cs.LGMar 24, 2026
SaveVision-based Deep Learning Analysis of Unordered Biomedical Tabular Datasets via Optimal Spatial Cartography
Organizations: Department of Radiation Oncology, Stanford University, Stanford, California, USA · Department of Radiology, Stanford University, Stanford, California, USA · Institute for Stem Cell Biology and Regenerative Medicine, Stanford University, Stanford, California, USA · Stanford Cancer Institute, Stanford University, Stanford, California, USA
Abstract
Tabular data are central to biomedical research, from liquid biopsy and bulk and single-cell transcriptomics to electronic health records and phenotypic profiling. Unlike images or sequences, however, tabular datasets lack intrinsic spatial organization: features are treated as unordered dimensions, and their relationships must be inferred implicitly by the model. This limits the ability of vision architectures to exploit local structure and higher-order feature interactions in non-spatial biomedical data. Here we introduce Dynamic Feature Mapping (Dynomap), an end-to-end deep learning framework that learns a task-optimized spatial topology of features directly from data. Dynomap jointly optimizes feature placement and prediction through a fully differentiable rendering mechanism, without relying on heuristics, predefined groupings, or external priors. By transforming high-dimensional tabular vectors into learned feature maps, Dynomap enables vision-based models to operate effectively on unordered biomedical inputs. Across multiple clinical and biological datasets, Dynomap consistently outperformed classical machine learning, modern deep tabular models, and existing vector-to-image approaches. In liquid biopsy data, Dynomap organized clinically relevant gene signatures into coherent spatial patterns and improved multiclass cancer subtype prediction accuracy by up to 18%. In a Parkinson disease voice dataset, it clustered disease-associated acoustic descriptors and improved accuracy by up to 8%. Similar gains and interpretable feature organization were observed in additional biomedical datasets. These results establish Dynomap as a general strategy for bridging tabular and vision-based deep learning and for uncovering structured, clinically relevant patterns in high-dimensional biomedical data.
Figures & tables
Figure 1: Overview of the Dynomap framework for spatial representation learning of tabular data. a , Tabular biomedical measurements are first represented as a feature matrix in which each column corresponds to a biological variable (e.g., gene expression, molecular measurement, or phenotypic descriptor) and each row corresponds to a sample. Dynomap assigns each feature a learnable coordinate in a continuous two-dimensional space, allowing relationships among variables to be represented as spatial proximity. b , During training, feature coordinates and rendering parameters are optimized jointly with the predictive model. Each feature contributes to the image through a Gaussian kernel whose location and intensity depend on the learned coordinates and feature values, producing a continuous spatial map for each sample (Dynomap). These sample-specific spatial representations are processed by a convolutional neural network to perform downstream tasks such as classification or regression. Because the spatial layout is learned directly from the prediction objective, features that contribute to the same biological signal tend to form coherent spatial neighborhoods.
Figure 2: Dynomap performance and learned representations for liquid biopsy cfRNA classification. a–f , Comparative evaluation of Dynomap and eleven baseline methods across three prediction tasks using circulating cell-free RNA profiles. Models were assessed on binary healthy versus cancer classification ( a , b ), multiclass cancer subtype prediction ( c , d ), and cancer stage classification ( e , f ). For each task, performance is reported under two feature regimes: highly variable genes (left panels) and a curated gene signature panel (right panels). Metrics include accuracy, macro-F1 score, recall, and specificity. Error bars indicate standard deviation across five cross-validation folds. Dynomap achieves the highest performance across most reported metrics in both feature settings. g , Representative task-optimized image representations generated by Dynomap for subtype classification. Each group of four images corresponds to samples from a distinct cancer class. The images exhibit reproducible spatial patterns within classes, reflecting task-adaptive spatial organization learned directly from tabular gene expression inputs.
Figure 3: Task-dependent gene attribution patterns learned by Dynomap in liquid biopsy cfRNA. a , Normalized mean absolute Integrated Gradients (|IG|) for cancer stage classification using highly variable genes. Rows correspond to stage classes (I–IV), and columns denote the highest-attribution genes. Distinct stages are associated with different gene attribution profiles. b , Stage classification using the 622-gene signature panel. Attribution patterns remain class-dependent. c , Multiclass subtype classification using highly variable genes. Each tumor type (LIHC, LUAD, PAAD, PRAD) is characterized by a distinct subset of high-attribution genes. d , Subtype classification under the signature panel setting, showing task-adaptive shifts in emphasized genes relative to the full-gene regime. e , Differential attribution for binary healthy versus cancer prediction using highly variable genes. Bars indicate normalized class-specific attribution differences (delta |IG|), with positive values favoring healthy prediction and negative values favoring cancer prediction. f , Differential attribution under the signature panel setting. Cancer and healthy-associated genes exhibit minimal overlap and form distinct attribution profiles. Together, these panels demonstrate that Dynomap learns task and class-dependent gene importance patterns that vary across prediction objectives and feature regimes.
Figure 4: Benchmarking Dynomap on bulk transcriptomic classification (GSE68086). a , Binary healthy versus cancer classification. Performance is reported across accuracy, macro-F1 score, recall, and specificity for Dynomap and eleven baseline methods. Dynomap achieves the highest performance across all reported metrics, with consistent gains in both sensitivity- and specificity-based measures. b , Multiclass tissue-of-origin classification. Despite increased class complexity, Dynomap maintains superior accuracy, macro-F1 score, and recall relative to conventional tabular baselines. Specificity remains high across methods, while Dynomap preserves balanced class discrimination. Error bars represent standard deviation across five cross-validation folds.
Figure 5: Class-specific spatial organization and attribution structure in bulk transcriptomic data (GSE68086). a , Learned gene layouts with class-specific attribution overlaid. Gray points represent all genes positioned in the optimized two-dimensional layout. Colored points indicate genes with high Integrated Gradients attribution for the specified class. Top row: binary classification (Cancer, left; Healthy, right). Middle row: multiclass setting (Pancreas, left; Breast, right). Bottom row: multiclass setting (Glioblastoma, left; Colorectal cancer, right). Distinct classes activate spatially localized gene regions rather than overlapping uniformly across the map. b , Heatmap of normalized mean absolute attribution across cancer types for the highest-ranked genes. Rows correspond to genes and columns to tumor classes. Distinct attribution profiles are observed for different cancer types, with limited overlap among the most emphasized genes. c , Differential attribution for binary classification. Bars represent normalized class-specific attribution differences, with positive values favoring healthy prediction and negative values favoring cancer prediction. d , Quantification of spatial structure. Moran’s I (spatial autocorrelation) and kNN purity scores are shown for each cancer type. Observed values exceed null expectations derived from shuffled layouts, indicating that class-associated genes form statistically significant spatial neighborhoods in the learned representation.
Figure 6: Spatial organization and phenomic feature attribution in Parkinson’s disease classification. a , Quantification of spatial structure in the learned feature layout. Moran’s I (spatial autocorrelation) and kNN purity are shown for Control and Parkinson classes. Observed values are compared to null expectations derived from shuffled layouts, indicating non-random spatial clustering of class-associated features. b , kNN family coherence across engineered feature families (e.g., tqwt, MFCC, delta, and related descriptors). Observed coherence exceeds null distributions, indicating that features derived from similar extraction families occupy nearby spatial regions in the learned layout. c , Differential feature attribution for binary classification. Bars represent normalized class-specific attribution differences (delta |IG|), with positive values favoring Parkinson prediction and negative values favoring Control prediction. Distinct sets of acoustic features contribute to each class. d , Confusion matrix showing counts of true and predicted labels for Control and Parkinson samples. e , Comparative performance across models. Accuracy, macro-F1 score, recall, and specificity are reported for Dynomap and eleven baseline methods. Dynomap achieves the strongest overall performance across class-balanced metrics. Error bars represent standard deviation across five cross-validation folds.
Figure 7: Binary and molecular subtype classification in breast cancer transcriptomes (TCGA-BRCA). a , Comparative performance of Dynomap and eleven baseline methods for binary classification of non-aggressive versus aggressive tumors. Metrics include accuracy, macro-F1 score, recall, and specificity. Dynomap achieves the highest overall performance across class-balanced measures. Error bars indicate standard deviation across five cross-validation folds. b , Multiclass molecular subtype classification (Basal, HER2, LumA, LumB, Normal). Dynomap maintains superior accuracy and balanced performance across macro-F1, recall, and specificity relative to conventional and advanced tabular baselines. c , Precision-Recall curve for subtype classification. d , Normalized Integrated Gradients attribution for representative genes across molecular subtypes. Distinct gene groups are preferentially associated with individual subtypes. e , Differential attribution for binary stratification into non-aggressive and aggressive tumors. Bars represent class-specific attribution differences (delta |IG|), with positive values indicating greater contribution to aggressive prediction and negative values to non-aggressive prediction.
Figure 8: Cell-type classification and spatial organization in single-cell transcriptomes (Tabula Muris). a , Comparative performance of Dynomap and eleven baseline methods for multiclass cell-type classification. Metrics include accuracy, macro-F1 score, recall, and macro-specificity. Dynomap achieves the highest overall performance across class-balanced measures. Error bars indicate standard deviation across cross-validation folds. b , Spatial organization analysis for representative cell types. Moran’s I (spatial autocorrelation) and kNN purity are shown alongside null expectations derived from shuffled layouts. Observed values exceed null distributions, indicating non-random clustering of cell-type–associated genes in the learned layout. c , Precision–recall curve demonstrating stable performance across recall thresholds. d , Normalized Integrated Gradients attribution for representative genes across selected cell types. Distinct gene groups are preferentially associated with individual cellular identities, indicating class-dependent attribution structure within the learned spatial representation.
Appendix figures & tables29 assets
Supplementary material from the paper’s appendix.
Appendix
Figure S1: Detailed illustration of Dynomap construction from learned feature coordinates. a , Tabular biomedical measurements are first organized into a feature matrix, where each column corresponds to a biological variable and each row represents a sample. Dynomap assigns every feature a learnable coordinate in a continuous two-dimensional space, establishing a spatial layout that reflects task-dependent relationships among variables. b , During model training, both the feature coordinates and rendering parameters are updated jointly with the predictive model. Feature values are projected onto the spatial grid through Gaussian kernels whose location corresponds to the learned feature coordinate and whose intensity reflects the feature magnitude. The resulting spatial maps are used as inputs to a convolutional neural network to perform downstream tasks such as classification or regression. c , Detailed rendering process for a single sample. Each feature value generates a Gaussian kernel centered at its learned coordinate. The superposition of all kernels produces a continuous two-dimensional surface, which is discretized into an image representation referred to as a Dynomap. This process preserves feature identity while translating tabular measurements into a spatial representation that can be analyzed using vision-based models.
Figure S2: Representative Dynomap image embeddings across RARE-Seq classes. Dynomap-generated image representations for individual RARE-Seq cfRNA samples, shown as class-wise examples across tasks. Within each class, samples exhibit visually consistent spatial organization, whereas different classes display distinct spatial configurations. These qualitative patterns illustrate that Dynomap maps tabular expression profiles into structured image-like representations without relying on a predefined gene layout. Color intensity denotes the normalized painted signal on the learned spatial canvas, with higher intensity corresponding to stronger localized contribution.
Figure S3: Spatial organization of class-specific gene attributions in RARE-Seq binary classification. Spatial autocorrelation and neighborhood consistency of Integrated Gradients (IG) attribution maps for healthy versus cancer prediction, quantified using Moran’s and kNN purity. a , Observed Moran’s values for cancer- and healthy-associated genes compared with null distributions generated by spatial permutation. Cancer-associated attributions exhibit stronger deviation from null expectations, indicating non-random spatial organization. b , kNN-based neighborhood purity for the same attribution maps. Cancer-associated genes show elevated local neighborhood consistency relative to null expectations, whereas healthy-associated attributions display weaker spatial structure. Together, these results demonstrate that Dynomap organizes cancer-relevant genes into spatially coherent regions even in a binary classification setting.
Figure S4: Stage-specific spatial structure of gene attributions in RareSeq. Spatial statistics of Integrated Gradients (IG) attribution maps for cancer stage prediction (Stages I–IV), assessed using Moran’s and kNN purity. a , Observed Moran’s values across stages compared with null distributions, revealing heterogeneous spatial organization of stage-specific gene importance. Stages II and IV show stronger spatial autocorrelation than expected under random layouts. b , kNN purity analysis indicates elevated local neighborhood consistency for multiple stages, confirming that genes emphasized for the same stage tend to cluster spatially. These results indicate that Dynomap adapts its spatial organization to disease progression, redistributing predictive gene signal in a stage-dependent manner.
Figure S5: Subtype-dependent spatial clustering of gene attributions in RareSeq. Quantification of spatial autocorrelation and neighborhood consistency for subtype-specific Integrated Gradients (IG) attribution maps across multiple cancer types. a , Moran’s values for liver hepatocellular carcinoma (LIHC), lung adenocarcinoma (LUAD), pancreatic adenocarcinoma (PAAD), and prostate adenocarcinoma (PRAD), shown alongside null expectations. Subtypes exhibit distinct autocorrelation profiles, reflecting task-specific spatial organization. b , kNN purity scores demonstrate consistently elevated neighborhood consistency across subtypes relative to null distributions, indicating robust spatial clustering of subtype-relevant genes. These patterns show that Dynomap induces subtype-specific spatial structure rather than relying on a shared set of globally dominant genes.
Figure S6: Class-specific feature attribution projected onto the Dynomap layout for RARE-Seq binary classification. a,b , Cancer-class layouts showing gene positions colored by normalized mean Integrated Gradients (IG) values within class. c,d , Corresponding healthy-class layouts. Gray points indicate all genes in the layout, while colored points highlight genes with higher class-specific attribution.
Figure S7: Stage-specific Dynomap layouts for RARE-Seq stages I and II. a,b , Stage I layouts showing IG-weighted gene importance. c,d , Stage II layouts. Gene positions are fixed across stages, enabling direct comparison of how discriminative regions shift with disease progression.
Figure S8: Stage-specific Dynomap layouts for RARE-Seq stages III and IV. a,b , Stage III layouts colored by normalized IG values. c,d , Stage IV layouts. Later-stage disease is associated with altered spatial emphasis patterns while preserving the underlying gene layout geometry.
Figure S9: Subtype-specific Dynomap layouts for RARE-Seq (subset 1). a,b , IG-weighted gene layouts for two molecular subtypes. Colored points represent genes with higher subtype-specific attribution, while gray points denote the full gene set. Distinct spatial emphasis patterns are observed across subtypes within a shared layout.
Figure S10: Subtype-specific Dynomap layouts for RARE-Seq (subset 2). a,b , Additional subtype layouts highlighting class-specific attribution patterns. c,d , Corresponding complementary subtypes. The reuse of a common spatial scaffold allows subtype distinctions to emerge through localized attribution rather than global rearrangement.
Figure S11: Effect of highly variable gene (HVG) selection on classification performance in RareSeq. Classification accuracy is shown as a function of the number of HVGs used to construct the input representation. Top , Binary cancer versus healthy classification. Bottom , Multiclass subtype classification. Dynomap maintains consistently higher accuracy across a wide range of HVG counts compared with baseline methods, demonstrating robustness to feature dimensionality and stability of the learned representation under varying gene selection regimes.
Figure S12: Differential gene importance for binary healthy vs. cancer detection. Horizontal bars indicate the normalized difference in Integrated Gradients (IG) attribution strength between classes. a , Differential attribution using the full gene set shows distinct molecular signatures for healthy (red) and cancer (blue) predictions. b , Differential attribution using the 622-gene signature panel reveals a more concentrated set of discriminative features. The shift in specific top-ranked genes across settings demonstrates that Dynomap adapts its feature selection strategy based on the available genomic space.
Figure S13: Subtype-specific gene attribution across cfRNA profiles. Heatmaps of normalized Integrated Gradients (IG) show distinct transcriptional programs utilized for multiclass cancer subtype classification. a , Gene utilization for subtype prediction (LIHC, LUAD, PAAD, PRAD) using the full gene set. b , Subtype-specific attribution patterns using the 622-gene signature panel. While top predictive genes differ between feature regimes, the model consistently identifies non-overlapping gene sets for each tumor class, supporting the emergence of class-separable spatial representations.
Figure S14: Gene-level attribution for liquid biopsy cancer stage prediction. Task-adaptive feature importance profiles across clinical stages (I, II, III, and IV). a , Normalized mean Integrated Gradients (|IG|) for top predictive genes using the full gene set. b , Stage-specific attribution using the 622-gene signature panel. The model identifies a more compact set of stage-informative genes, reflecting a redistribution of predictive signal when the feature space is restricted. The distinct patterns across columns confirm that Dynomap captures subtle signals necessary for fine-grained clinical stratification.
| Fcer1g | Ubb | Cd79a | Cd79b | Cd3g | Bst2 | Il1b | Vpreb3 |
| Cfh | Cst3 | Fxyd5 | Tmsb10 | Laptm5 | Lsp1 | Gnas | Gng11 |
| S100a4 | Alox5ap | Ly6c1 | Plvap | Ctsl | Irf8 | H2_K1 | Tpm2 |
| Klf2 | Lyz2 | Sepp1 | Ccl3 | Vim | Socs3 | Lyz1 | Igfbp2 |
| Krt14 | Ramp2 | Ckb | Oaz1 | Gm1821 | Marcksl1 | Arpc2 | Arpc3 |
| Hbb_b2 | Car2 | Scgb1a1 | Prss34 | Ccl9 | Defb1 | Tyrobp | Gzma |
| AW112010 | Nkg7 | Ifitm1 | Tg | H2_D1 | Emp3 | Hmgb2 | Lgals1 |
Table S1: Tabula Muris SHAP gene list (part 1 of 3; first 400 genes).
| Park7 | Rpl17 | Sub1 | Ube2i | Erp29 | Mcpt8 | Icam1 | Tsc22d1 |
| Atp5e | Fxyd3 | Rps18 | Ndufb9 | x3110003A17Rik | Dmkn | Uqcrfs1 | Rps19 |
| Rps25 | Ltb | Hnrnpab | Plac9 | Dnaja1 | Itm2b | Id1 | Ier3 |
| Rarres2 | Csrp2 | Mmp3 | Calm1 | Gnai2 | Pfdn5 | Sumo2 | Ctnnb1 |
| Atp5j | Cox4i1 | Rpsa | Slc25a4 | Cct7 | Ddx5 | Atp5h | Rpl23a |
| Snrpd2 | Tagln | Chmp2a | Ndufa4 | Ccl5 | Nbl1 | Rps21 | Uqcrb |
| Rpl10 | Arpc1a | Rpl10a | Akr1a1 | Etfb | Pomp | Srgn | Ubc |
Table S2: Tabula Muris SHAP gene list (part 2 of 3; next 400 genes).
| Acp5 | Rap1b | Hspb8 | Col2a1 | Il6 | Tomm20 | Dsp | Klf4 |
| Malat1 | Epsti1 | Ccl2 | Has1 | Neat1 | Prelid1 | Calr | Hspb1 |
| P4hb | Ppib | Fdps | Mup3 | Cxcl14 | Cxcl2 | x2010107E04Rik | Hrsp12 |
| Miox | Cat | Col8a1 | Cxcl10 | Mgst1 | C1qc | Rpl13a | Mpo |
| Lcn2 | Prtn3 | Eif3e | Gas5 | Impdh2 | Npm1 | Tagln2 | Cox7b |
| Hsp90ab1 | Tcp1 | Procr | Psmb1 | Trf | Emp1 | x1500015O10Rik | Hist1h2ao |
| Myl7 | Tpm1 | Rab11a | Akr1b8 | Rpl36 | Scgb3a2 | Sbpl | Scgb3a1 |
Table S3: Tabula Muris SHAP gene list (part 3 of 3; remaining 288 genes).
Figure S15: Precision-Recall and ROC analysis for Tabula Muris cell type classification. a , Receiver Operating Characteristic (ROC) curve showing the True Positive Rate (TPR) against the False Positive Rate (FPR). Dynomap (solid orange line) achieves near-perfect area under the curve (AUC), significantly outperforming baseline methods. b , Precision-Recall curves across various cell types. Dynomap maintains high precision across the entire recall range, demonstrating robust classification even for rare or heterogeneous cell populations.
Figure S16: Quantification of spatial organization across cell lineages in the Tabula Muris atlas. Observed Moran’s I (spatial autocorrelation, dark red circles) and kNN purity (neighborhood consistency, light orange squares) are compared against null distributions (blue diamonds and triangles with error bars). For nearly all cell types, including immune and stromal populations, the observed scores significantly exceed null expectations. This confirms that cell-type-specific transcriptional programs are organized into coherent spatial neighborhoods within the learned Dynomap layout.
Figure S17: Jaccard similarity matrix of learned spatial neighborhoods for cell types. Heatmap values represent the overlap between the top predictive feature sets of different cell types. The strong diagonal indicates highly stable and distinct spatial neighborhoods for individual classes. Sparse off-diagonal signals reveal biologically expected similarities between related cell lineages, such as different subtypes of immune or endothelial cells.
Figure S18: Hierarchical clustering of cell type attribution profiles. This dendrogram illustrates the relationships between cell types based on their Integrated Gradients (IG) feature importance. Closely related cell types, such as various B cell stages or lung-specific populations, cluster together. This demonstrates that the Dynomap framework captures a hierarchical representation of biological identity directly from single-cell transcriptomic data.
Figure S19: Hierarchical organization of predictive genes in the Tabula Muris dataset. The dendrogram shows clustering of genes based on their spatial proximity and attribution patterns across cell types. Functional gene modules associated with specific cellular processes form distinct branches. This indicates that Dynomap learns to group genes with similar biological roles into organized spatial structures.
Figure S20: Comprehensive feature attribution heatmap for single-cell lineages. The heatmap displays normalized Integrated Gradients (IG) values for top predictive genes (rows) across dozens of cell types (columns). Distinct vertical bands highlight marker genes uniquely utilized by the model for specific lineages, such as Cd3g for T cells and Hepatocyte -specific markers. The sparse structure confirms that the model relies on specialized transcriptional signatures to distinguish between complex cellular identities.
Figure S21: Class-specific gene attribution for breast cancer risk stratification. Heatmap of normalized Integrated Gradients (IG) for the top 50 predictive genes in the binary task (Aggressive vs. Non-aggressive). The model utilizes distinct sets of genes to identify aggressive phenotypes, including C6orf211 and ARSG , while non-aggressive tumors are characterized by a different molecular signature featuring KCNQ5 and DLGAP1 . The clear vertical separation of high-attribution scores confirms that Dynomap learns non-overlapping transcriptional programs for clinical risk assessment.
Figure S22: Predictive performance for binary risk stratification in TCGA-BRCA. a , Receiver Operating Characteristic (ROC) curve and b , Precision-Recall (PR) curve for the Aggressive vs. Non-aggressive classification task. Dynomap (solid line) achieves high area under the curve (AUC) values, demonstrating robust discrimination even in the presence of tumor heterogeneity. The high precision maintained across recall levels indicates that the model’s risk assessments are highly reliable for aggressive cases.
Figure S23: Multiclass performance for breast cancer molecular subtype prediction. a , ROC and b , Precision-Recall curves for five intrinsic subtypes (LumA, LumB, Basal, HER2, and Normal-like). Dynomap maintains superior precision-recall trade-offs across all subtypes compared to baseline averages. Performance is particularly strong for the Basal and HER2-enriched subtypes, which exhibit the most distinct molecular signatures in the learned spatial representation.
Figure S24: Hierarchical relationship of breast cancer subtype attribution profiles. The dendrogram illustrates the clustering of molecular subtypes based on similarities in their feature attribution (Integrated Gradients) profiles. Luminal A and Luminal B subtypes cluster together, reflecting their shared hormonal signaling pathways, while the Basal-like subtype forms a distinct branch. This hierarchical structure confirms that the model’s internal logic aligns with established clinical and biological relationships between tumor subtypes.
Figure S25: Spatial quantification of learned representations in TCGA-BRCA. Observed Moran’s I (spatial autocorrelation) and kNN purity (neighborhood consistency) for the binary (red) and multiclass (blue) tasks are compared against null distributions. In both experimental settings, the observed metrics significantly exceed random expectations. This demonstrates that Dynomap consistently organizes subtype-specific and risk-associated genes into coherent spatial neighborhoods regardless of the classification objective.
Figure S26: Reproducibility and stability of learned spatial layouts in Parkinson’s disease classification. a, Mean consensus layout across repeated training runs. Feature coordinates are averaged following Procrustes alignment to account for rotational and translational invariance. The resulting configuration demonstrates stable spatial organization of phenomic features across independent model initializations. b, Layout consensus uncertainty. The spatial dispersion of each feature across repeated runs is quantified as coordinate variance after alignment. Most features exhibit low positional variance, indicating convergence toward a consistent spatial configuration. c, Pairwise Procrustes distance matrix between independently trained layouts. Distances are computed after optimal alignment of feature coordinates. Low pairwise distances confirm high structural similarity between learned layouts across runs, demonstrating that the spatial representation is reproducible rather than driven by random initialization.
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