Sparse autoencoders reveal organized biological knowledge but minimal regulatory logic in single-cell foundation models: a comparative atlas of Geneformer and scGPT

Ihor Kendiukhov

q-bio.GNMar 3, 2026

Sparse autoencoders reveal organized biological knowledge but minimal regulatory logic in single-cell foundation models: a comparative atlas of Geneformer and scGPT

Authors: Ihor Kendiukhov

Organizations: Department of Computer Science, University of Tübingen, Tübingen, Germany

Abstract

Background: Single-cell foundation models such as Geneformer and scGPT encode rich biological information, but whether this includes causal regulatory logic rather than statistical co-expression remains unclear. Sparse autoencoders (SAEs) can resolve superposition in neural networks by decomposing dense activations into interpretable features, yet they have not been systematically applied to biological foundation models. Results: We trained TopK SAEs on residual stream activations from all layers of Geneformer V2-316M (18 layers, d=1152) and scGPT whole-human (12 layers, d=512), producing atlases of 82525 and 24527 features, respectively. Both atlases confirm massive superposition, with 99.8 percent of features invisible to SVD. Systematic characterization reveals rich biological organization: 29 to 59 percent of features annotate to Gene Ontology, KEGG, Reactome, STRING, or TRRUST, with U-shaped layer profiles reflecting hierarchical abstraction. Features organize into co-activation modules (141 in Geneformer, 76 in scGPT), exhibit causal specificity (median 2.36x), and form cross-layer information highways (63 to 99.8 percent). When tested against genome-scale CRISPRi perturbation data, only 3 of 48 transcription factors (6.2 percent) show regulatory-target-specific feature responses. A multi-tissue control yields marginal improvement (10.4 percent, 5 of 48 TFs), establishing model representations as the bottleneck. Conclusions: These models have internalized organized biological knowledge, including pathway membership, protein interactions, functional modules, and hierarchical abstraction, yet they encode minimal causal regulatory logic. We release both feature atlases as interactive web platforms enabling exploration of more than 107000 features across 30 layers of two leading single-cell foundation models.

Figures & tables

Layer	VarExpl	Alive	Dead	SVD	Novel	MeanCos	Ann%	Enrichments
0	83.9%	4,608	0	41	4,567	0.033	58.6%	23,959
1	84.6%	4,606	2	27	4,579	0.033	57.4%	23,131
2	84.8%	4,601	7	29	4,572	0.034	55.5%	23,383
3	85.2%	4,595	13	12	4,583	0.035	56.4%	21,922
4	85.3%	4,583	25	13	4,570	0.037	53.9%	19,910
5	84.6%	4,576	32	8	4,568	0.036	52.1%	17,865

Table 1: Geneformer SAE training and annotation statistics. Each SAE uses a 4

\times

overcomplete dictionary (4,608 features) with TopK

k{=}32

sparsity. VarExpl = variance explained. Dead =

4{,}608-\text{Alive}

. MeanCos = mean absolute pairwise cosine between decoder vectors. Ann% = fraction of alive features with

\geq

1 significant enrichment (FDR

<0.05

). Enrichments = unique (feature, term) pairs. Per-database breakdown in Additional file 1: Table S1.

Figure 1: Geneformer V2-316M SAE feature atlas. TopK SAEs on all 18 layers yield 82,525 features. Reconstruction quality declines with depth while dead features increase.

Figure 2: 99.8% of SAE features are invisible to SVD. Novel features carry 98.7% of annotations and explain 2.4

\times

more variance.

Layer	VarExpl	Alive	Dead	MeanCos	Ann%	Modules
0	92.0%	2,027	21	0.038	32.7%	6
1	93.0%	2,035	13	0.041	30.8%	6
2	93.2%	2,038	10	0.040	28.7%	5
3	93.2%	2,045	3	0.041	31.6%	7
4	93.5%	2,048	0	0.041	30.4%	6
5	92.1%	2,048	0	0.042	29.6%	7

Table 2: scGPT SAE training and annotation statistics. 4

\times

dictionary (2,048 features), TopK

k{=}32

, 3.56M positions/layer. Notation as in Table 1 .

Metric	Geneformer	scGPT
Architecture	18 layers, $d{=}1{,}152$	12 layers, $d{=}512$
Training data	$\sim$ 30M cells	$\sim$ 33M cells
Input encoding	Rank-value tokens	Continuous expression
Training objective	Next-token prediction	Masked gene prediction
Features per layer	4,608	2,048
Total alive features	82,525	24,527

Table 3: Cross-model comparison. Both models analyzed with identical TopK SAE pipeline (4

\times

expansion,

k{=}32

Figure 3: Cross-model comparison on normalized depth. (A) scGPT has higher variance explained at all depths. (B) Geneformer has higher annotation rates. (C) Summary. (D) Dead feature profiles differ.

Feature	Top Genes	Biological Identity	Databases
Layer 0 — Molecular Programs
F3717	CDK1, CDC20, DLGAP5, PBK	Cell cycle (G2/M)	GO, KEGG, React., STRING
F3607	RRM1, E2F1, MCM4, MCM6, RAD51	DNA replication / repair	GO, KEGG, React., STRING, TRRUST
F1116	ARL6IP4, SQSTM1, JAK1	B cell activation	GO, KEGG, Reactome
F4536	DYNC1H1, TLN1, MYH9, SPTAN1	Cytoskeleton / focal adhesion	GO, KEGG, Reactome
F2829	TGFB1, PKN1, GADD45A, ZBTB7A	MAPK/TGF $\beta$ signaling	GO, KEGG, React., STRING, TRRUST

Table 4: Representative SAE features. Top genes = highest mean activation magnitude. Databases = ontology sources with significant enrichments.

Figure 4: U-shaped annotation profile across 18 layers. Early layers encode molecular programs; middle layers develop abstract representations; later layers re-specialize then optimize for prediction.

Figure 5: Co-activation modules evolve across layers. Identity shifts from molecular machinery (L0) to integrative programs (L11), reflecting hierarchical abstraction.

Metric	Value
Features tested	50
Mean specificity ratio	8.98
Median specificity ratio	2.36
Specific ( $>$ 2 $\times$ )	30/50 (60%)
Highly specific ( $>$ 10 $\times$ )	6/50 (12%)
Mean target logit diff	$-$ 0.116

Table 5: Causal patching summary. 50 features at layer 11, 200 cells each. Specificity =

|\Delta\text{logit}_{\text{target}}|/|\Delta\text{logit}_{\text{other}}|

Figure 6: SAE features are causally necessary. Ablating a single feature specifically disrupts its annotated gene set. Median 2.36 $\times$ ; top feature 114.5 $\times$ .

Figure 7: 97–99.8% of features form information highways. Biological information flows through functional connections between distinct feature sets across layers.

Metric	Value
Perturbation targets tested	100
Targets causing feature changes	92/100 (92%)
TRRUST TFs tested	48
TFs with specific response	3/48 (6.2%)
Mean responding features per target	2.54
Mean specific features per target	0.03

Table 6: Perturbation response mapping (K562-only SAE, layer 11). 100 CRISPRi targets tested. TF specificity = fraction of TFs with target-specific responding features.

Figure 8: 92% perturbation detection but only 6.2% TF specificity. Features respond to cell-state shifts, not specific regulatory consequences.

SAE Training Data	Layer	TFs Specific	Rate
K562-only	11	3/48	6.2%
K562 + Tabula Sapiens	0	0/48	0.0%
K562 + Tabula Sapiens	5	4/48	8.3%
K562 + Tabula Sapiens	11	5/48	10.4%
K562 + Tabula Sapiens	17	1/48	2.1%

Table 7: K562-only vs. multi-tissue SAE perturbation specificity. Specificity = TRRUST TFs (48 total) with target-specific responding features.

Figure 9: Multi-tissue SAE yields marginal improvement (6.2%

\to

10.4%). Non-systematic gains establish Geneformer’s representations as the bottleneck.

Criterion	Target	Result	Status
Modules match pathways	$\geq$ 20 total	141 (6–12/layer)	Exceeded
Causal specificity	Majority $>$ 2 $\times$	60% $>$ 2 $\times$ , median 2.36 $\times$	Exceeded
Perturbation specificity	$\geq$ 30%	6.2% (3/48 TFs)	Not met
Unannotated structure	$\geq$ 10% in clusters	95–98.5% in modules ∗	Partial
Cross-layer tracking	$\geq$ 50%	97–99.8% highways	Exceeded
∗ Co-activation module membership, not standalone clusters (2–3%).

Table 8: Success criteria scorecard. The unmet criterion (perturbation specificity) is the paper’s central finding.

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Layer	GO BP	KEGG	Reactome	STRING	TRRUST TF	TRRUST Edges
0	10,153	2,650	11,001	302	155	42
1	10,022	2,433	10,512	258	164	48
2	9,948	2,495	10,790	283	150	32
3	9,726	2,514	9,525	273	157	37
4	8,537	2,045	9,195	248	133	30
5	7,695	1,845	8,189	216	136	24

Appendix

Table S1 : Per-ontology enrichment counts across all 18 Geneformer layers. Each entry is the number of significant enrichments (FDR

<0.05

) for features at that layer. GO BP = Gene Ontology Biological Process. TRRUST columns show enrichment for TF target sets (TF) and individual TF

\to

target edges (Edges).

L0 $\to$ Target	Matches (cos $>0.7$ )	Rate
L0 $\to$ L1	114	2.5%
L0 $\to$ L2	93	2.0%
L0 $\to$ L4	67	1.5%
L0 $\to$ L6	25	0.5%
L0 $\to$ L8	10	0.2%
L0 $\to$ L10	1	$\sim$ 0%

Appendix

Table S2 : Cross-layer feature persistence from layer 0. Matches = features at L0 with cosine similarity

>0.7

to any feature at the target layer. The model undergoes radical representational transformation: by layer 6, essentially all features are novel with no L0 ancestry.

Layer	Modules	Feats in Modules	PMI Edges	Coverage
0	6	4,577	446,324	99.3%
1	8	4,562	440,681	99.0%
2	7	4,536	404,403	98.6%
3	8	4,518	393,574	98.3%
4	9	4,502	393,194	98.2%
5	12	4,472	390,845	97.7%

Appendix

Table S3 : Co-activation module statistics across all 18 layers. PMI-based graphs with Leiden clustering (resolution = 1.0). Modules = number of distinct communities. Coverage = fraction of alive features in at least one module.

Feature	Annotation	Specificity	$\Delta$ Target	$\Delta$ Other
F2035	Cell Differentiation (neg. reg.)	114.5 $\times$	$-$ 0.208	$+$ 0.002
F3692	ERAD Pathway	108.1 $\times$	$-$ 0.129	$-$ 0.001
F3933	Intracellular Signaling (neg. reg.)	55.7 $\times$	$-$ 0.196	$-$ 0.004
F157	Golgi Vesicle Transport	25.4 $\times$	$-$ 0.056	$-$ 0.002
F3532	Protein Metabolic Process (pos. reg.)	11.2 $\times$	$-$ 0.127	$-$ 0.011
F4516	Mitotic Spindle Microtubules	10.6 $\times$	$+$ 0.672	$+$ 0.063

Appendix

Table S4 : Top 10 causally specific SAE features at layer 11.

\Delta

Target and

\Delta

Other = mean logit change at target and off-target gene positions, respectively, upon zeroing the feature. Specificity ratios were computed from unrounded values; displayed

\Delta

values are rounded to three decimal places.

Layer Pair	Feats w/ Deps	Mean Max PMI	Median Max PMI	Max PMI	Highways
L0 $\to$ L5	4,604	6.61	6.72	11.10	4,530 (98.4%)
L5 $\to$ L11	4,518	6.63	6.71	10.87	4,401 (97.4%)
L11 $\to$ L17	4,555	6.79	6.86	10.66	4,544 (99.8%)

Appendix

Table S5 : Geneformer cross-layer information highways. PMI between SAE feature activations at source and target layers (500K positions each). A highway = source feature with

\geq

1 target-layer feature at PMI

>3

Layer Pair	PMI Edges	Upstream	Downstream	Max PMI
L0 $\to$ L4	75,305	1,935/2,027 (95.5%)	1,960/2,048 (95.7%)	9.15
L4 $\to$ L8	61,263	1,955/2,048 (95.5%)	1,723/2,048 (84.1%)	9.26
L8 $\to$ L11	45,258	1,773/2,048 (86.6%)	1,289/2,048 (62.9%)	10.78

Appendix

Table S6 : scGPT cross-layer information highways. Same methodology as Table S5 . Note the progressive drop in downstream connectivity.

Pair	Source Feature	Target Feature	Biological Logic	PMI
L0 $\to$ L5	Protein Processing in ER	unlabeled	ER stress cascade	11.10
L0 $\to$ L5	mTORC1 Regulation	Autophagy	mTORC1 $\to$ autophagy	9.55
L0 $\to$ L5	Wnt Signaling	unlabeled	Wnt pathway processing	9.48
L5 $\to$ L11	Protein Polyubiq.	unlabeled	Protein quality control	10.87
L5 $\to$ L11	Translation	unlabeled	Translational regulation	10.35
L5 $\to$ L11	RNA Splicing (neg. reg.)	unlabeled	Post-transcriptional	10.21

Appendix

Table S7 : Top cross-layer biological cascades. Strongest annotated PMI connections between layer pairs. “Unlabeled” = the target feature lacks direct ontology annotation.

TF	K562-SAE Specific	MT-SAE Specific	Change
ATF5	0	1	gained
BRCA1	0	1	gained
GATA1	0	1	gained
RBMX	0	1	gained
NFRKB	0	1	gained
MAX	1	0	lost

Appendix

Table S8 : Per-TF head-to-head comparison at layer 11. Only TFs with changed specificity are shown; 40 additional TFs had no specific features in either condition.

SAE	Features with TFs in top genes	TF-dominant ( $\geq$ 3 TFs)
K562-only L11	2,967/4,598 (64.5%)	424
Multi-tissue L0	2,796/4,608 (60.7%)	452
Multi-tissue L5	2,777/4,568 (60.8%)	337
Multi-tissue L11	2,782/4,601 (60.5%)	343
Multi-tissue L17	2,680/4,603 (58.2%)	346

Appendix

Table S9 : TF feature diagnostics. Features with known TFs in top-20 genes and TF-dominant features (

\geq

3 TFs in top genes). Denominators = features with non-empty top-20 gene lists (may differ from alive counts because some features that are “dead” on the 100K held-out sample still produce gene lists from the full training data). K562-only SAE has more TF-associated features than the multi-tissue SAE.

Layer	Annotated	Unannotated	Clusters	Co-activate w/ Annotated	Isolated
0	2,702	1,906	15 (48 feats)	1,876 (98.4%)	30 (1.6%)
5	2,383	2,193	19 (69 feats)	2,090 (95.3%)	103 (4.7%)
11	2,583	2,015	11 (47 feats)	1,984 (98.5%)	28 (1.4%)
17	2,154	2,426	12 (58 feats)	2,334 (96.2%)	75 (3.1%)

Appendix

Table S10 : Unannotated feature analysis. Co-activate = unannotated feature belongs to a co-activation module containing annotated features. Isolated = no module membership. A small number of features (3 at L11, 17 at L17) belong to modules containing only unannotated features and are excluded from both columns. Clusters = standalone gene-set clusters among unannotated features.

Figure S1 : scGPT cross-layer connectivity reveals progressive information concentration. (A) Upstream connectivity remains high (86–96%) but downstream connectivity drops sharply from 96% to 63% across layer pairs, indicating progressive bottlenecking. (B) PMI edge density decreases from 75K to 45K edges across the three layer pairs. (C) Comparison with Geneformer: Geneformer maintains near-complete downstream connectivity (97–100%) while scGPT drops to 63%, suggesting fundamentally different information flow architectures.

Figure S2 : Co-activation network layout of SAE features across layers. Left column: force-directed graph layout of intra-module co-activation edges, colored by Leiden module membership. Each module forms a spatially distinct community. Right column: same layouts colored by annotation richness (log-transformed number of significant enrichment terms). Unassigned features (gray) cluster centrally. Module count varies from 6 (L0) to 12 (L5), reflecting the complexity of co-activation patterns at different layers.

Figure S3 : Six-panel co-activation layout of layer 11 SAE features. (a) Eight Leiden modules form spatially distinct communities. (b) Annotated features (blue) distribute across all module clusters; unannotated features (gray) concentrate centrally. (c) Top ontology source reveals module-specific enrichment patterns: certain modules are dominated by GO BP (green), others by STRING interactions (pink) or Reactome pathways (purple). (d) Annotation richness gradient across modules. (e) Activation frequency varies systematically across modules. (f) SVD-aligned features (orange, $n=4$ ) are scattered across different modules, while 4,594 novel features (blue) fill the landscape.

Figure S4 : Annotation-based projections provide independent validation. (a) UMAP of TF-IDF weighted ontology term vectors for layer 11 (4,608 features). Annotated features (left cluster) separate from unannotated features (right blob), with internal structure reflecting shared biological annotations. (b) t-SNE of TF-IDF annotation vectors for annotated features only ( $n=2{,}583$ ). Fine-grained subclusters partially correspond to co-activation modules, confirming that module structure reflects genuine biological similarity.

Genomic Foundation Models

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Mar 2, 2026

Causal Circuit Tracing Reveals Distinct Computational Architectures in Single-Cell Foundation Models: Inhibitory Dominance, Biological Coherence, and Cross-Model Convergence

Motivation: Sparse autoencoders (SAEs) decompose foundation model activations into interpretable features, but causal feature-to-feature interactions across network depth remain unknown for biological foundation models. Results: We introduce causal circuit tracing by ablating SAE features and measuring downstream responses, and apply it to Geneformer V2-316M and scGPT whole-human across four conditions (96,892 edges, 80,191 forward passes). Both models show approximately 53 percent biological coherence and 65 to 89 percent inhibitory dominance, invariant to architecture and cell type. scGPT produces stronger effects (mean absolute d = 1.40 vs. 1.05) with more balanced dynamics. Cross-model consensus yields 1,142 conserved domain pairs (10.6x enrichment, p < 0.001). Disease-associated domains are 3.59x more likely to be consensus. Gene-level CRISPRi validation shows 56.4 percent directional accuracy, confirming co-expression rather than causal encoding.

Ihor Kendiukhov

Department of Computer Science, University of Tübingen, Tübingen, Germany

Mechanistic Interpretability Causal Interpretability

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Feb 25, 2026

What Topological and Geometric Structure Do Biological Foundation Models Learn? Evidence from 141 Hypotheses

When biological foundation models such as scGPT and Geneformer process single-cell gene expression, what geometric and topological structure forms in their internal representations? Is that structure biologically meaningful or a training artifact, and how confident should we be in such claims? We address these questions through autonomous large-scale hypothesis screening: an AI-driven executor-brainstormer loop that proposed, tested, and refined 141 geometric and topological hypotheses across 52 iterations, covering persistent homology, manifold distances, cross-model alignment, community structure, and directed topology, all with explicit null controls and disjoint gene-pool splits. Three principal findings emerge. First, the models learn genuine geometric structure. Gene embedding neighborhoods exhibit non-trivial topology, with persistent homology significant in 11 of 12 transformer layers at p < 0.05 in the weakest domain and 12 of 12 in the other two. A multi-level distance hierarchy shows that manifold-aware metrics outperform Euclidean distance for identifying regulatory gene pairs, and graph community partitions track known transcription factor target relationships. Second, this structure is shared across independently trained models. CCA alignment between scGPT and Geneformer yields canonical correlation of 0.80 and gene retrieval accuracy of 72 percent, yet none of 19 tested methods reliably recover gene-level correspondences. The models agree on the global shape of gene space but not on precise gene placement. Third, the structure is more localized than it first appears. Under stringent null controls applied across all null families, robust signal concentrates in immune tissue, while lung and external lung signals weaken substantially.

Ihor Kendiukhov

Department of Computer Science, University of Tübingen, Tübingen, Germany

Neural Representation Geometry Genomic Foundation Models Geometric Representation Learning Topological Representation Learning Single-Cell Transcriptomics

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Feb 24, 2026

Multi-Dimensional Spectral Geometry of Biological Knowledge in Single-Cell Transformer Representations

Single-cell foundation models such as scGPT learn high-dimensional gene representations, but what biological knowledge these representations encode remains unclear. We systematically decode the geometric structure of scGPT internal representations through 63 iterations of automated hypothesis screening (183 hypotheses tested), revealing that the model organizes genes into a structured biological coordinate system rather than an opaque feature space. The dominant spectral axis separates genes by subcellular localization, with secreted proteins at one pole and cytosolic proteins at the other. Intermediate transformer layers transiently encode mitochondrial and ER compartments in a sequence that mirrors the cellular secretory pathway. Orthogonal axes encode protein-protein interaction networks with graded fidelity to experimentally measured interaction strength (Spearman rho = 1.000 across n = 5 STRING confidence quintiles, p = 0.017). In a compact six-dimensional spectral subspace, the model distinguishes transcription factors from their target genes (AUROC = 0.744, all 12 layers significant). Early layers preserve which specific genes regulate which targets, while deeper layers compress this into a coarser regulator versus regulated distinction. Repression edges are geometrically more prominent than activation edges, and B-cell master regulators BATF and BACH2 show convergence toward the B-cell identity anchor PAX5 across transformer depth. Cell-type marker genes cluster with high fidelity (AUROC = 0.851). Residual-stream geometry encodes biological structure complementary to attention patterns. These results indicate that biological transformers learn an interpretable internal model of cellular organization, with implications for regulatory network inference, drug target prioritization, and model auditing.

Ihor Kendiukhov

Department of Computer Science University of Tübingen Tübingen, Germany

Transformer Interpretability Single-Cell Transcriptomics

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Abstract

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