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LLM Interpretability with Identifiable Temporal-Instantaneous Representation

Xiangchen Song, Jiaqi Sun, Zijian Li, Yujia Zheng, Kun Zhang

TL;DR

The paper tackles the challenge of interpreting Large Language Models by addressing the limitations of sparse autoencoders in capturing temporal and instantaneous relationships and lacking identifiability guarantees. It proposes a identifiable temporal causal representation learning framework that extends SAEs with a linear, scalable model incorporating time-delayed and instantaneous edges, and provides theoretical identifiability guarantees under clearly stated assumptions. The authors develop a three-component estimation pipeline (observation reconstruction, independent noise estimation, and sparsity regularization) and validate the approach through synthetic, semi-synthetic, and real LLM activation experiments, showing recovery of latent concepts and causal graphs, as well as improved interpretability metrics. The work demonstrates that modeling both temporal and instantaneous conceptual relationships yields more informative representations for LLM activations, with practical implications for interpretability, debugging, and alignment research.

Abstract

Despite Large Language Models' remarkable capabilities, understanding their internal representations remains challenging. Mechanistic interpretability tools such as sparse autoencoders (SAEs) were developed to extract interpretable features from LLMs but lack temporal dependency modeling, instantaneous relation representation, and more importantly theoretical guarantees, undermining both the theoretical foundations and the practical confidence necessary for subsequent analyses. While causal representation learning (CRL) offers theoretically grounded approaches for uncovering latent concepts, existing methods cannot scale to LLMs' rich conceptual space due to inefficient computation. To bridge the gap, we introduce an identifiable temporal causal representation learning framework specifically designed for LLMs' high-dimensional concept space, capturing both time-delayed and instantaneous causal relations. Our approach provides theoretical guarantees and demonstrates efficacy on synthetic datasets scaled to match real-world complexity. By extending SAE techniques with our temporal causal framework, we successfully discover meaningful concept relationships in LLM activations. Our findings show that modeling both temporal and instantaneous conceptual relationships advances the interpretability of LLMs.

LLM Interpretability with Identifiable Temporal-Instantaneous Representation

TL;DR

The paper tackles the challenge of interpreting Large Language Models by addressing the limitations of sparse autoencoders in capturing temporal and instantaneous relationships and lacking identifiability guarantees. It proposes a identifiable temporal causal representation learning framework that extends SAEs with a linear, scalable model incorporating time-delayed and instantaneous edges, and provides theoretical identifiability guarantees under clearly stated assumptions. The authors develop a three-component estimation pipeline (observation reconstruction, independent noise estimation, and sparsity regularization) and validate the approach through synthetic, semi-synthetic, and real LLM activation experiments, showing recovery of latent concepts and causal graphs, as well as improved interpretability metrics. The work demonstrates that modeling both temporal and instantaneous conceptual relationships yields more informative representations for LLM activations, with practical implications for interpretability, debugging, and alignment research.

Abstract

Despite Large Language Models' remarkable capabilities, understanding their internal representations remains challenging. Mechanistic interpretability tools such as sparse autoencoders (SAEs) were developed to extract interpretable features from LLMs but lack temporal dependency modeling, instantaneous relation representation, and more importantly theoretical guarantees, undermining both the theoretical foundations and the practical confidence necessary for subsequent analyses. While causal representation learning (CRL) offers theoretically grounded approaches for uncovering latent concepts, existing methods cannot scale to LLMs' rich conceptual space due to inefficient computation. To bridge the gap, we introduce an identifiable temporal causal representation learning framework specifically designed for LLMs' high-dimensional concept space, capturing both time-delayed and instantaneous causal relations. Our approach provides theoretical guarantees and demonstrates efficacy on synthetic datasets scaled to match real-world complexity. By extending SAE techniques with our temporal causal framework, we successfully discover meaningful concept relationships in LLM activations. Our findings show that modeling both temporal and instantaneous conceptual relationships advances the interpretability of LLMs.

Paper Structure

This paper contains 71 sections, 4 theorems, 46 equations, 7 figures, 11 tables.

Table of Contents

  1. Introduction
  2. Problem Setting
  3. Remark on the Linearity of the Model
  4. Theoretical Guarantees
  5. Proof Sketch
  6. Discussion
  7. Discussion
  8. Implementation
  9. Observation Reconstruction
  10. Independent Noise Estimation
  11. Sparsity Regularization
  12. Experiments
  13. Synthetic Data Experiments
  14. Identifiability Verification
  15. Challenges on Scaling to Large Language Model Activation Dimensions
  16. ...and 56 more sections

Key Result

Theorem 1

Suppose the estimated model $(\hat{\mathbf{A}},\{\hat{\mathbf{B}}_{\tau}\}_{\tau=1}^L,\hat{\mathbf{M}},p_{\boldsymbol{\hat{\epsilon}}})$ and the true model $(\mathbf{A},\{\mathbf{B}_{\tau}\}_{\tau=1}^L,\mathbf{M},p_{\boldsymbol{\epsilon}})$ both generate $\mathbf{x}_t$ according to Eq. eq:data_gener where $\mathbf{S}\in\mathbb{R}^{n\times n}$ is invertible and $\mathbf{P}$ is a signed permutation

Figures (7)

  • Figure 1: Graphical illustration of the data generation process.
  • Figure 2: Illustration of estimation process. $\hat{\mathbf{B}}_{\tau}$ represents the learned time-delayed causal relation and $\hat{\mathbf{M}}$ is the instantaneous causal relation.
  • Figure 3: Visualization of recovered causal graphs of latent variables. (a) and (b) show the ground truth and estimated time-delayed matrix, respectively. (c) and (d) show the ground truth and the estimated instantaneous causal relations, respectively. (e) displays the correlation between the ground truth and recovered latent variables.
  • Figure 4: Computation time and memory usage for a single-step Jacobian as a function of input dimensionality. Both metrics grow superlinearly and exceed the capacity of modern GPUs when the input dimension is greater than $1000$.
  • Figure 5: MCC and total compute time in hours required to train the linear model as a function of input dimension.
  • ...and 2 more figures

Theorems & Definitions (7)

  • Theorem 1: Latent Indeterminacy
  • Corollary 1: Component-wise Identifiability
  • proof
  • Corollary 2: Subspace Identifiability
  • proof
  • Theorem 1: Latent Indeterminacy
  • proof