# Quantifying LLM Attention-Head Stability: Implications for Circuit Universality

arXiv: https://arxiv.org/abs/2602.16740 · HTML: https://mlsanity.com/paper/2602.16740/

## 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 24 of its 41 references that are in the map.
- First posted on arXiv 17 Feb 2026.

## Placed in

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

## Builds on (most cited first, 24 of 24)

- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Analyzing Multi-Head Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Pruned](https://mlsanity.com/paper/1905.09418/) (2019)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [The Loss Surfaces of Multilayer Networks](https://mlsanity.com/paper/1412.0233/) (2014)
- [Small-scale proxies for large-scale Transformer training instabilities](https://mlsanity.com/paper/2309.14322/) (2023)
- [DeepNet: Scaling Transformers to 1,000 Layers](https://mlsanity.com/paper/2203.00555/) (2022)
- [A Toy Model of Universality: Reverse Engineering How Networks Learn Group Operations](https://mlsanity.com/paper/2302.03025/) (2023)
- [Three Mechanisms of Weight Decay Regularization](https://mlsanity.com/paper/1810.12281/) (2018)
- [The MultiBERTs: BERT Reproductions for Robustness Analysis](https://mlsanity.com/paper/2106.16163/) (2021)
- [Reliability of CKA as a Similarity Measure in Deep Learning](https://mlsanity.com/paper/2210.16156/) (2022)
- [Disentangling the Causes of Plasticity Loss in Neural Networks](https://mlsanity.com/paper/2402.18762/) (2024)
- [Why Do We Need Weight Decay in Modern Deep Learning?](https://mlsanity.com/paper/2310.04415/) (2023)
- [Which Shortcut Cues Will DNNs Choose? A Study from the Parameter-Space Perspective](https://mlsanity.com/paper/2110.03095/) (2021)
- [PolyPythias: Stability and Outliers across Fifty Language Model Pre-Training Runs](https://mlsanity.com/paper/2503.09543/) (2025)
- [Analyzing Feed-Forward Blocks in Transformers through the Lens of Attention Maps](https://mlsanity.com/paper/2302.00456/) (2023)
- [Subspace Chronicles: How Linguistic Information Emerges, Shifts and Interacts during Language Model Training](https://mlsanity.com/paper/2310.16484/) (2023)
- [B2T Connection: Serving Stability and Performance in Deep Transformers](https://mlsanity.com/paper/2206.00330/) (2022)

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

- [Learning What Matters: Supervising Global Context Pruning with Causal Evidence Sets](https://mlsanity.com/paper/2607.21692/) (2026)
- [Circuit Condensation: Post-Training that Concentrates a Behavior's Causal Circuit](https://mlsanity.com/paper/2608.27254/) (2026)

## Abstract (arXiv)

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.