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

Seungik Cho; Betul Orcan-Ekmekci

cs.LGAug 25, 2026

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

Authors: Seungik Cho, Betul Orcan-Ekmekci

Organizations: Department of Physics and Astronomy Rice University Houston, TX 77005 · Department of Mathematics Rice University Houston, TX 77005

Abstract

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.

Figures & tables

Figure 1: BioKERN overview. Multimodal image and gene representations are regularized during training using a biological reference kernel combining transcriptomic and spatial similarity. The kernel defines graded neighborhoods and supervises global and local embedding geometry; inference requires only the learned image and transcriptomic embeddings.

Dataset / Scale	Ridge	PLIP linear	BLEEP	BLEEP ∗	BioKERN
Mouse Brain SS	0.4902	0.5407 $\pm$ .0033	0.5087 $\pm$ .0033	0.5327 $\pm$ .0036	0.6190 $\pm$ .0023
Mouse Brain MS	0.5567	0.5831 $\pm$ .0023	0.4960 $\pm$ .0056	0.5541 $\pm$ .0040	0.6716 $\pm$ .0021
Human Liver SS	0.0383	0.0307 $\pm$ .0001	0.0302 $\pm$ .0005	0.0309 $\pm$ .0004	0.0396 $\pm$ .0007
Human Liver MS	0.0403	0.0319 $\pm$ .0005	0.0312 $\pm$ .0005	0.0321 $\pm$ .0005	0.0408 $\pm$ .0005

Table 1: Biological-neighborhood retrieval across tissues and scales. Bio-mAP uses the same fixed

K_{\mathrm{eval}}

for every method; stochastic methods are mean

\pm

standard deviation over five seeds.

Appendix figures & tables12 assets

Supplementary material from the paper’s appendix.

Appendix

Method	Bio-mAP $\uparrow$	BioR@5% $\uparrow$	GeneR@5% $\uparrow$	SpatR@5% $\uparrow$	ClsHit@10 $\uparrow$	ExR@10 $\uparrow$	MedRank $\downarrow$	PCC@10 $\uparrow$
CCA	0.3910 $\pm$ 0.0000	0.3677 $\pm$ 0.0000	0.3558 $\pm$ 0.0000	0.3100 $\pm$ 0.0000	0.6409 $\pm$ 0.0000	0.3709 $\pm$ 0.0000	18.00 $\pm$ 0.00	0.7782 $\pm$ 0.0000
Ridge	0.4902 $\pm$ 0.0000	0.3919 $\pm$ 0.0000	0.4094 $\pm$ 0.0000	0.2941 $\pm$ 0.0000	0.6105 $\pm$ 0.0000	0.2509 $\pm$ 0.0000	27.00 $\pm$ 0.00	0.7670 $\pm$ 0.0000
PLIP zero-shot	0.1653 $\pm$ 0.0000	0.0647 $\pm$ 0.0000	0.0794 $\pm$ 0.0000	0.0599 $\pm$ 0.0000	0.1469 $\pm$ 0.0000	0.0327 $\pm$ 0.0000	202.50 $\pm$ 0.00	0.6716 $\pm$ 0.0000
PLIP linear	0.5407 $\pm$ 0.0033	0.4685 $\pm$ 0.0025	0.4288 $\pm$ 0.0028	0.4068 $\pm$ 0.0016	0.7175 $\pm$ 0.0042	0.4956 $\pm$ 0.0162	10.80 $\pm$ 0.75	0.7852 $\pm$ 0.0003
BLEEP	0.5087 $\pm$ 0.0033	0.4510 $\pm$ 0.0024	0.4034 $\pm$ 0.0043	0.3979 $\pm$ 0.0033	0.6928 $\pm$ 0.0045	0.4938 $\pm$ 0.0096	10.80 $\pm$ 0.75	0.7842 $\pm$ 0.0003
BLEEP ∗	0.5327 $\pm$ 0.0036	0.4674 $\pm$ 0.0036	0.4250 $\pm$ 0.0028	0.4091 $\pm$ 0.0048	0.7136 $\pm$ 0.0046	0.4887 $\pm$ 0.0086	10.90 $\pm$ 0.20	0.7851 $\pm$ 0.0004

Appendix

Table D.1: Biological Neighborhood Retrieval on Mouse Brain Visium (single-scale, PLIP

96\times 96

). Mean

\pm

standard deviation over five random seeds. All methods use the same fixed

K_{\mathrm{eval}}

; bold indicates the best value in each column.

Method	Bio-mAP $\uparrow$	BioR@5% $\uparrow$	GeneR@5% $\uparrow$	SpatR@5% $\uparrow$	ClsHit@10 $\uparrow$	ExR@10 $\uparrow$	MedRank $\downarrow$	PCC@10 $\uparrow$
CCA	0.2813 $\pm$ 0.0000	0.2661 $\pm$ 0.0000	0.2585 $\pm$ 0.0000	0.2316 $\pm$ 0.0000	0.5162 $\pm$ 0.0000	0.2673 $\pm$ 0.0000	34.00 $\pm$ 0.00	0.7662 $\pm$ 0.0000
Ridge	0.5567 $\pm$ 0.0000	0.4596 $\pm$ 0.0000	0.4692 $\pm$ 0.0000	0.3484 $\pm$ 0.0000	0.6931 $\pm$ 0.0000	0.3327 $\pm$ 0.0000	19.00 $\pm$ 0.00	0.7753 $\pm$ 0.0000
PLIP zero-shot	0.0956 $\pm$ 0.0000	0.0178 $\pm$ 0.0000	0.0255 $\pm$ 0.0000	0.0197 $\pm$ 0.0000	0.0660 $\pm$ 0.0000	0.0036 $\pm$ 0.0000	326.00 $\pm$ 0.00	0.6399 $\pm$ 0.0000
PLIP linear	0.5831 $\pm$ 0.0023	0.5109 $\pm$ 0.0039	0.4494 $\pm$ 0.0037	0.4588 $\pm$ 0.0016	0.7471 $\pm$ 0.0051	0.5418 $\pm$ 0.0072	9.00 $\pm$ 0.00	0.7858 $\pm$ 0.0003
BLEEP	0.4960 $\pm$ 0.0056	0.4647 $\pm$ 0.0037	0.4074 $\pm$ 0.0033	0.4263 $\pm$ 0.0048	0.7183 $\pm$ 0.0043	0.5298 $\pm$ 0.0154	9.40 $\pm$ 0.49	0.7864 $\pm$ 0.0004
BLEEP ∗	0.5541 $\pm$ 0.0040	0.4981 $\pm$ 0.0032	0.4465 $\pm$ 0.0035	0.4458 $\pm$ 0.0023	0.7506 $\pm$ 0.0030	0.5549 $\pm$ 0.0071	8.60 $\pm$ 0.49	0.7876 $\pm$ 0.0002

Appendix

Table D.2: Biological Neighborhood Retrieval on Mouse Brain Visium (multi-scale, PLIP

96\times 96+224\times 224

). All methods use the same fixed

K_{\mathrm{eval}}

. Bold indicates the best value in each column.

Method	Bio-mAP $\uparrow$	BioR@5% $\uparrow$	GeneR@5% $\uparrow$	SpatR@5% $\uparrow$	ClsHit@10 $\uparrow$	ExR@10 $\uparrow$	MedRank $\downarrow$	PCC@10 $\uparrow$
CCA	0.0265 $\pm$ 0.0000	0.0513 $\pm$ 0.0000	0.0518 $\pm$ 0.0000	0.0511 $\pm$ 0.0000	0.1974 $\pm$ 0.0000	0.0053 $\pm$ 0.0000	1129.0 $\pm$ 0.0	0.8574 $\pm$ 0.0000
Ridge	0.0383 $\pm$ 0.0000	0.0696 $\pm$ 0.0000	0.0742 $\pm$ 0.0000	0.0552 $\pm$ 0.0000	0.1916 $\pm$ 0.0000	0.0048 $\pm$ 0.0000	1152.0 $\pm$ 0.0	0.8366 $\pm$ 0.0000
PLIP zero-shot	0.0312 $\pm$ 0.0000	0.0553 $\pm$ 0.0000	0.0754 $\pm$ 0.0000	0.0498 $\pm$ 0.0000	0.3088 $\pm$ 0.0000	0.0057 $\pm$ 0.0000	951.0 $\pm$ 0.0	0.8322 $\pm$ 0.0000
PLIP linear	0.0307 $\pm$ 0.0001	0.0612 $\pm$ 0.0003	0.0585 $\pm$ 0.0012	0.0597 $\pm$ 0.0006	0.1869 $\pm$ 0.0007	0.0048 $\pm$ 0.0010	1140.4 $\pm$ 5.95	0.8527 $\pm$ 0.0003
BLEEP	0.0302 $\pm$ 0.0005	0.0578 $\pm$ 0.0012	0.0494 $\pm$ 0.0012	0.0651 $\pm$ 0.0014	0.2125 $\pm$ 0.0017	0.0074 $\pm$ 0.0012	1043.0 $\pm$ 23.1	0.8551 $\pm$ 0.0004
BLEEP ∗	0.0309 $\pm$ 0.0004	0.0580 $\pm$ 0.0011	0.0498 $\pm$ 0.0012	0.0688 $\pm$ 0.0009	0.2116 $\pm$ 0.0043	0.0076 $\pm$ 0.0014	1020.2 $\pm$ 4.31	0.8525 $\pm$ 0.0002

Appendix

Table D.3: Biological Neighborhood Retrieval on Human Liver GSE240429 (single-scale). Train: A1+B1+D1; test: C1. All methods use the same fixed

K_{\mathrm{eval}}

. Bold indicates the best value in each column.

Method	Bio-mAP $\uparrow$	BioR@5% $\uparrow$	GeneR@5% $\uparrow$	SpatR@5% $\uparrow$	ClsHit@10 $\uparrow$	ExR@10 $\uparrow$	MedRank $\downarrow$	PCC@10 $\uparrow$
CCA	0.0271 $\pm$ 0.0000	0.0546 $\pm$ 0.0000	0.0532 $\pm$ 0.0000	0.0534 $\pm$ 0.0000	0.2035 $\pm$ 0.0000	0.0062 $\pm$ 0.0000	1084.0 $\pm$ 0.0	0.8578 $\pm$ 0.0000
Ridge	0.0403 $\pm$ 0.0000	0.0765 $\pm$ 0.0000	0.0761 $\pm$ 0.0000	0.0589 $\pm$ 0.0000	0.1945 $\pm$ 0.0000	0.0075 $\pm$ 0.0000	1097.0 $\pm$ 0.0	0.8381 $\pm$ 0.0000
PLIP zero-shot	0.0293 $\pm$ 0.0000	0.0527 $\pm$ 0.0000	0.0638 $\pm$ 0.0000	0.0522 $\pm$ 0.0000	0.2553 $\pm$ 0.0000	0.0053 $\pm$ 0.0000	1072.0 $\pm$ 0.0	0.8317 $\pm$ 0.0000
PLIP linear	0.0319 $\pm$ 0.0005	0.0645 $\pm$ 0.0015	0.0571 $\pm$ 0.0015	0.0607 $\pm$ 0.0010	0.1822 $\pm$ 0.0022	0.0062 $\pm$ 0.0014	1109.6 $\pm$ 13.2	0.8528 $\pm$ 0.0003
BLEEP	0.0312 $\pm$ 0.0005	0.0601 $\pm$ 0.0010	0.0481 $\pm$ 0.0029	0.0688 $\pm$ 0.0012	0.2122 $\pm$ 0.0021	0.0068 $\pm$ 0.0017	970.4 $\pm$ 10.9	0.8556 $\pm$ 0.0006
BLEEP ∗	0.0321 $\pm$ 0.0005	0.0604 $\pm$ 0.0010	0.0486 $\pm$ 0.0017	0.0718 $\pm$ 0.0010	0.2116 $\pm$ 0.0017	0.0098 $\pm$ 0.0014	960.0 $\pm$ 12.8	0.8532 $\pm$ 0.0004

Appendix

Table D.4: Biological Neighborhood Retrieval on Human Liver GSE240429 (multi-scale). All methods use the same fixed

K_{\mathrm{eval}}

. Bold indicates the best value in each column.

Scale	Method	Bio-mAP	Step $\Delta$	Interpretation
SS	BLEEP	0.5087	–	baseline
	BLEEP ∗	0.5327	+0.0240	architecture
	Ret-only	0.5364	+0.0037	objective
	BioKERN	0.6190	+0.0826	biological regularization
	Shuffled Kernel	0.4939	–	sanity check
MS	BLEEP	0.4960	–	baseline

Appendix

Table E.1: Sequential effect decomposition on Mouse Brain Visium. “Step

\Delta

” is the change from the preceding model in the additive path. The biological regularization step explains 74.9% (SS) and 63.4% (MS) of the total gain.

Scale	Method	Bio-mAP	Step $\Delta$	Interpretation
SS	BLEEP	0.0302	–	baseline
	BLEEP ∗	0.0309	+0.0007	architecture
	Ret-only	0.0313	+0.0004	objective
	BioKERN	0.0396	+0.0083	biological regularization
	Shuffled Kernel	0.0301	–	sanity check
MS	BLEEP	0.0312	–	baseline

Appendix

Table E.2: Sequential effect decomposition on Human Liver GSE240429. The biological regularization step explains 88.3% (SS) and 90.6% (MS) of the total gain.

Kernel design
Setting	Bio-mAP	BioR@5%	GeneR@5%	SpatR@5%	ClsHit@10	ExR@10	MedRank	PCC@10
BioKERN	0.6190 $\pm$ 0.0023	0.5155 $\pm$ 0.0028	0.4482 $\pm$ 0.0021	0.4348 $\pm$ 0.0029	0.7241 $\pm$ 0.0034	0.4938 $\pm$ 0.0107	10.50 $\pm$ 0.45	0.7862 $\pm$ 0.0002
w/o Bio Kernel	0.5370 $\pm$ 0.0042	0.4714 $\pm$ 0.0043	0.4277 $\pm$ 0.0049	0.4110 $\pm$ 0.0017	0.7195 $\pm$ 0.0060	0.4818 $\pm$ 0.0040	10.40 $\pm$ 0.49	0.7855 $\pm$ 0.0002
$K_{\mathrm{gene}}$ only	0.5834 $\pm$ 0.0009	0.4953 $\pm$ 0.0024	0.4496 $\pm$ 0.0018	0.4081 $\pm$ 0.0018	0.7228 $\pm$ 0.0043	0.4775 $\pm$ 0.0112	11.40 $\pm$ 0.49	0.7862 $\pm$ 0.0003
$K_{\mathrm{spat}}$ only	0.5880 $\pm$ 0.0026	0.4969 $\pm$ 0.0020	0.4254 $\pm$ 0.0032	0.4344 $\pm$ 0.0035	0.7191 $\pm$ 0.0014	0.5018 $\pm$ 0.0103	11.00 $\pm$ 0.00	0.7853 $\pm$ 0.0003
Fixed $\alpha=0.5$	0.6201 $\pm$ 0.0035	0.5154 $\pm$ 0.0034	0.4458 $\pm$ 0.0037	0.4351 $\pm$ 0.0010	0.7223 $\pm$ 0.0015	0.4855 $\pm$ 0.0141	11.20 $\pm$ 0.68	0.7860 $\pm$ 0.0004

Appendix

Table F.1: Ablation study on Mouse Brain Visium, single-scale. All variants share the ResidualAdapter backbone and the same fixed evaluation kernel as the main benchmark.

Setting	Bio-mAP	BioR@5%	GeneR@5%	SpatR@5%	ClsHit@10	ExR@10	MedRank	PCC@10
BioKERN	0.6716 $\pm$ 0.0021	0.5587 $\pm$ 0.0034	0.4713 $\pm$ 0.0024	0.4764 $\pm$ 0.0018	0.7596 $\pm$ 0.0033	0.5455 $\pm$ 0.0125	8.90 $\pm$ 0.20	0.7881 $\pm$ 0.0002
w/o Bio Kernel	0.5628 $\pm$ 0.0052	0.5044 $\pm$ 0.0038	0.4499 $\pm$ 0.0027	0.4508 $\pm$ 0.0032	0.7597 $\pm$ 0.0032	0.5542 $\pm$ 0.0031	9.20 $\pm$ 0.40	0.7882 $\pm$ 0.0004
$K_{\mathrm{gene}}$ only	0.6157 $\pm$ 0.0031	0.5278 $\pm$ 0.0028	0.4688 $\pm$ 0.0027	0.4401 $\pm$ 0.0020	0.7616 $\pm$ 0.0025	0.5255 $\pm$ 0.0173	9.70 $\pm$ 0.75	0.7880 $\pm$ 0.0002
$K_{\mathrm{spat}}$ only	0.6308 $\pm$ 0.0036	0.5313 $\pm$ 0.0047	0.4335 $\pm$ 0.0027	0.4760 $\pm$ 0.0028	0.7428 $\pm$ 0.0043	0.5433 $\pm$ 0.0072	9.00 $\pm$ 0.00	0.7864 $\pm$ 0.0002
Fixed $\alpha=0.5$	0.6711 $\pm$ 0.0032	0.5577 $\pm$ 0.0031	0.4668 $\pm$ 0.0030	0.4812 $\pm$ 0.0020	0.7580 $\pm$ 0.0047	0.5425 $\pm$ 0.0096	9.00 $\pm$ 0.55	0.7876 $\pm$ 0.0004
Shuffled Kernel	0.5042 $\pm$ 0.0056	0.4683 $\pm$ 0.0045	0.4172 $\pm$ 0.0034	0.4259 $\pm$ 0.0053	0.7317 $\pm$ 0.0027	0.5222 $\pm$ 0.0161	9.80 $\pm$ 0.40	0.7866 $\pm$ 0.0004

Appendix

Table F.2: Ablation study on Mouse Brain Visium, multi-scale. All variants use the same fixed evaluation kernel as the main benchmark.

Setting	Bio-mAP	BioR@5%	GeneR@5%	SpatR@5%	ClsHit@10	ExR@10	MedRank	PCC@10
BioKERN	0.0396 $\pm$ 0.0007	0.0802 $\pm$ 0.0017	0.0835 $\pm$ 0.0023	0.0694 $\pm$ 0.0005	0.2175 $\pm$ 0.0021	0.0077 $\pm$ 0.0016	964.2 $\pm$ 5.34	0.8576 $\pm$ 0.0002
w/o Bio Kernel	0.0314 $\pm$ 0.0003	0.0584 $\pm$ 0.0008	0.0502 $\pm$ 0.0016	0.0686 $\pm$ 0.0009	0.2099 $\pm$ 0.0050	0.0079 $\pm$ 0.0018	1012.0 $\pm$ 9.94	0.8527 $\pm$ 0.0005
$K_{\mathrm{gene}}$ only	0.0445 $\pm$ 0.0003	0.0895 $\pm$ 0.0014	0.1197 $\pm$ 0.0010	0.0617 $\pm$ 0.0002	0.2171 $\pm$ 0.0061	0.0063 $\pm$ 0.0007	1028.2 $\pm$ 5.46	0.8573 $\pm$ 0.0002
$K_{\mathrm{spat}}$ only	0.0298 $\pm$ 0.0005	0.0548 $\pm$ 0.0014	0.0404 $\pm$ 0.0017	0.0722 $\pm$ 0.0006	0.2055 $\pm$ 0.0034	0.0094 $\pm$ 0.0010	968.2 $\pm$ 11.7	0.8531 $\pm$ 0.0004
Fixed $\alpha=0.5$	0.0376 $\pm$ 0.0007	0.0752 $\pm$ 0.0016	0.0727 $\pm$ 0.0036	0.0707 $\pm$ 0.0009	0.2175 $\pm$ 0.0029	0.0067 $\pm$ 0.0007	969.2 $\pm$ 9.43	0.8567 $\pm$ 0.0003
Shuffled Kernel	0.0294 $\pm$ 0.0004	0.0559 $\pm$ 0.0013	0.0473 $\pm$ 0.0019	0.0663 $\pm$ 0.0004	0.2081 $\pm$ 0.0048	0.0070 $\pm$ 0.0017	1019.6 $\pm$ 12.0	0.8543 $\pm$ 0.0005

Appendix

Table F.3: Ablation study on Human Liver GSE240429, single-scale. All variants use the same fixed evaluation kernel and cross-slice spatial masking as the main benchmark.

Setting	Bio-mAP	BioR@5%	GeneR@5%	SpatR@5%	ClsHit@10	ExR@10	MedRank	PCC@10
BioKERN	0.0408 $\pm$ 0.0005	0.0820 $\pm$ 0.0014	0.0802 $\pm$ 0.0016	0.0725 $\pm$ 0.0012	0.2173 $\pm$ 0.0041	0.0097 $\pm$ 0.0015	923.8 $\pm$ 16.3	0.8581 $\pm$ 0.0002
w/o Bio Kernel	0.0320 $\pm$ 0.0004	0.0597 $\pm$ 0.0009	0.0485 $\pm$ 0.0013	0.0708 $\pm$ 0.0008	0.2086 $\pm$ 0.0017	0.0080 $\pm$ 0.0004	979.6 $\pm$ 21.0	0.8532 $\pm$ 0.0004
$K_{\mathrm{gene}}$ only	0.0403 $\pm$ 0.0002	0.0824 $\pm$ 0.0007	0.0793 $\pm$ 0.0016	0.0634 $\pm$ 0.0008	0.2124 $\pm$ 0.0051	0.0074 $\pm$ 0.0006	1004.2 $\pm$ 14.6	0.8583 $\pm$ 0.0002
$K_{\mathrm{spat}}$ only	0.0318 $\pm$ 0.0006	0.0603 $\pm$ 0.0018	0.0446 $\pm$ 0.0019	0.0726 $\pm$ 0.0006	0.2116 $\pm$ 0.0012	0.0080 $\pm$ 0.0003	917.8 $\pm$ 15.0	0.8538 $\pm$ 0.0005
Fixed $\alpha=0.5$	0.0382 $\pm$ 0.0005	0.0763 $\pm$ 0.0016	0.0689 $\pm$ 0.0025	0.0740 $\pm$ 0.0012	0.2128 $\pm$ 0.0035	0.0083 $\pm$ 0.0009	918.6 $\pm$ 14.2	0.8570 $\pm$ 0.0003
Shuffled Kernel	0.0291 $\pm$ 0.0005	0.0558 $\pm$ 0.0013	0.0441 $\pm$ 0.0024	0.0676 $\pm$ 0.0007	0.2066 $\pm$ 0.0036	0.0091 $\pm$ 0.0011	984.6 $\pm$ 8.19	0.8549 $\pm$ 0.0004

Appendix

Table F.4: Ablation study on Human Liver GSE240429, multi-scale. All variants use the same fixed evaluation kernel and cross-slice spatial masking as the main benchmark.

$\lambda_{s}$	Bio-mAP	BioR@5%	BioR@10%	ExR@10
0.0	0.5556	0.4776	0.5209	0.5018
0.1	0.5863	0.4962	0.5509	0.4855
0.2	0.6048	0.5086	0.5709	0.4891
0.3	0.6216	0.5165	0.5855	0.4909
0.5	0.6412	0.5288	0.6018	0.4745
1.0	0.6671	0.5415	0.6127	0.4382

Appendix

Table G.1: Sensitivity to

\lambda_{s}

on Mouse Brain Visium single-scale (seed 42). The default setting is

\lambda_{s}=0.3

Epoch	$\alpha$ (mean $\pm$ std)	Dominant signal
5	0.6022 $\pm$ 0.0003	gene
10	0.6048 $\pm$ 0.0005	gene
20	0.6093 $\pm$ 0.0008	gene
30	0.6124 $\pm$ 0.0009	gene
40	0.6142 $\pm$ 0.0009	gene
50	0.6149 $\pm$ 0.0009	gene

Appendix

Table G.2: Trajectory of the learned biological-kernel weight

\alpha

on Mouse Brain Visium (single-scale, five seeds).

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Cross-Modal Knowledge Distillation from Spatial Transcriptomics to Histology

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