Neural Circuit Function Inference with LLMs

Large Language Models (LLMs) have demonstrated remarkable performance across diverse tasks, from text summarization to question answering. Despite these capabilities, their black-box nature obscures internal decision-making processes. Mechanistic interpretability (MI) aims to address this by reverse-engineering neural networks into human-understandable algorithms. Current MI approaches for LLMs typically follow a two-stage paradigm: first identifying important components (circuit discovery), where components are typically individual nodes such as an attention head or feedforward neuron, and second determining the role they play in a certain task (functional interpretation). However, this sequential approach overlooks a fundamental insight: a component's importance and its functional role are inherently codependent. Unifying these stages presents two key challenges: (1) functional roles are often tied to specific nodes or components, limiting generalization, and (2) their identification relies on subjective interpretation rather than quantifiable metrics. To address these challenges, we propose S^3martCirc (Self-supervised Smart Circuit Discovery), a unified framework that simultaneously discovers circuits and interprets functionality. S^3martCirc abstracts node behavior into two general computational roles that generalize across tasks and defines a quantitative metric for assigning them, enabling importance and functional role to be discovered jointly rather than in sequence. Extensive experiments show that our framework outperforms existing methods in circuit discovery.

Mechanistic interpretability produces circuit-level causal analyses of neural network behaviour, but discovered circuits often remain isolated experimental artefacts: there is no shared formal representation for what circuits compute, how they relate, or when two findings provide evidence for the same mechanism. This work provides a formal infrastructure for cumulative mechanistic science by treating circuit interpretation as inductive theory construction. Each circuit is characterised at two levels: a Causal Functional Signature (CFS), which grounds component behaviour in causal attribution evidence and token role profiles, and an architectural signature $τ_{\mathrm{arch}}$, learned by inductive logic programming (ILP) from scale-invariant structural predicates. Together, these constitute a formal coherence layer that makes mechanistic claims explicit, comparable via $θ$-subsumption, and portable across model scales. CFS reveals qualitatively distinct computational strategies across task types, including attention-mediated copying versus MLP-mediated binding. ILP signatures achieve substantially better structural separation than graph kernel and feature-vector baselines, and support principled transfer across model scales and architecture families.

In this paper, we present empirical and theoretical evidence against a central but largely implicit assumption in circuit and sheaf discovery (CSD), which we term the Functional Anisotropy Hypothesis: the idea that functions in large language models (LLMs) are localised to a unique or near-unique internal mechanism. We show that a single LLM task can instead be supported by multiple, structurally distinct circuits or sheaves that are simultaneously faithful, sparse, and complete. To systematically uncover such competing mechanisms, we introduce Overlap-Aware Sheaf Repulsion, a method that augments the CSD objective with an explicit penalty on structural overlap across multiple discovery runs, enabling the discovery of circuits or sheaves with strong task performance but minimal shared structure across a plethora of common CSD benchmarks. We find that this phenomenon becomes increasingly pronounced as the number of discovered sheaves grows and persists robustly across major CSD methods. We further identify an ultra-sparse three-edge sheaf and show that none of its edges is individually indispensable, undermining even weakened notions of canonical or essential components. To explain these findings, we propose a Distributive Dense Circuit Hypothesis and provide a theoretical analysis demonstrating that non-unique, low-overlap circuit explanations arise naturally from high-dimensional superposition under mild assumptions. Together, our results suggest that mechanistic explanations in LLMs are inherently non-canonical and call for a rethinking of how CSD results should be interpreted and evaluated.