Measuring Uncertainty in Transformer Circuits with Effective Information Consistency
Main Article Content
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 (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.
Article Details
References
2. Anthropic. Circuit Tracing / Attribution Graphs: Methods & Applications: Transformer Circuits Team. 2025. Access mode: https://transformer-circuits.pub/2025/attribution-graphs/ (accessed: 2025-08-20).
3. Yao Y., Zhang N., Xi Z., Wang M., Xu Z., Deng S., and Chen H. Knowledge Circuits in Pretrained Transformers // Advances in Neural Information Processing Systems (NeurIPS). 2024. Vol. 37. P. 118571–118602.
4. Krasnovsky A.A. Sheaf-Theoretic Causal Emergence for Resilience Analysis in Distributed Systems. 2025. arXiv : 2503.14104.
5. Hansen J., Ghrist R. Toward a Spectral Theory of Cellular Sheaves // Journal of Applied and Computational Topology. 2019. Vol. 3, No. 4. P. 315–358.
6. Robinson M. Topological Signal Processing. Springer, 2014.
7. Rosas F.E., Mediano P.A.M., Jensen H.J., Seth A.K., Barrett A.B., Carhart-Harris R.L., and Bor D. Reconciling Emergences: An Information-Theoretic Approach to Identify Causal Emergence in Multivariate Data // PLOS Computational Biology. 2020. Vol. 16, No. 12. P. e1008289.
8. Tononi G., Sporns O. Measuring Information Integration // BMC Neuroscience. 2003. Vol. 4. P. 31.
9. Oizumi M., Albantakis L., Tononi G. From the Phenomenology to the Mechanisms of Consciousness: Integrated Information Theory 3.0 // PLOS Computational Biology. 2014. Vol. 10, No. 5. P. e1003588.
10. Angelopoulos A.N., Bates S. A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification. 2021. arXiv : 2107.07511.
11. Guo C., Pleiss G., Sun Y., and Weinberger K.Q. On Calibration of Modern Neural Networks // Proceedings of the 34th International Conference on Machine Learning (ICML). PMLR. 2017. P. 1321–1330.
12. Lakshminarayanan B., Pritzel A., Blundell C. Simple and Scalable Predictive Uncertainty Estimation Using Deep Ensembles // Advances in Neural Information Processing Systems (NeurIPS). 2017. Vol. 30.
13. Bayesian Low-rank Adaptation for Large Language Models (Laplace-LoRA). 2023. ICLR 2024 version. arXiv : 2308.13111.
14. Does Localization Inform Editing? Surprising Differences in Causality-Based Localization vs. Knowledge Editing in Language Models / Hase P., Bansal M., Kim B., and Ghandeharioun A. // Advances in Neural Information Processing Systems (NeurIPS). 2023. Vol. 36. P. 17643–17668.
15. Huang L., Yu W., Ma W., Zhong W., Feng Z., Wang H., Chen Q., Peng W., Feng X., Qin B., et al. A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions // ACM Transactions on Information Systems. 2025. Vol. 43, No. 2. P. 1–55.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Presenting an article for publication in the Russian Digital Libraries Journal (RDLJ), the authors automatically give consent to grant a limited license to use the materials of the Kazan (Volga) Federal University (KFU) (of course, only if the article is accepted for publication). This means that KFU has the right to publish an article in the next issue of the journal (on the website or in printed form), as well as to reprint this article in the archives of RDLJ CDs or to include in a particular information system or database, produced by KFU.
All copyrighted materials are placed in RDLJ with the consent of the authors. In the event that any of the authors have objected to its publication of materials on this site, the material can be removed, subject to notification to the Editor in writing.
Documents published in RDLJ are protected by copyright and all rights are reserved by the authors. Authors independently monitor compliance with their rights to reproduce or translate their papers published in the journal. If the material is published in RDLJ, reprinted with permission by another publisher or translated into another language, a reference to the original publication.
By submitting an article for publication in RDLJ, authors should take into account that the publication on the Internet, on the one hand, provide unique opportunities for access to their content, but on the other hand, are a new form of information exchange in the global information society where authors and publishers is not always provided with protection against unauthorized copying or other use of materials protected by copyright.
RDLJ is copyrighted. When using materials from the log must indicate the URL: index.phtml page = elbib / rus / journal?. Any change, addition or editing of the author's text are not allowed. Copying individual fragments of articles from the journal is allowed for distribute, remix, adapt, and build upon article, even commercially, as long as they credit that article for the original creation.
Request for the right to reproduce or use any of the materials published in RDLJ should be addressed to the Editor-in-Chief A.M. Elizarov at the following address: amelizarov@gmail.com.
The publishers of RDLJ is not responsible for the view, set out in the published opinion articles.
We suggest the authors of articles downloaded from this page, sign it and send it to the journal publisher's address by e-mail scan copyright agreements on the transfer of non-exclusive rights to use the work.