mlsanityData to 7 Oct 2026

Measuring Affinity between Attention-Head Weight Subspaces via the Projection Kernel

arXiv 2601.10266 ↗First posted 15 Jan 2026cs.CLcited by 5

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Abstract (arXiv)

Understanding relationships between attention heads is essential for interpreting the internal structure of Transformers, yet existing metrics do not capture this structure well. We focus on the subspaces spanned by attention-head weight matrices and quantify head-to-head relationships using the Projection Kernel (PK), a principal-angle-based measure of subspace similarity. Experiments show that PK reproduces known head-to-head interactions on the IOI task more clearly than prior metrics such as the Composition Score. We further introduce a framework to quantify the informativeness of PK distributions by comparing them with a reference distribution derived from random orthogonal subspaces. As an application, we analyze a directed graph constructed from PK and show that, in GPT2-small, L4H7 acts as a hub by functioning as an identity head.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 32 of its 64 references that are in the map. First posted on arXiv 15 Jan 2026.

Builds on

32 of 64 references.

References · 32

  1. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,204
  2. 2016Layer Normalizationcited by 5,579
  3. 2021RoFormer: Enhanced Transformer with Rotary Position Embeddingcited by 4,581
  4. 2023Efficient Streaming Language Models with Attention Sinkscited by 2,115
  5. 2019Similarity of Neural Network Representations Revisitedcited by 1,695
  6. 2019Root Mean Square Layer Normalizationcited by 1,425
  7. 2022Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 smallcited by 1,130
  8. 2019What Does BERT Look At? An Analysis of BERT's Attentioncited by 994
  9. 2019Are Sixteen Heads Really Better than One?cited by 803
  10. 2023Towards Automated Circuit Discovery for Mechanistic Interpretabilitycited by 700
  11. 2019Attention is not not Explanationcited by 629
  12. 2019Is Attention Interpretable?cited by 387
20 more
  1. 2017All-but-the-Top: Simple and Effective Postprocessing for Word Representationscited by 205
  2. 2019Learning to Deceive with Attention-Based Explanationscited by 111
  3. 2024Universal Neurons in GPT2 Language Modelscited by 100
  4. 2024Information Flow Routes: Automatically Interpreting Language Models at Scalecited by 92
  5. 2024What needs to go right for an induction head? A mechanistic study of in-context learning circuits and their formationcited by 86
  6. 2023Successor Heads: Recurring, Interpretable Attention Heads In The Wildcited by 77
  7. 2025Attention Sinks and Compression Valleys in LLMs are Two Sides of the Same Coincited by 47
  8. 2024Talking Heads: Understanding Inter-layer Communication in Transformer Language Modelscited by 39
  9. 2024Towards Universality: Studying Mechanistic Similarity Across Language Model Architecturescited by 31
  10. 2024The Same But Different: Structural Similarities and Differences in Multilingual Language Modelingcited by 27
  11. 2013Robust subspace clusteringcited by 24
  12. 2024Efficient Automated Circuit Discovery in Transformers using Contextual Decompositioncited by 23
  13. 2019From Balustrades to Pierre Vinken: Looking for Syntax in Transformer Self-Attentionscited by 22
  14. 2024You can remove GPT2's LayerNorm by fine-tuningcited by 11
  15. 2024Abrupt Learning in Transformers: A Case Study on Matrix Completioncited by 11
  16. 2024Axis Tour: Word Tour Determines the Order of Axes in ICA-transformed Embeddingscited by 6
  17. 2024Revisiting Cosine Similarity via Normalized ICA-transformed Embeddingscited by 5
  18. 2025Weight-based Analysis of Detokenization in Language Models: Understanding the First Stage of Inference Without Inferencecited by 5
  19. 2024Sparse Attention Decomposition Applied to Circuit Tracingcited by 4
  20. 2025The geometry of BERTcited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 5.

5 papers.

  1. 2026Conditional Co-Ablation: Recovering Self-Repair Backups in Transformer Circuitscited by 6
  2. 2026The Communication Map of a Transformercited by 1
  3. 2026Flag Varieties: A Geometric Framework for Deep Network Alignmentcited by 0
  4. 2026Scaled Idempotence in Transformer Attention: Paired OV Geometry and Shared-Value Algebrascited by 0
  5. 2026The Linear Representation Hypothesis Needs a Group Actioncited by 0