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Article · Automatic Documentation and Mathematical Linguistics · December 1, 2025

Measuring Uncertainty in Transformer Circuits with Effective Information Consistency

Anatoly Krasnovsky
Open via DOIPDF

Abstract

Abstract Mechanistic interpretability has identified functional subgraphs within large language models (LLMs), known as transformer circuits (TCs), that appear to implement specific algorithms. Yet we lack a formal, single-pass way to quantify when an active circuit is behaving coherently and thus likely trustworthy. Building on the author’s prior sheaf-theoretic formulation of causal emergence (Krasnovsky, 2025) we specialize it to transformer circuits and introduce the single-pass, dimensionless effective-information consistency score (EICS). EICS combines a normalized sheaf inconsistency computed from local Jacobians and activations with a Gaussian EI proxy for circuit-level causal emergence derived from the same forward state. The construction is white-box, single-pass, and makes units explicit so that the score is dimensionless. We further provide practical guidance on score interpretation, computational overhead (with fast and exact modes), and a toy sanity-check analysis.

Explainable Artificial Intelligence (XAI)Diverse Interdisciplinary Research StudiesTopic Modelingtransformer circuitseffective informationcausal emergence

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