Quantifying LLM Attention-Head Stability: Implications for Circuit Universality

Karan Bali, Jack Stanley, Praneet Suresh, Danilo Bzdok
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:5911-5944, 2026.

Abstract

In mechanistic interpretability, recent work scrutinizes transformer “circuits”—sparse, mono or multi layer sub computations, that may reflect human understandable functions. Yet, these network circuits are rarely acid-tested for their stability across different instances of the same deep learning architecture. Without this, it remains unclear whether reported circuits emerge universally across labs or turn out to be idiosyncratic to a particular estimation instance, potentially limiting confidence in safety-critical settings. Here, we systematically study stability across-refits in increasingly complex transformer language models of various sizes. We quantify, layer by layer, how similarly attention heads learn representations across independently initialized training runs. Our rigorous experiments show that (1) middle-layer heads are the least stable yet the most representationally distinct; (2) deeper models exhibit stronger mid-depth divergence; (3) unstable heads in deeper layers become more functionally important than their peers from the same layer; (4) applying weight decay optimization substantially improves attention-head stability across random model initializations; and (5) the residual stream is comparatively stable. Our findings establish the cross-instance robustness of circuits as an essential yet underappreciated prerequisite for scalable oversight, drawing contours around possible white-box monitorability of AI systems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-bali26a, title = {Quantifying {LLM} Attention-Head Stability: Implications for Circuit Universality}, author = {Bali, Karan and Stanley, Jack and Suresh, Praneet and Bzdok, Danilo}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {5911--5944}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/bali26a/bali26a.pdf}, url = {https://proceedings.mlr.press/v306/bali26a.html}, abstract = {In mechanistic interpretability, recent work scrutinizes transformer “circuits”—sparse, mono or multi layer sub computations, that may reflect human understandable functions. Yet, these network circuits are rarely acid-tested for their stability across different instances of the same deep learning architecture. Without this, it remains unclear whether reported circuits emerge universally across labs or turn out to be idiosyncratic to a particular estimation instance, potentially limiting confidence in safety-critical settings. Here, we systematically study stability across-refits in increasingly complex transformer language models of various sizes. We quantify, layer by layer, how similarly attention heads learn representations across independently initialized training runs. Our rigorous experiments show that (1) middle-layer heads are the least stable yet the most representationally distinct; (2) deeper models exhibit stronger mid-depth divergence; (3) unstable heads in deeper layers become more functionally important than their peers from the same layer; (4) applying weight decay optimization substantially improves attention-head stability across random model initializations; and (5) the residual stream is comparatively stable. Our findings establish the cross-instance robustness of circuits as an essential yet underappreciated prerequisite for scalable oversight, drawing contours around possible white-box monitorability of AI systems.} }
Endnote
%0 Conference Paper %T Quantifying LLM Attention-Head Stability: Implications for Circuit Universality %A Karan Bali %A Jack Stanley %A Praneet Suresh %A Danilo Bzdok %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-bali26a %I PMLR %P 5911--5944 %U https://proceedings.mlr.press/v306/bali26a.html %V 306 %X In mechanistic interpretability, recent work scrutinizes transformer “circuits”—sparse, mono or multi layer sub computations, that may reflect human understandable functions. Yet, these network circuits are rarely acid-tested for their stability across different instances of the same deep learning architecture. Without this, it remains unclear whether reported circuits emerge universally across labs or turn out to be idiosyncratic to a particular estimation instance, potentially limiting confidence in safety-critical settings. Here, we systematically study stability across-refits in increasingly complex transformer language models of various sizes. We quantify, layer by layer, how similarly attention heads learn representations across independently initialized training runs. Our rigorous experiments show that (1) middle-layer heads are the least stable yet the most representationally distinct; (2) deeper models exhibit stronger mid-depth divergence; (3) unstable heads in deeper layers become more functionally important than their peers from the same layer; (4) applying weight decay optimization substantially improves attention-head stability across random model initializations; and (5) the residual stream is comparatively stable. Our findings establish the cross-instance robustness of circuits as an essential yet underappreciated prerequisite for scalable oversight, drawing contours around possible white-box monitorability of AI systems.
APA
Bali, K., Stanley, J., Suresh, P. & Bzdok, D.. (2026). Quantifying LLM Attention-Head Stability: Implications for Circuit Universality. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:5911-5944 Available from https://proceedings.mlr.press/v306/bali26a.html.

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