mlsanityData to 14 Oct 2026

K-MSHC: Unmasking Minimally Sufficient Head Circuits in Large Language Models with Experiments on Syntactic Classification Tasks

arXiv 2505.12268 ↗First posted 18 May 2025cs.CL cs.LGcited by 2

On the map: Mechanistic interpretability → Circuits and mechanistic analysis

Abstract (arXiv)

Understanding which neural components drive specific capabilities in mid-sized language models (≤10B parameters) remains a key challenge. We introduce the (bmK, ε)-Minimum Sufficient Head Circuit (K-MSHC), a methodology to identify minimal sets of attention heads crucial for classification tasks as well as Search-K-MSHC, an efficient algorithm for discovering these circuits. Applying our Search-K-MSHC algorithm to Gemma-9B, we analyze three syntactic task families: grammar acceptability, arithmetic verification, and arithmetic word problems. Our findings reveal distinct task-specific head circuits, with grammar tasks predominantly utilizing early layers, word problems showing pronounced activity in both shallow and deep regions, and arithmetic verification demonstrating a more distributed pattern across the network. We discover non-linear circuit overlap patterns, where different task pairs share computational components at varying levels of importance. While grammar and arithmetic share many "weak" heads, arithmetic and word problems share more consistently critical "strong" heads. Importantly, we find that each task maintains dedicated "super-heads" with minimal cross-task overlap, suggesting that syntactic and numerical competencies emerge from specialized yet partially reusable head circuits.

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 22 of its 36 references that are in the map. First posted on arXiv 18 May 2025.

Builds on

22 of 36 references.

Closest ancestors · 3

Same direction, newest first

  1. 2024The Computational Complexity of Circuit Discovery for Inner Interpretability10 Oct
  2. 2024Transcoders Find Interpretable LLM Feature Circuits17 Jun
  3. 2024Automatically Identifying Local and Global Circuits with Linear Computation Graphs22 May

Other references · 19

  1. 2021Training Verifiers to Solve Math Word Problemscited by 10,109
  2. 2023A Survey of Large Language Modelscited by 2,576
  3. 2016Understanding intermediate layers using linear classifier probescited by 1,353
  4. 2020Transformer Feed-Forward Layers Are Key-Value Memoriescited by 1,336
  5. 2019BERT Rediscovers the Classical NLP Pipelinecited by 1,059
  6. 2019What Does BERT Look At? An Analysis of BERT's Attentioncited by 1,003
  7. 2019Analyzing Multi-Head Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Prunedcited by 856
  8. 2019Are Sixteen Heads Really Better than One?cited by 816
  9. 2019BLiMP: The Benchmark of Linguistic Minimal Pairs for Englishcited by 564
  10. 2024Scaling and evaluating sparse autoencoderscited by 553
  11. 2024Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Modelscited by 435
  12. 2024Do Large Language Models Latently Perform Multi-Hop Reasoning?cited by 169
7 more
  1. 2024Arithmetic Without Algorithms: Language Models Solve Math With a Bag of Heuristicscited by 97
  2. 2023A Mechanistic Interpretation of Arithmetic Reasoning in Language Models using Causal Mediation Analysiscited by 89
  3. 2025Language Models Use Trigonometry to Do Additioncited by 70
  4. 2024Evidence of Learned Look-Ahead in a Chess-Playing Neural Networkcited by 34
  5. 2024The Same But Different: Structural Similarities and Differences in Multilingual Language Modelingcited by 28
  6. 2024Planning in a recurrent neural network that plays Sokobancited by 18
  7. 2025Interpreting Emergent Planning in Model-Free Reinforcement Learningcited by 15

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Formal Mechanistic Interpretability: Automated Circuit Discovery with Provable Guaranteescited by 11
  2. 2026CircuitTree: Composing Circuits into A Syllable Transcribercited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024Sparse Autoencoders Enable Scalable and Reliable Circuit Identification in Language Models
  2. 2026Linear Predictability of Attention Heads in Large Language Models
  3. 2024Circuit Compositions: Exploring Modular Structures in Transformer-Based Language Models
  4. 2026Exploring the Limits of Pruning: Task-Specific Neurons, Model Collapse, and Recovery in Task-Specific Large Language Models
  5. 2026CSP-Atlas: Concept-Specific Neural Circuits in a Sparse Python Transformer
  6. 2026Operationalising the Superficial Alignment Hypothesis via Task Complexity
  7. 2026A Single Layer to Explain Them All:Understanding Massive Activations in Large Language Models
  8. 2026From Early Encoding to Late Suppression: Interpreting LLMs on Character Counting Tasks