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Exhaustive Circuit Mapping of a Single-Cell Foundation Model Reveals Massive Redundancy, Heavy-Tailed Hub Architecture, and Layer-Dependent Differentiation Control

Ihor Kendiukhov

Abstract

Mechanistic interpretability of biological foundation models has relied on selective feature sampling, pairwise interaction testing, and observational trajectory analysis. Each of these can introduce systematic bias. Here we present three experiments that address these limitations through exhaustive circuit tracing, higher order combinatorial ablation, and causal trajectory steering in Geneformer, a transformer based single cell foundation model. First, exhaustive tracing of all 4065 active sparse autoencoder features at layer 5 yields 1393850 significant downstream edges, a 27 fold expansion over selective sampling. This reveals a heavy tailed hub distribution in which 1.8 percent of features account for disproportionate connectivity and 40 percent of the top 20 hubs lack biological annotation. These results indicate systematic annotation bias in prior selective analyses. Second, three way combinatorial ablation across 8 feature triplets shows that redundancy deepens monotonically with interaction order, with a three way ratio of 0.59 versus a pairwise ratio of 0.74, and with zero synergy. This confirms that the model architecture is subadditive at all tested orders. Third, trajectory guided feature steering establishes a causal link between layer position and differentiation directionality. Late layer features at L17 consistently push cell states toward maturity, with fraction positive equal to 1.0. Early and mid layer features at L0 and L11 mostly push away from maturity, with fraction positive ranging from 0.00 to 0.58. Together these results move from correlation toward causal evidence for layer dependent control of cell state.

Exhaustive Circuit Mapping of a Single-Cell Foundation Model Reveals Massive Redundancy, Heavy-Tailed Hub Architecture, and Layer-Dependent Differentiation Control

Abstract

Mechanistic interpretability of biological foundation models has relied on selective feature sampling, pairwise interaction testing, and observational trajectory analysis. Each of these can introduce systematic bias. Here we present three experiments that address these limitations through exhaustive circuit tracing, higher order combinatorial ablation, and causal trajectory steering in Geneformer, a transformer based single cell foundation model. First, exhaustive tracing of all 4065 active sparse autoencoder features at layer 5 yields 1393850 significant downstream edges, a 27 fold expansion over selective sampling. This reveals a heavy tailed hub distribution in which 1.8 percent of features account for disproportionate connectivity and 40 percent of the top 20 hubs lack biological annotation. These results indicate systematic annotation bias in prior selective analyses. Second, three way combinatorial ablation across 8 feature triplets shows that redundancy deepens monotonically with interaction order, with a three way ratio of 0.59 versus a pairwise ratio of 0.74, and with zero synergy. This confirms that the model architecture is subadditive at all tested orders. Third, trajectory guided feature steering establishes a causal link between layer position and differentiation directionality. Late layer features at L17 consistently push cell states toward maturity, with fraction positive equal to 1.0. Early and mid layer features at L0 and L11 mostly push away from maturity, with fraction positive ranging from 0.00 to 0.58. Together these results move from correlation toward causal evidence for layer dependent control of cell state.
Paper Structure (26 sections, 4 equations, 6 figures, 4 tables)

This paper contains 26 sections, 4 equations, 6 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Results
  3. Exhaustive circuit tracing reveals the complete L5 computational graph
  4. Heavy-tailed hub distribution
  5. Signal attenuation across layers
  6. Annotation bias in selective tracing
  7. Higher-order ablation confirms redundancy deepens with interaction order
  8. Redundancy deepens monotonically
  9. Zero synergy persists at third order
  10. Trajectory-guided feature steering reveals layer-dependent directionality
  11. Layer position determines steering directionality
  12. Effect sizes are small but directionally consistent
  13. Gene-level effects are biologically coherent
  14. Discussion
  15. Annotation bias as a systematic confound
  16. ...and 11 more sections

Figures (6)

  • Figure 1: Exhaustive L5 circuit map overview. (A) Distribution of edge counts across all 4,065 features, showing heavy-tailed distribution with mean 343 and median 284. (B) Comparison of selective (30 features, 52K edges) versus exhaustive (4,065 features, 1.39M edges) tracing. (C) Signal attenuation across downstream layers: L6 (695K) $\to$ L11 (443K) $\to$ L17 (256K).
  • Figure 2: Hub architecture and annotation bias. (A) Features ranked by edge count, colored by annotation status (blue = annotated, red = unannotated). (B) Top 20 hub features with edge counts, colored by annotation status. (C) Fraction of annotated features among all features, top 100, and top 20, showing no enrichment for annotation in hubs.
  • Figure 3: Redundancy deepens with interaction order. (A) Grouped bars comparing mean pairwise ratio (0.74) and three-way ratio (0.59) across pathways. (B) Box plot of marginal third-feature contribution C$|$AB, showing near-zero values for most triplets. (C) Stacked bars showing the fraction of subadditive, additive, and superadditive targets per triplet---subadditivity dominates universally.
  • Figure 4: Trajectory steering directionality. (A) Fraction of cells showing positive state shift per feature at $\alpha = 5$, colored by layer. L17 features universally push toward maturity (frac. pos. = 1.0); L0 features push away. (B) Mean state shift magnitude at $\alpha = 5$. (C) Box plot of fraction positive grouped by layer, showing that L17 features universally push toward maturity while earlier layers produce mixed or negative shifts.
  • Figure 5: Gene-level steering effects at $\alpha = 5$. (A) L5 F4349 (Pre-mRNA Processing): top 10 upregulated and downregulated genes. (B) L0 F1483 (L-amino Acid Transport): top 10 genes. (C) L17 F3730 (Protein-RNA Complex Assembly): top 10 genes.
  • ...and 1 more figures