From Sparse Features to Trustworthy Proxies: Certifying SAE-Based Interpretability

2026-06-16

AI Summary

This work addresses the challenge of verifying whether features extracted by sparse autoencoders (SAEs) faithfully reflect the behavior of frozen language models. It introduces the first theoretically grounded framework for quantitatively certifying the faithfulness of SAE-based interpretations. By constructing a posterior generalization analysis, the method replaces original hidden states with sparse activations reconstructed by the SAE and derives non-vacuous upper bounds on the expected risk of the original model using four measurable quantities. The approach achieves effective certification across GPT-2 Small, Gemma-2B, and Llama-3-8B, revealing that increased model depth enhances certifiability. Moreover, it distinguishes semantic alignment from mere sparsity, offering both diagnostic utility and rigorous theoretical guarantees.

Abstract

Sparse autoencoders (SAEs) are increasingly used to extract interpretable features from language models (LMs), yet a central question remains: when can an SAE-based explanation be treated as a faithful view of an underlying frozen LM We study this through a post-hoc generalization framework that certifies the LM via a sparse proxy, obtained by replacing a native hidden activation with its pretrained SAE reconstruction. Our framework derives an upper bound on the base model's expected risk using four measurable quantities: proxy risk, SAE reconstruction gap, concept-pool mismatch, and sparse complexity. We interpret this certificate as an operational criterion for explanatory faithfulness. In particular, a non-vacuous bound indicates that the extracted sparse features retain meaningful predictive information, while small reconstruction and mismatch errors indicate that the proxy remains behaviorally close to the original model. Empirically, we show that the bound becomes non-vacuous on GPT-2 Small, Gemma-2B, and Llama-3-8B at practical sample sizes. A detailed layerwise analysis of Llama-3-8B reveals a strong depth dependence, with later layers becoming much easier to certify, associated with both stronger local fidelity and weaker downstream error amplification. Finally, through feature-shuffling ablations, we show that the decomposition distinguishes genuine semantic alignment from mere statistical sparsity, providing a useful diagnostic for when SAE-based explanations become less reliable.

Problem

• Sparse Autoencoders
• Interpretability
• Faithfulness
• Language Models
• Explanatory Certification

Innovation

• sparse autoencoders
• interpretability certification
• post-hoc generalization
• faithful explanation
• proxy model