTarget-side distributional augmentation was introduced to address the scarcity of unique transcriptomic samples relative to the abundance of connectome data, inspired by principles of curriculum learning/scheduled sampling. The strategy involves replacing target connectivity values with realistic alternatives drawn from the population distribution, intended as an ad-hoc pretraining/regularization strategy. As shown in Fig 4 and 7, the augmentation provides a modest performance gain across test and validation splits. While the effect is limited in the current setup, we believe this protocol offers a promising foundation for future work, particularly when combined with distribution-based loss functions or alternative sampling schedules, and may be useful for others tackling data imbalanced biological prediction problems.\n\n### Coordinate linear projection\nIn Figure 6, the Euclidean coordinates are projected through a linear layer into the same embedding space as the gene tokens, functioning as a CLS token that participates in attention. The projection weights are initialized from a uniform distribution between –k and k, where k is equal to 1 divided by the number of input features; in the learned case, the layer is differentiable, while in the fixed case, the weights remain frozen throughout training.\n\n### SMT/MLP details\nDetails on hyperparameter selection and search ranges are provided in Section A.2 of the supplement, and the exact grids for each model are available in the repository alongside model code in the /models directory. The MLP used in this study is a 2/3 layer architecture with dropout, layer norm, and AdamW optimizer trained on MSE loss, with learning rate scheduling and early stopping. The SMT uses a 2/4-layer transformer encoder with 2/4 attention heads and a similar MLP decoder; its token-based input reduces parameter count and encourages biologically meaningful genomic interactions.\n\n### Response to Questions\n1. The UMAP analysis for the MLP was omitted due to space limitations and because the MLP lacks a dedicated encoder, however, embeddings could be extracted from its final layer. We can include this analysis in the revised version for completeness.\n2. The results for SMT w/ CLS are present in Table 5.\n\nReferences\n1. Kovács, I. A. et al. Uncovering the genetic blueprint of the C. elegans nervous system. 2020.\n2. Qiao, M. Deciphering the genetic code of neuronal type connectivity through bilinear modeling. 2024\n3. Nguyen, E. et al. HyenaDNA: Long-range genomic sequence modeling at single nucleotide resolution. 2023\n4. Devlin, J. et al. BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding, 2019\n5. Yang, F. et al. scBERT as a large-scale pretrained deep language model for cell type annotation of single-cell RNA-seq data. 2022"}]

Author rebuttal:

Meta-review: Summary
This paper introduces the Spatiomolecular Transformer (SMT), a transformer-based framework for predicting functional brain connectivity from population-level regional gene expression. Intuitively, the architecture has two stages: first, an encoder builds region-level representations from transcriptomic data (Allen Human Brain Atlas), grouping genes into tokens ordered by transcription start site and adding a region CLS token processed by a transformer to output a region embedding; second, a decoder MLP uses pairs of these region embeddings to predict functional connectivity. The transcriptomic atlas is constant (6 AHBA donors), while target functional connectivities are varied during training across subjects (these are from UKBB, MPI-LEMON, HCP-YA). This pairing allows the model to generalize by exposing the fixed transcriptome to multiple subject-level connectomes (also functioning as label augmentation). A novel spatiomolecular null baseline is introduced to control for spatial autocorrelation.

Strengths
- Tackles a fundamental and timely neuroscience problem with careful experimental design.
- Rigorous evaluation across datasets, parcellations, and train/test split strategies, including stringent spatial splits and null baselines.
- Demonstrates that nonlinear models (MLP, SMT) consistently outperform linear and bilinear methods, with SMT showing additional strengths for long-range/geodesic connections.

Weaknesses
- Gains of SMT over simpler MLP baselines are modest, raising questions about the necessity of the transformer.
- Gene tokenization by TSS is based on a rough biological prior (genomic distance).

Decision Rationale
The consensus among reviewers is that this is a technically sound and carefully executed paper whose main strength lies in the modeling for linking transcriptomic and connectomic data, with thoughtful baselines and evaluations. The rebuttal added substantial new experiments (spatial splits, HCP-YA replication) that directly addressed key technical concerns and convinced one initially negative reviewer to raise their score, leading to a positive consensus. While the incremental gains of SMT over MLP remain debated, the reviewers agreed that the overall contribution is meaningful: it demonstrates the utility of nonlinear models in this domain while maintaining interpretability despite added complexity. I recommend poster here given the specialized scope of the application.

Reviewer Discussion
- All reviewers engaged constructively; the authors’ new experiments on spatial splits and HCP replication were well received.
- Reviewer Jt3G raised their score significantly after the rebuttal, shifting the consensus toward acceptance.
Decision: Accept (poster)