# Measuring Uncertainty in Transformer Circuits with Effective Information Consistency

arXiv: https://arxiv.org/abs/2509.07149 · HTML: https://mlsanity.com/paper/2509.07149/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Circuits and mechanistic analysis, one of 13 directions in Mechanistic interpretability.
- Builds on 10 of its 15 references that are in the map.
- First posted on arXiv 8 Sep 2025.

## Placed in

- Mechanistic interpretability / [Circuits and mechanistic analysis](https://mlsanity.com/mechinterp/circuits-and-mechanistic-analysis/)

## Builds on (most cited first, 10 of 10)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Does Localization Inform Editing? Surprising Differences in Causality-Based Localization vs. Knowledge Editing in Language Models](https://mlsanity.com/paper/2301.04213/) (2023)
- [Bayesian Low-rank Adaptation for Large Language Models](https://mlsanity.com/paper/2308.13111/) (2023)
- [Knowledge Circuits in Pretrained Transformers](https://mlsanity.com/paper/2405.17969/) (2024)
- [Reconciling emergences: An information-theoretic approach to identify causal emergence in multivariate data](https://mlsanity.com/paper/2004.08220/) (2020)
- [Sheaf-Theoretic Causal Emergence for Resilience Analysis in Distributed Systems](https://mlsanity.com/paper/2503.14104/) (2025)

## Built on by (most cited first, 2 of 2)

- [CIRCUS: Circuit Consensus under Uncertainty via Stability Ensembles](https://mlsanity.com/paper/2603.00523/) (2026)
- [Gluing Local Contexts into Global Meaning: A Sheaf-Theoretic Decomposition of Transformer Representations](https://mlsanity.com/paper/2610.17117/) (2026)

## Abstract (arXiv)

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 prior systems-theoretic proposals, we specialize a sheaf/cohomology and causal emergence perspective to TCs and introduce the Effective-Information Consistency Score (EICS). EICS combines (i) a normalized sheaf inconsistency computed from local Jacobians and activations, with (ii) 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. Empirical validation on LLM tasks is deferred.