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Hierarchical Sparse Circuit Extraction from Billion-Parameter Language Models through Scalable Attribution Graph Decomposition

Mohammed Mudassir Uddin, Shahnawaz Alam, Mohammed Kaif Pasha

TL;DR

This work tackles the scalability barrier in mechanistic interpretability by introducing Hierarchical Attribution Graph Decomposition (HAGD), which reduces circuit discovery from $O(2^n)$ to $O(n^2 \log n)$ via multi-resolution abstractions and differentiable search. It integrates cross-layer transcoders for monosemantic feature extraction, a graph neural network-guided circuit search, and a causal validation protocol to yield verified sparse circuits across models from 117M to 70B parameters. Empirical results show high behavioral preservation on algorithmic tasks ($82\%-97\%$) and substantial-but-lower preservation on NLP benchmarks ($74\%-88\%$), with cross-architecture similarity averaging around $67\%$ across model families. The findings demonstrate scalability of circuit extraction to very large models while highlighting limitations such as incomplete attention-path modeling, a 15–20% reconstruction dark matter, and the need for labeled data to train the GNN, pointing to clear directions for future work and potential safety applications.

Abstract

Mechanistic interpretability seeks to reverse-engineer neural network computations into human-understandable algorithms, yet extracting sparse computational circuits from billion-parameter language models remains challenging due to exponential search complexity and pervasive polysemanticity. The proposed Hierarchical Attribution Graph Decomposition (HAGD) framework reduces circuit discovery complexity from O(2^n) exhaustive enumeration to O(n^2 log n) through multi-resolution abstraction hierarchies and differentiable circuit search. The methodology integrates cross-layer transcoders for monosemantic feature extraction, graph neural network meta-learning for topology prediction, and causal intervention protocols for validation. Empirical evaluation spans GPT-2 variants, Llama-7B through Llama-70B, and Pythia suite models across algorithmic tasks and natural language benchmarks. On modular arithmetic tasks, the framework achieves up to 91% behavioral preservation ($\pm$2.3\% across runs) while maintaining interpretable subgraph sizes. Cross-architecture transfer experiments suggest that discovered circuits exhibit moderate structural similarity (averaging 67%) across model families, indicating potential shared computational patterns. These results provide preliminary foundations for interpretability at larger model scales while identifying significant limitations in current attribution methodologies that require future advances.

Hierarchical Sparse Circuit Extraction from Billion-Parameter Language Models through Scalable Attribution Graph Decomposition

TL;DR

This work tackles the scalability barrier in mechanistic interpretability by introducing Hierarchical Attribution Graph Decomposition (HAGD), which reduces circuit discovery from to via multi-resolution abstractions and differentiable search. It integrates cross-layer transcoders for monosemantic feature extraction, a graph neural network-guided circuit search, and a causal validation protocol to yield verified sparse circuits across models from 117M to 70B parameters. Empirical results show high behavioral preservation on algorithmic tasks () and substantial-but-lower preservation on NLP benchmarks (), with cross-architecture similarity averaging around across model families. The findings demonstrate scalability of circuit extraction to very large models while highlighting limitations such as incomplete attention-path modeling, a 15–20% reconstruction dark matter, and the need for labeled data to train the GNN, pointing to clear directions for future work and potential safety applications.

Abstract

Mechanistic interpretability seeks to reverse-engineer neural network computations into human-understandable algorithms, yet extracting sparse computational circuits from billion-parameter language models remains challenging due to exponential search complexity and pervasive polysemanticity. The proposed Hierarchical Attribution Graph Decomposition (HAGD) framework reduces circuit discovery complexity from O(2^n) exhaustive enumeration to O(n^2 log n) through multi-resolution abstraction hierarchies and differentiable circuit search. The methodology integrates cross-layer transcoders for monosemantic feature extraction, graph neural network meta-learning for topology prediction, and causal intervention protocols for validation. Empirical evaluation spans GPT-2 variants, Llama-7B through Llama-70B, and Pythia suite models across algorithmic tasks and natural language benchmarks. On modular arithmetic tasks, the framework achieves up to 91% behavioral preservation (2.3\% across runs) while maintaining interpretable subgraph sizes. Cross-architecture transfer experiments suggest that discovered circuits exhibit moderate structural similarity (averaging 67%) across model families, indicating potential shared computational patterns. These results provide preliminary foundations for interpretability at larger model scales while identifying significant limitations in current attribution methodologies that require future advances.
Paper Structure (31 sections, 1 theorem, 10 equations, 4 figures, 6 tables, 1 algorithm)

This paper contains 31 sections, 1 theorem, 10 equations, 4 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Mechanistic Interpretability Foundations
  4. Sparse Autoencoder Methods
  5. Attribution and Pruning Approaches
  6. Theoretical Frameworks
  7. Validation Methodologies
  8. Methodology
  9. Framework Overview
  10. Sparse Feature Extraction
  11. Attribution Graph Construction
  12. Hierarchical Decomposition Algorithm
  13. Circuit Search with Graph Neural Networks
  14. Causal Validation Protocol
  15. Experimental Design
  16. ...and 16 more sections

Key Result

Theorem 1

Let $\mathcal{G}$ be an attribution graph with $n$ vertices. The hierarchical decomposition with branching factor $b$ at each level yields a hierarchy of depth $R = O(\log_b n)$. Circuit search through the hierarchy admits worst-case complexity $O(n^2 \log n)$ compared to $O(2^n)$ for exhaustive enu

Figures (4)

  • Figure 1: Hierarchical circuit extraction pipeline from language model through verified circuit output.
  • Figure 2: Behavioral preservation versus circuit size across task types.
  • Figure 3: Cross-architecture circuit transfer coefficients averaged across tasks.
  • Figure 4: Complexity comparison showing polynomial scaling of the hierarchical method versus alternatives.

Theorems & Definitions (3)

  • Definition 1: Hierarchical Decomposition
  • Theorem 1: Complexity Reduction
  • proof