From Circuit Evidence to Mechanistic Theory: An Inductive Logic Approach

• URL: http://arxiv.org/abs/2605.21303v1
• Date: Wed, 20 May 2026 15:33:14 GMT
• Title: From Circuit Evidence to Mechanistic Theory: An Inductive Logic Approach
• Abstract summary: This work provides a formal infrastructure for cumulative mechanistic science by treating circuit interpretation as inductive theory construction.<n>Each circuit is characterised at two levels: a Causal Functional Signature (CFS), which grounds component behaviour in causal attribution evidence, and an architectural signature $_mathrmarch$, learned by inductive logic programming (ILP) from scale-invariant structural predicates.
• Score: 4.3997570047987775
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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