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BioKERN: Biological Kernel Regularization for Histology-to-Transcriptomics Neighborhood Retrieval

Seungik Cho, Betul Orcan-Ekmekci

arXiv:2608.24823v1cs.LGq-bio.QM

TL;DR

Exact-pair objectives can miss biologically related non-paired spots, motivating representations that preserve neighborhood structure. BioKERN learns a transcriptomic–spatial kernel for graded supervision and embedding regularization, improving biological-neighborhood retrieval across mouse brain and human liver while controlled experiments attribute most gain to the regularizer. The study is limited to two single-donor benchmarks and a scalar kernel mixture.

  • Problem

    Exact image–spot matching does not fully capture biologically related spots that share molecular or spatial context, while transcriptomic and spatial signals can vary in usefulness across tissues.

  • Method

    BioKERN learns a biological kernel combining transcriptomic similarity and spatial proximity, then uses it for graded neighborhood supervision and representation regularization.

  • Results

    BioKERN consistently improves biological-neighborhood retrieval over BLEEP across Mouse Brain Visium and Human Liver GSE240429 in single- and multi-scale settings, with most improvement attributed to biological-kernel regularization.

  • Takeaways & Limitations

    Explicit biological geometry provides an interpretable inductive bias for multimodal spatial representation learning within the evaluated settings.

  • Takeaways & Limitations

    Evaluation is limited to two single-donor benchmarks, and the method uses a scalar kernel mixture rather than richer region-dependent weighting.

Abstract

from arXiv · show

Spatially resolved biology requires representations that preserve biological neighborhood structure rather than only exact cross-modal correspondences. Existing histology--transcriptomics objectives can emphasize instance-level matching even when non-paired spots share molecular or spatial context. We introduce BioKERN, a multimodal spatial representation-learning framework that incorporates biological structure as an explicit, learnable inductive bias. BioKERN constructs a training-time biological kernel by combining transcriptomic similarity and spatial proximity, then uses it to provide graded neighborhood supervision and regularize embedding geometry. Evaluation uses a fixed, model-independent biological neighborhood definition shared by all methods. Across Mouse Brain Visium and Human Liver GSE240429, BioKERN consistently improves biological-neighborhood retrieval over BLEEP in both single- and multi-scale settings. Controlled shared-architecture experiments show that most of the improvement arises from biological-kernel regularization rather than increased model capacity. These results support explicit biological geometry as an interpretable inductive bias for multimodal learning in spatial biology.

1 Introduction

BioKERN addresses the limits of exact image–spot matching by learning representations that preserve graded biological neighborhoods. It combines transcriptomic and spatial structure through an explicit, learnable kernel and validates the approach with controlled comparisons.

  • Spatially adjacent spots, shared tissue domains, and transcriptionally similar locations can represent related biological states despite lacking exact correspondence.
  • Transcriptomic similarity and spatial proximity provide complementary biological signals whose relative utility can vary across tissues.
  • BioKERN learns a molecular–spatial reference kernel and uses it to regularize H&E–transcriptomics representations.
  • Biological neighborhood retrieval evaluates whether an H&E query retrieves transcriptomic states from the same biological neighborhood rather than only its exact pair.
  • BioKERN augments instance-level alignment with graded supervision derived from explicit biological neighborhood similarity.
  • A learned scalar weight combines transcriptomic similarity and spatial proximity into a compact, interpretable biological prior.
  • Shared-architecture controls, shuffled-kernel controls, and ablations indicate that biological-kernel regularization accounts for most improvement in biological-neighborhood retrieval.

2 Related Work

Prior work supports multimodal retrieval, spatial or graph-aware representations, and relational supervision beyond one-hot labels. BioKERN adapts these relational ideas by defining an explicit biological target geometry from transcriptomic and spatial similarity.

  • BLEEP learns a joint image–gene representation for retrieval-based expression prediction and uses similarity-smoothed targets to reduce purely instance-discriminative supervision.
  • Other multimodal and spatial methods incorporate spatial context or graph structure, including mclSTExp, ConGcR, SpaGCN, STAGATE, and GraphST.
  • Kernel alignment, relational representation learning, and supervised contrastive learning show that pairwise structure can guide representations beyond one-hot instance labels.
  • BioKERN adapts relational supervision to spatial biology through a learnable molecular–spatial reference kernel.

3 Method

BioKERN learns shared image–gene embeddings and constructs a biological reference kernel from transcriptomic and spatial similarity. Kernel-based neighborhood supervision and geometry regularization preserve biological structure during training, while inference uses only learned embeddings.

  • BioKERN combines multimodal representation learning, a learnable biological reference kernel, and kernel-regularized neighborhood supervision.
  • Frozen PLIP and PCA-based gene features are projected by ResidualAdapters into a shared d = 128 dimensional ℓ2-normalized space.
  • Single-scale uses a 96 × 96 H&E patch, while multi-scale fuses 96 × 96 and 224 × 224 patches to incorporate broader tissue context.
  • The training-time biological kernel combines transcriptomic and spatial similarity to define graded neighborhoods and supervise global and local embedding geometry.
  • BioKERN learns the molecular–spatial weighting end-to-end; across sections, spatial affinities are restricted within sections while transcriptomic affinities remain available across sections.
  • The retrieval objective retains exact image–gene correspondence while adding top-k non-self neighbors under K⋆ as graded biological targets.
  • At inference, an H&E query is ranked directly against reference transcriptomic embeddings by cosine similarity, without constructing the biological kernel.

4 Results

BioKERN was evaluated on Mouse Brain Visium and Human Liver GSE240429 using fixed biological-neighborhood labels across single- and multi-scale settings. It improved retrieval over BLEEP, with controlled experiments attributing most gains to biological-kernel regularization.

  • Benchmark setup: BioKERN achieved the highest Bio-mAP among shown baselines across both tissues and image-context settings.Human Liver gains were smaller but persisted under cross-slice transfer and remained competitive with Ridge.
  • Benchmark results: 0.6190 versus 0.5087 Bio-mAP on Mouse Brain SS, and 0.6716 versus 0.4960 on MS, marked BioKERN's gains over BLEEP.The comparison uses the exact Bio-mAP values reported for BLEEP and BioKERN in each setting.
  • Controlled analysis: 63–91% of total Bio-mAP improvement across four settings was attributed to biological regularization in the additive decomposition.On Mouse Brain SS, architecture, objective change, and biological regularization contributed +0.0240, +0.0037, and +0.0826, respectively.
  • Controlled analysis: The shuffled-kernel control indicates that meaningful biological pairwise structure matters rather than merely adding another relational loss.This control supports the specificity of the biological structure used for supervision.
  • Ablations: Removing biological-kernel supervision substantially reduced Bio-mAP, and removing Lsoft caused the largest degradation among the three biological objectives.The relative value of molecular and spatial structure also varied by tissue and scale; combined signals performed best on Mouse Brain and Human Liver MS, while Human Liver SS favored transcriptomic-only structure.

5 Conclusion

BioKERN introduces explicit biological geometry as an inductive bias for multimodal spatial representation learning. Its reported gains support biological-context retrieval, while the study remains bounded by limited benchmark diversity and a scalar kernel mixture.

  • 5 Conclusion: BioKERN uses a learnable molecular–spatial reference geometry for graded neighborhood supervision and relational regularization.This distinguishes it from approaches using only exact-pair matching or generic non-one-hot supervision.
  • 5 Conclusion: Across mouse brain and human liver, BioKERN improves biological-context retrieval, with controlled experiments attributing most gain to biological regularization rather than architectural complexity.The conclusion summarizes the cross-tissue result and the controlled attribution.
  • Limitations: The study is limited to two single-donor benchmarks and a scalar kernel mixture.The stated future directions include cross-donor and cross-platform transfer, richer region-dependent priors, and larger spatial resources.
  • 5 Conclusion: BioKERN provides a simple mechanism for injecting explicit biological structure into foundation-model-based multimodal representations for spatial biology.This is the paper's broader supported consequence within the stated scope.
  • Related work: Related work spans histology–transcriptomics alignment, direct gene-expression prediction, spatial neighborhood modeling, and kernel or relational regularization.BioKERN specifically studies explicit molecular–spatial target geometry within this broader literature.

B Additional Method Details

The method defines spatial-transcriptomics observations, projects image and gene modalities into a shared representation, and builds biological kernels for training-time neighborhood supervision and regularization.

  • B.1 Problem Definition: Each observation contains an H&E patch xi, gene-expression profile gi, and spatial coordinate si.The dataset is represented as D = {(xi, gi, si)}^N_i=1.
  • B.1 Problem Definition: The learned representation is intended to retrieve transcriptomic states in the same biological neighborhood rather than only the exact paired spot.This reframes the task from exact correspondence toward biological-neighborhood retrieval.
  • B.2 Image and Gene Representation: A frozen PLIP encoder and processed gene-expression features are projected by ResidualAdapters into a shared d = 128 dimensional space.The adapters operate on morphology and PCA-reduced transcriptomic inputs.
  • B.2 Image and Gene Representation: ResidualAdapters combine a linear projection with a two-layer GELU MLP and a learnable residual scale while keeping backbone parameters frozen.The MLP uses hidden dimension 256 and 10% dropout; the residual scale is initialized to 0.1.
  • Biological kernel: BioKERN constructs transcriptomic and spatial kernels, combines them into a reference biological kernel, and uses that kernel in the training objective.Spatial kernel values are zeroed across tissue sections, and bandwidths use the training-set median pairwise-distance heuristic.
  • Kernel-regularized training: The objective combines exact retrieval loss, soft neighborhood loss, and local kernel alignment.Soft neighborhoods use the top-k non-self neighbors with k = 20 within the current minibatch.
  • Inference: The biological kernel supplies training-time supervision but is not required for query-time ranking, which uses cosine similarity between embedded H&E queries and transcriptomic references.This separates biological-structure supervision from inference-time retrieval.

C.1 Datasets

The benchmark uses fixed train/test settings for Mouse Brain Visium and Human Liver GSE240429, with shared retrieval protocols and model-independent neighborhood evaluation. Experiments compare external and shared-backbone baselines across single- and multi-scale image contexts.

  • Datasets: Mouse Brain uses 2,200 spots split into 1,650 training and 550 test spots, with preprocessing fitted only on training spots.The fixed subset and split are used identically for all methods.
  • Datasets: Human Liver uses slices A1+B1+D1 for training and slice C1 for testing, with training-only preprocessing.The setting contains 6,963 training spots and 2,273 test spots.
  • Image contexts: Single-scale experiments use 96 × 96 H&E patches, while multi-scale experiments combine 96 × 96 and 224 × 224 representations with learned fusion.Both image-context settings are evaluated for the datasets.
  • Retrieval protocol: Retrieval receives only the H&E patch, while transcriptomic profiles form the held-out gallery and query-side biology supplies evaluation labels only.The exact paired profile remains in the gallery for exact-retrieval metrics but is excluded from biological-neighborhood positives.
  • Baselines: Baselines include CCA, Ridge, PLIP linear probe, naive PLIP zero-shot, BLEEP, and shared-ResidualAdapter variants.The internal variants are BLEEP∗, Ret-only, Rank, and Shuffled Kernel.
  • Evaluation: All methods share fixed biological-neighborhood definitions, including top-50 Bio-mAP positives and top-p% BioR positives after removing the exact paired index.BioR is reported for p ∈ {1, 5, 10}; GeneR and SpatR separately assess transcriptomic and spatial neighborhoods.
  • Metrics: MedRank measures exact-pair rank, PCC@k measures correlation with the mean retrieved expression profile, and ExR@k measures exact-pair top-k inclusion.Cluster-hit evaluation uses fixed Leiden labels, which are never provided to retrieval models.
  • Training: Neural models use AdamW, initial learning rate 3 × 10^-4, weight decay 10^-4, cosine annealing, batch size 256, and 60 epochs.Neighborhood size and loss weights are selected on held-out training data before final test evaluation.

D Full Benchmark Results

Across the four dataset and image-context benchmarks, the tables report biological-neighborhood retrieval under a common evaluation kernel and support sequential attribution of gains to architecture, objective, and biological regularization.

  • Full benchmark results: Mouse Brain single-scale and multi-scale benchmarks report biological-neighborhood retrieval for PLIP 96 × 96 and PLIP 96 × 96 + 224 × 224 settings.Both tables use the same fixed Keval and identify the best value in each column.
  • Full benchmark results: Human Liver single-scale and multi-scale benchmarks evaluate transfer from A1+B1+D1 to C1 under the same fixed Keval.The corresponding tables cover both image-context settings.
  • Effect decomposition: The additive decomposition defines sequential changes as architecture, objective, and biological-regularization steps from BLEEP through BLEEP∗ and Ret-only to BioKERN.The shuffled-kernel model is a separate sanity check rather than part of the additive path.
  • Effect decomposition: The biological-regularization step explains 74.9% of the Mouse Brain single-scale gain and 63.4% of the multi-scale gain.These percentages are reported in the Mouse Brain sequential effect decomposition.
  • Effect decomposition: The biological-regularization step explains 88.3% of the Human Liver single-scale gain and 90.6% of the multi-scale gain.These percentages are reported in the Human Liver sequential effect decomposition.
  • Ablations: Mouse Brain ablations keep the ResidualAdapter backbone and fixed evaluation kernel, while Human Liver ablations use the same fixed evaluation kernel and cross-slice masking.The ablation tables therefore control key evaluation and architecture conditions within each setting.

G Sensitivity and Learned Biological Weighting

Sensitivity analysis shows a trade-off between biological-neighborhood retrieval and exact-pair retrieval, while learned molecular–spatial weighting is stable across initializations and differs by tissue.

  • λs sensitivity: Increasing λs improves Bio-mAP while reducing exact-pair retrieval in the reported Mouse Brain sensitivity run.This post-hoc analysis supports selecting λs = 0.3 as a conservative validation-based operating point.
  • λs sensitivity: The sensitivity analysis is post hoc and is not used for test-set hyperparameter selection.The reported default is λs = 0.3.
  • Learned weighting: The learned biological-kernel weight α changes from 0.600 at initialization to approximately 0.615 on Mouse Brain single-scale.The trajectory is reported across five seeds.
  • Learned weighting: Additional α initializations of 0.2, 0.5, and 0.8 converge to similar final weights with Bio-mAP differences within seed-level variability.This indicates stability across the tested initializations.
  • Learned weighting: Human Liver consistently converges to a larger transcriptomic weight than Mouse Brain.The passage reports this as a cross-tissue pattern in learned weighting.

H Implementation and Reproducibility Details

Implementation details define training-only preprocessing, frozen PLIP image features, kernel construction and masking, constrained parameters, optimization, and reproducibility procedures.

  • Preprocessing: Mouse Brain preprocessing selects 3,000 highly variable genes after a fixed 1,650/550 train/test split and fits transformations on training data.Counts are normalized to 10,000 per spot and log1p transformed.
  • Preprocessing: Human Liver preprocessing fits gene selection, standardization, and PCA-128 on A1+B1+D1, then transforms C1 without refitting.Cross-slice spatial affinities are masked to zero.
  • Image features: Image features use 96 × 96 crops and optional 224 × 224 crops centered at each spot, processed by the frozen pretrained PLIP image encoder.Multi-scale experiments use both crop sizes.
  • Kernel construction: Kgene and Kspat are RBF kernels with bandwidths set by the median pairwise-distance heuristic on training data, and the biological kernel is recomputed per minibatch using current α.Human Liver sets Kspat(i, j) = 0 across different slices.
  • Evaluation controls: Evaluation uses a fixed model-independent kernel and removes the exact paired index before defining Bio-mAP, BioR, GeneR, and SpatR positives.The evaluation kernel is constructed independently of model predictions.
  • Optimization: Training uses AdamW with weight decay 10^-4, β1 = 0.9, β2 = 0.999, learning rate 3 × 10^-4, cosine annealing, batch size 256, and 60 epochs.Experiments run on a single NVIDIA A100 40 GB GPU without early stopping.
  • Parameterization: Constrained mixture weights are parameterized with sigmoid transforms, with α, ρ, and ws derived from unconstrained parameters.The unconstrained parameters and kernel-related terms use stated logit and logarithmic initializations.
  • Reproducibility: Loss weights and neighborhood size are selected on held-out training validation data, losses use mean normalization, and stochastic results average five random seeds.These procedures support reproducible final test evaluation.

I Limitations and Broader Directions

BioKERN’s evaluation is limited to two single-donor benchmarks and defines biological neighborhoods using a model-independent molecular–spatial kernel rather than expert annotations. Broader validation is needed to test transfer across tissues, datasets, donors, disease states, protocols, and platforms.

  • Evaluation scope: Evaluation uses only two single-donor benchmarks, limiting evidence across donors, disease states, processing protocols, and spatial-transcriptomics platforms.Human Liver tests cross-slice transfer within one donor, whereas Mouse Brain uses a within-section split.
  • Neighborhood definition: Biological neighborhoods rely on transcriptomic similarity and spatial proximity rather than external expert annotations.Bio-mAP uses a fixed, model-independent molecular–spatial kernel and should be interpreted alongside multiple complementary metrics.
  • Neighborhood definition: A single training-time mixture parameter α cannot represent region-specific changes in which biological signal is most informative.The scalar is stable to initialization but provides only global weighting within each trained model.
  • Broader directions: Larger-scale validation is needed to determine whether learned molecular–spatial weighting transfers across tissues and datasets.Proposed directions include multi-donor and disease-stratified evaluation and richer biological, morphological, pathway, and interaction priors.
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