BASILISC: Bayesian Alignment of Siamese-Integrated Latents for Inferring Single-cell Correspondence

Sepideh Saran; Mahsa Ghanbari; Uwe Ohler

cs.LGOct 28, 2026

BASILISC: Bayesian Alignment of Siamese-Integrated Latents for Inferring Single-cell Correspondence

Authors: Sepideh Saran, Mahsa Ghanbari, Uwe Ohler

Organizations: The Berlin Institute for Medical Systems Biology, Max Delbrück Center for Molecular Medicine, Germany · Department of Electrical Engineering and Computer Science, Technical University of Berlin, Germany · Department of Biology, Humboldt University of Berlin, Germany · Department of Computer Science, Humboldt University of Berlin, Germany

Abstract

Single-cell assays study the genome one cell at a time. Unimodal assays measure one molecular layer, the newer multimodal assays measure several. Most data are single-modality, so integrating them relies on models trained on multimodal assays, where the cell correspondence across modalities is known. These models return a matching, but rarely a confidence measure. We present BASILISC (Bayesian Alignment of Siamese-Integrated Latents for Inferring Single-cell Correspondence), a framework for matching single-cell representations with uncertainty on the correspondence itself. A BASILISC model is a probabilistic siamese network over the two modalities with a predictive distribution over the correspondence for a cross-modal pair of cells. We instantiate it at two levels: at the cell-type level the question is whether two cells share a cell type, at the cell level which cell is the partner in the other modality. To our knowledge, this is the first uncertainty score on a learned cross-modal correspondence evaluated against a known ground-truth pairing. BASILISC learns a similarity across modalities that reflects cell lineage: an unseen cell type is matched to its lineage relative, matching still works on such held-out types (balanced accuracy 0.86 on unseen against 0.93 on seen types), and the predictive uncertainty rises on these out-of-distribution cells. The uncertainty score also selects high-quality matches for downstream analysis: discarding the least certain fifth of the pairs raises accuracy from 0.93 to 0.98. At the cell level, a deep ensemble of the deterministic matcher reaches 0.062 matching accuracy on the benchmark test set, above the competition winner; on the Bayesian matcher's assignment, the posterior flags the wrong matches that cross a cell-type boundary better than a deterministic read of the same scores (AUROC 0.68 against 0.64).

Figures & tables

Figure 1: Basilisc at the cell-type level: from frozen embeddings to a predictive distribution. The boxed region, panels (b) and (c), is the siamese model with deterministic legs and shared layers and a probabilistic head; (a) is the frozen embedding as input and (d) is a readout of the predictive distribution over

200

posterior draws.

Figure 2: Basilisc at the cell level: from raw counts to an assignment and its uncertainty. The boxed region, panels (b) and (c), is the trained model, with legs initialized from single-modality Liam weights and a shared projection; (a) is the raw-count input, and (d) is the readout: one assignment

\pi

over the batch, and the two uncertainty scores

u_{i}

and

v_{i}

read from 200 posterior draws per seed, pooled over the five seeds.

Figure 3: Uncertainty at the cell-type level. (A) Each method’s own uncertainty score on the 110 cross-batch LOCTO runs: AUROC for detecting its own errors on seen-type pairs against AUROC for detecting the held-out type’s positives among seen positives. The shaded region is above 0.55 on both. (B) The share of runs in which one score clears 0.55 on both jobs, for both pair populations. (C–E) An unseen type’s negatives, split by whether the partner is the seen type nearest to it in the input embedding or any other seen type: (C) predictive SD and (D) predictive mean of the two groups, pooled over 219 runs (one run has no nearest-type pair); (E) per-run AUROC of each score for separating the two groups, one point per run, dashed line at chance.

score	any wrong	same-type	cross-type	cross-type, partner is
				a relative	another family
transport-plan posterior $v_{i}$	0.804	0.821	0.679	0.676	0.686
top-1 vote $u_{i}$	0.777	0.790	0.678	0.672	0.697
Sinkhorn weight, best $T$ ( $T=0.5$ )	0.792	0.812	0.635	0.646	0.603
Sinkhorn weight, $T=1$	0.785	0.804	0.639	0.641	0.631
seed stability	0.701	0.707	0.656	0.654	0.662

Table 1: Detecting a wrong assignment, by the kind of error. AUROC of each score for separating wrong assignments of the given kind from correct matches, Bayesian arm, pooled over the three test batches of the competition split (20,009 cells; 19,053 wrong, of which 16,852 same-type and 2,201 cross-type; of the cross-type errors 1,642 go to a lineage relative and 559 to another family).

Appendix figures & tables20 assets

Supplementary material from the paper’s appendix.

Appendix

	Multiome	CITE-seq
Modalities	GEX, ATAC	GEX, ADT
Cells	69,249	90,261
Features	13,431 genes, 116,490 peaks	13,953 genes, 134 proteins
Annotated cell types	22	45
Types used	22	38 ( $\geq 200$ cells)
Batches (site $\times$ donor)	13	12

Appendix

Table S1: The two datasets of the NeurIPS 2021 multimodal single-cell benchmark used in this work. Multiome: gene expression and chromatin accessibility in the same nucleus. CITE-seq: gene expression and surface protein abundance in the same cell. A batch is one site–donor combination. The cell-level test set is the competition’s test set, 20,009 nuclei drawn from the three batches of site 4; it exists for the multiome data only.

Multiome , 22 types
Family	$n$	Cell types
T	4	CD4+ T naive, CD8+ T naive, CD4+ T activated, CD8+ T
innate lymphoid	2	ILC, NK
B	5	Lymph prog, Transitional B, Naive CD20+ B, B1 B, Plasma cell
mono/DC	4	CD14+ Mono, CD16+ Mono, ID2-hi myeloid prog, cDC2
progenitor	3	HSC, G/M prog, MK/E prog

Appendix

Table S2: The lineage families used for the leave-one-family-out, leave-two-families-out and few-shot settings, and for reading where a wrong match goes. The multiome table partitions the 22 annotated types into seven families; the CITE-seq table partitions the 38 types with at least 200 cells into the same seven families.

Multiome
Cell type	Cells
CD8+ T	11,589
CD14+ Mono	10,843
NK	6,929
CD4+ T activated	5,526
Naive CD20+ B	5,052

Appendix

Table S3: Cells per annotated cell type in the two datasets, sorted by count. Multiome: 69,249 nuclei, 22 types. CITE-seq: 90,261 cells, 45 types; the seven types marked

\dagger

have fewer than 200 cells and are excluded from the cell-type-level experiments, leaving 38.

Cell type	s1d1	s1d2	s1d3	s2d1	s2d4	s2d5	s3d3	s3d6	s3d7	s3d10	s4d1	s4d8	s4d9
CD8+ T	725	1,632	1,020	169	230	752	378	488	110	432	759	4,089	805
CD14+ Mono	921	704	242	1,308	1,140	1,716	855	208	674	1,603	1,014	458	–
NK	591	982	696	269	136	848	477	126	256	545	1,124	421	458
CD4+ T activated	836	709	392	446	385	493	228	276	102	207	619	684	149
Naive CD20+ B	386	121	133	289	590	105	393	18	190	421	626	883	897
Erythroblast	797	136	374	478	1,485	64	246	84	31	391	474	266	90

Appendix

Table S4: Multiome: nuclei per cell type and batch (site–donor). A dash marks a type absent from a batch. The three site-4 batches form the cell-level test set.

Cell type	s1d1	s1d2	s1d3	s2d1	s2d4	s2d5	s3d1	s3d6	s3d7	s4d1	s4d8	s4d9
CD14+ Mono	734	726	309	2,958	1,294	2,561	2,915	2,927	6,056	637	466	110
CD4+ T activated	381	848	547	690	364	1,009	816	544	380	577	134	676
CD4+ T naive	591	304	833	883	266	631	681	349	219	583	87	470
NK	94	458	271	282	76	1,128	84	415	1,242	511	268	605
Reticulocyte	605	279	929	270	580	116	587	244	291	194	50	127
Erythroblast	228	57	228	1,202	471	61	622	524	307	150	35	154

Appendix

Table S5: CITE-seq: cells per cell type and batch (site–donor). A dash marks a type absent from a batch.

Figure S1: Lineage map of the 22 bone marrow cell types present in the multiome data, drawn from the literature. Arrows run in the direction of increasing differentiation. Solid arrows are established transitions, dashed arrows are contested, and a bar marks a type with no further annotated state in this annotation. The three background bands are the broad compartments: lymphoid, myeloid, and erythroid,/MK. The literature does not agree on every transition, and some of the placements are still debated; therefore, the map can be wrong in some details.

level	data	construction	arms	runs per arm
cell type	multiome	mix	BNN, legs, MCD, ENS, DET, $k$ -NN, cosine, logistic	10
cell type	multiome	LOCTO (22 types)	same	220
cell type	multiome	LOFO (7 families)	BNN	70
cell type	multiome	LTFO (21 pairs)	BNN	210
cell type	multiome	few-shot ( $k\in\{0,5,10,20,30,50\}$ , 3 rules)	BNN	1,260
cell type	multiome	width ladder ( $\lambda\in\{0,0.1,0.3\}$ )	BNN	660

Appendix

Table S6: The experiments. Each cell-type-level run is one trained model on one dataset (construction

\times

seed

\times

pair population); the arms share every dataset. Each cell-level run is one trained matcher.

$\lambda$	$\sigma$	mix AUROC	error AUROC, $p_{\mathrm{sd}}$ $-$ margin	gain at 50%, $-$ margin	novelty AUROC, $p_{\mathrm{sd}}$	Spearman( $p_{\mathrm{sd}}$ , margin)
0	0.004	0.978	$-0.001$ [ $-0.002$ , $+0.001$ ]	$+0.001$	0.584	0.956 $\pm$ 0.027
0.01	0.042	0.978	–	–	–	0.984 $\pm$ 0.011
0.1	0.262	0.976	$+0.005$ [ $+0.003$ , $+0.007$ ]	$+0.003$	0.612	0.989 $\pm$ 0.008
0.3	0.489	0.976	$+0.007$ [ $+0.004$ , $+0.010$ ]	$+0.005$	0.623	0.987 $\pm$ 0.008
1	0.750	0.976	$+0.007$ [ $+0.003$ , $+0.011$ ]	$+0.006$	0.627	0.986 $\pm$ 0.005

Appendix

Table S7: The posterior’s width against what it buys. Test split, clustered by held-out type,

n=22

types; brackets are 95% intervals. Classification AUROC is on the mix datasets,

n=10

runs. The last column is the per-pair Spearman correlation of

p_{\mathrm{sd}}

with the confidence margin, mean

\pm

SD over the mix runs.

method	accuracy	AUROC	Brier	NLL	ECE
BASILISC (MFVI)	0.932 $\pm$ 0.006	0.976 $\pm$ 0.002	0.053 $\pm$ 0.004	0.191 $\pm$ 0.012	0.014 $\pm$ 0.004
MC dropout	0.938 $\pm$ 0.003	0.981 $\pm$ 0.001	0.048 $\pm$ 0.002	0.168 $\pm$ 0.007	0.017 $\pm$ 0.004
deep ensemble (5)	0.938 $\pm$ 0.004	0.980 $\pm$ 0.002	0.048 $\pm$ 0.003	0.171 $\pm$ 0.012	0.011 $\pm$ 0.001
deterministic (no sampling)	0.932 $\pm$ 0.002	0.976 $\pm$ 0.002	0.052 $\pm$ 0.001	0.186 $\pm$ 0.007	0.013 $\pm$ 0.002
linear pair classifier	0.917 $\pm$ 0.006	0.969 $\pm$ 0.002	0.063 $\pm$ 0.003	0.218 $\pm$ 0.010	0.022 $\pm$ 0.005
aligned cosine (Procrustes + Platt)	0.914 $\pm$ 0.004	0.965 $\pm$ 0.003	0.066 $\pm$ 0.004	0.229 $\pm$ 0.011	0.013 $\pm$ 0.003

Appendix

Table S8: Classification and probability quality of the seven methods on pairs of seen types (mix, cross-batch pairs, test split, mean

\pm

SD over five seeds). Every method reads the same frozen embeddings and the same pairs. Brier score, NLL, and ECE are lower-is-better; the three baselines use no network.

	cross-batch pairs			within-batch pairs
method	error AUROC	unseen AUROC	both $>0.55$	error AUROC	unseen AUROC	both $>0.55$
BASILISC (MFVI)	0.834	0.619	69%	0.833	0.635	75%
MC dropout	0.843	0.707	88%	0.864	0.710	85%
deep ensemble (5)	0.850	0.671	82%	0.870	0.679	84%
deterministic (no sampling)	0.840	0.564	53%	0.856	0.582	61%
linear pair classifier	0.844	0.490	45%	0.852	0.451	38%

Appendix

Table S9: One score, two jobs. For each method, the AUROC of its own uncertainty score for detecting its own errors on seen-type pairs and for detecting the held-out type’s positives among seen positives, over the 110 LOCTO runs of each pair population, and the share of those runs in which the same score clears 0.55 on both. The deterministic network is the identical architecture with sampling switched off.

Figure S2: Selective prediction on the mix datasets, ten runs. (A) Accuracy on the pairs kept when the least certain are discarded, ranked by predictive SD (solid) or by the confidence margin (dashed); the band is the run-to-run range and the dotted line is accuracy on every pair. (B) Accuracy gain from keeping the most certain half, one point per run.

Figure S3: Learned similarity between cell types. Entry $(T,X)$ is the mean predicted probability that a cell of type $T$ and a cell of type $X$ share a type, read from the LOCTO runs in which $T$ was held out (five seeds, both pair populations); the diagonal is $T$ ’s own positives. Rows and columns are ordered by similarity. A square marks each row’s largest off-diagonal entry.

Figure S4: Few-shot recovery of a held-out lineage family. (A) Recall on the family’s positives against the number

k

of its cells returned to training, on both pair populations, with the seen-type recall of the same runs as reference; error bars are the standard error over 330 per-type rows per point (22 types

\times

five seeds

\times

three rules). (B) The share of the family’s sibling negatives called same, against

k

Figure S5: Where a wrong assignment goes, both arms. (a) The share of wrong assignments whose partner is another cell of the query’s own type. (b) Of those that leave the type, the share whose partner is a lineage relative. Grey bars are the same shares with the partners permuted within batch; error bars are bootstrap intervals over queries.

Figure S6: Detecting a wrong assignment, by kind of error, Bayesian arm. AUROC of each score for separating wrong assignments of the given kind from correct matches, pooled over the three test batches (bars) and per batch (points).

Figure S7: The same scores on the cross-type errors, split by whether the wrong partner is a lineage relative of the query’s type or belongs to another family.

Figure S8: A type never seen in training, at the cell level, Bayesian arm, 50 posterior draws per seed. For each of eight held-out types, the AUROC of each score for separating the held-out cells from seen cells in the same test batches; types are ordered by the number of held-out test cells.

	multiome	CITE-seq
mix AUROC, cross-batch / within-batch pairs	0.976 / 0.977	0.970 / 0.963
error detection, $p_{\mathrm{sd}}$ / margin	0.856 / 0.858	0.795 / 0.797
gain at 50% coverage, $p_{\mathrm{sd}}$ / margin	$+0.058$ / $+0.058$	$+0.073$ / $+0.071$
novelty detection, $p_{\mathrm{sd}}$	0.627	0.583
above 0.5 in	19 of 22 types	28 of 38 types
look-alike partner, median $p_{\mathrm{sd}}$ nearest / other	0.057 / 0.0015	0.029 / 0.0006

Appendix

Table S10: Every cell-type-level claim on both modality pairs. Multiome: 22 types, 230 runs; CITE-seq: 38 types, 390 runs. Novelty detection is on positives only, per run. Both-jobs shares are on cross-batch pairs. The learned-similarity rows are over ordered type pairs (462 multiome, 1,406 CITE-seq).

Figure S9: CITE-seq: one score, two jobs, over 190 LOCTO runs per pair population. The aligned cosine clears 0.55 on both jobs in no run.

Figure S10: CITE-seq: novelty detection per held-out type, split by whether a near-duplicate of the type stayed in training. One point per type (mean over its 10 runs), on the second test split; bars are group means, the dashed line is chance.

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