Ihor Kendiukhov

Ihor Kendiukhov

ergodicity is an open-source Python library for computational work on stochastic dynamics, with particular emphasis on non-ergodicity, time-average behavior, heavy-tailed processes, and decision making under uncertainty. The package brings together three layers that are often split across ad hoc scripts: process definitions and simulators, analysis and fitting tools, and agent-based experimentation. This article documents the implemented software rather than presenting new stochastic theory. We describe the package architecture, the supported process families, the analysis workflow, and the practical boundaries of the current implementation. We also provide fully reproducible examples covering heavy-tailed ensemble spread, multiplicative Levy growth diagnostics, adaptive memory mean reversion, preasymptotic fluctuation analysis, and partial stochastic differential equation simulation. The package is positioned as an integration layer on top of the scientific Python stack, reducing the amount of glue code required to move from process specification to diagnostics and comparative experiments.

Ihor Kendiukhov

We present a systematic evaluation framework - thirty-seven analyses, 153 statistical tests, four cell types, two perturbation modalities - for assessing mechanistic interpretability in single-cell foundation models. Applying this framework to scGPT and Geneformer, we find that attention patterns encode structured biological information with layer-specific organisation - protein-protein interactions in early layers, transcriptional regulation in late layers - but this structure provides no incremental value for perturbation prediction: trivial gene-level baselines outperform both attention and correlation edges (AUROC 0.81-0.88 versus 0.70), pairwise edge scores add zero predictive contribution, and causal ablation of regulatory heads produces no degradation. These findings generalise from K562 to RPE1 cells; the attention-correlation relationship is context-dependent, but gene-level dominance is universal. Cell-State Stratified Interpretability (CSSI) addresses an attention-specific scaling failure, improving GRN recovery up to 1.85x. The framework establishes reusable quality-control standards for the field.

Ihor Kendiukhov

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.

Ihor Kendiukhov

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

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.

Ihor Kendiukhov

We report the discovery and extraction of a compact hematopoietic algorithm from the single-cell foundation model scGPT, to our knowledge the first biologically useful, competitive algorithm extracted from a foundation model via mechanistic interpretability. We show that scGPT internally encodes a compact hematopoietic manifold with significant developmental branch structure, validated on a strict non-overlap Tabula Sapiens external panel and confirmed via frozen-head zero-shot transfer to an independent multi-donor immune panel. To isolate this geometry, we introduce a general three-stage extraction method consisting of direct operator export from frozen attention weights, a lightweight learned adaptor, and a task-specific readout, producing a standalone algorithm without target-dataset retraining. In 88-split donor-holdout benchmarks against scVI, Palantir, DPT, CellTypist, PCA, and raw-expression baselines, the extracted algorithm achieves the strongest pseudotime-depth ordering and leads on key subtype endpoints (CD4/CD8 AUROC 0.867, mono/macro AUROC 0.951). Compared to standard probing of frozen scGPT embeddings with a 3-layer MLP, the extracted head is BH-significantly better on 6/8 classification endpoints while completing a full 12-split evaluation campaign 34.5x faster with approximately 1000x fewer trainable parameters. The exported operator compresses from three pooled attention heads to a single head without statistically significant loss, and further to a rank-64 surrogate. Mechanistic interpretability of the compact operator reveals a concentrated four-factor core explaining 66.2% of ablation impact, with factors resolving into explicit T/lymphoid, B/plasma, granulocytic, and monocyte/macrophage gene programs. A supplementary second-manifold validation (intercellular communication geometry) confirms that the extraction method generalizes beyond hematopoiesis.

Ihor Kendiukhov

Neural scaling laws -- power-law relationships between loss, model size, and data -- have been extensively documented for language and vision transformers, yet their existence in single-cell genomics remains largely unexplored. We present the first systematic study of scaling behaviour for masked-reconstruction transformers trained on single-cell RNA sequencing (scRNA-seq) data. Using expression profiles from the CELLxGENE Census, we construct two experimental regimes: a data-rich regime (512 highly variable genes, 200,000 cells) and a data-limited regime (1,024 genes, 10,000 cells). Across seven model sizes spanning three orders of magnitude in parameter count (533 to 3.4 x 10^8 parameters), we fit the parametric scaling law to validation mean squared error (MSE). The data-rich regime exhibits clear power-law scaling with an irreducible loss floor of c ~ 1.44, while the data-limited regime shows negligible scaling, indicating that model capacity is not the binding constraint when data are scarce. These results establish that scaling laws analogous to those observed in natural language processing do emerge in single-cell transcriptomics when sufficient data are available, and they identify the data-to-parameter ratio as a critical determinant of scaling behaviour. A preliminary conversion of the data-rich asymptotic floor to information-theoretic units yields an estimate of approximately 2.30 bits of entropy per masked gene position. We discuss implications for the design of single-cell foundation models and outline the additional measurements needed to refine this entropy estimate.

Ihor Kendiukhov

Benchmark rankings are routinely used to justify scientific claims about method quality in gene regulatory network (GRN) inference, yet the stability of these rankings under plausible evaluation protocol choices is rarely examined. We present a systematic diagnostic framework for measuring ranking instability under protocol shift, including decomposition tools that separate base rate effects from discrimination effects. Using existing single cell GRN benchmark outputs across three human tissues and six inference methods, we quantify pairwise reversal rates across four protocol axes: candidate set restriction (16.3 percent, 95 percent CI 11.0 to 23.4 percent), tissue context (19.3 percent), reference network choice (32.1 percent), and symbol mapping policy (0.0 percent). A permutation null confirms that observed reversal rates are far below random order expectations (0.163 versus null mean 0.500), indicating partially stable but non invariant ranking structure. Our decomposition reveals that reversals are driven by changes in the relative discrimination ability of methods rather than by base rate inflation, a finding that challenges a common implicit assumption in GRN benchmarking. We propose concrete reporting practices for stability aware evaluation and provide a diagnostic toolkit for identifying method pairs at risk of reversal.

Ihor Kendiukhov

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.

Sohaib Imran, Ihor Kendiukhov, Matthew Broerman et al.

Do larger and more capable language models learn to update their "beliefs" about propositions more consistently with Bayes' theorem when presented with evidence in-context? To test this, we formulate a Bayesian Coherence Coefficient (BCC) metric and generate a dataset with which to measure the BCC. We measure BCC for multiple pre-trained-only language models across five model families, comparing against the number of model parameters, the amount of training data, and model scores on common benchmarks. Our results provide evidence for our hypothesis that larger and more capable pre-trained language models assign credences that are more coherent with Bayes' theorem. These results have important implications for our understanding and governance of LLMs.

Ihor Kendiukhov

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.

Pranav Mahajan, Ihor Kendiukhov, Syed Hussain et al.

Recent work identifies a stated-revealed (SvR) preference gap in language models (LMs): a mismatch between the values models endorse and the choices they make in context. Existing evaluations rely heavily on binary forced-choice prompting, which entangles genuine preferences with artifacts of the elicitation protocol. We systematically study how elicitation protocols affect SvR correlation across 24 LMs. Allowing neutrality and abstention during stated preference elicitation allows us to exclude weak signals, substantially improving Spearman's rank correlation ($ρ$) between volunteered stated preferences and forced-choice revealed preferences. However, further allowing abstention in revealed preferences drives $ρ$ to near-zero or negative values due to high neutrality rates. Finally, we find that system prompt steering using stated preferences during revealed preference elicitation does not reliably improve SvR correlation on AIRiskDilemmas. Together, our results show that SvR correlation is highly protocol-dependent and that preference elicitation requires methods that account for indeterminate preferences.

Ihor Kendiukhov

This review synthesizes the nascent but critical field of developmental interpretability for Large Language Models. We chart the field's evolution from static, post-hoc analysis of trained models to a dynamic investigation of the training process itself. We begin by surveying the foundational methodologies, including representational probing, causal tracing, and circuit analysis, that enable researchers to deconstruct the learning process. The core of this review examines the developmental arc of LLM capabilities, detailing key findings on the formation and composition of computational circuits, the biphasic nature of knowledge acquisition, the transient dynamics of learning strategies like in-context learning, and the phenomenon of emergent abilities as phase transitions in training. We explore illuminating parallels with human cognitive and linguistic development, which provide valuable conceptual frameworks for understanding LLM learning. Finally, we argue that this developmental perspective is not merely an academic exercise but a cornerstone of proactive AI safety, offering a pathway to predict, monitor, and align the processes by which models acquire their capabilities. We conclude by outlining the grand challenges facing the field, such as scalability and automation, and propose a research agenda for building more transparent, reliable, and beneficial AI systems.

Ihor Kendiukhov

Recent advances in the development of artificial intelligence, technological progress acceleration, long-term trends of macroeconomic dynamics increase the relevance of technological singularity hypothesis. In this paper, we build a model of finite-time technological singularity assuming that artificial intelligence will replace humans for artificial intelligence engineers after some point in time when it is developed enough. This model implies the following: let A be the level of development of artificial intelligence. Then, the moment of technological singularity n is defined as the point in time where artificial intelligence development function approaches infinity. Thus, it happens in finite time. Although infinite level of development of artificial intelligence cannot be reached practically, this approximation is useful for several reasons, firstly because it allows modeling a phase transition or a change of regime. In the model, intelligence growth function appears to be hyperbolic function under relatively broad conditions which we list and compare. Subsequently, we also add a stochastic term (Brownian motion) to the model and investigate the changes in its behavior. The results can be applied for the modeling of dynamics of various processes characterized by multiplicative growth.