Mechanistic Permutability: Match Features Across Layers (2410.07656v3)

Abstract: Understanding how features evolve across layers in deep neural networks is a fundamental challenge in mechanistic interpretability, particularly due to polysemanticity and feature superposition. While Sparse Autoencoders (SAEs) have been used to extract interpretable features from individual layers, aligning these features across layers has remained an open problem. In this paper, we introduce SAE Match, a novel, data-free method for aligning SAE features across different layers of a neural network. Our approach involves matching features by minimizing the mean squared error between the folded parameters of SAEs, a technique that incorporates activation thresholds into the encoder and decoder weights to account for differences in feature scales. Through extensive experiments on the Gemma 2 LLM, we demonstrate that our method effectively captures feature evolution across layers, improving feature matching quality. We also show that features persist over several layers and that our approach can approximate hidden states across layers. Our work advances the understanding of feature dynamics in neural networks and provides a new tool for mechanistic interpretability studies.

• The paper introduces SAE Match, a novel data-free technique that aligns Sparse Autoencoder features across neural network layers for improved interpretability.
• It employs a parameter folding technique that integrates activation thresholds into encoder and decoder weights to enhance matching accuracy.
• Extensive experiments on the Gemma 2 language model demonstrate reduced MSE and persistent feature evolution across layers.

Mechanistic Permutability: Match Features Across Layers

The paper "Mechanistic Permutability: Match Features Across Layers" introduces an innovative approach to understanding feature evolution in deep neural networks, particularly focusing on Sparse Autoencoders (SAEs) and their interpretability. This research addresses a fundamental challenge: aligning features across different layers in neural networks, which is pivotal for advancing mechanistic interpretability and understanding internal dynamics.

Key Contributions

The authors propose SAE Match, a data-free technique enabling the alignment of SAE features across layers in neural networks. This approach circumvents the conventional requirement of input data, offering insights into feature evolution through the model's layers. The primary contributions include:

1. SAE Match Methodology: Introduction of a novel method that aligns features without input data, facilitating the analysis of feature dynamics throughout a neural network.
2. Parameter Folding Technique: Incorporation of activation thresholds into encoder and decoder weights to address differences in feature scales, thereby enhancing feature matching accuracy.
3. Empirical Validation: Demonstration of the method's efficacy through extensive experiments on the Gemma 2 LLM, indicating improved quality in feature matching and revealing insights into feature persistence and transformation across layers.

Theoretical and Practical Implications

This research significantly impacts the field of mechanistic interpretability by providing a robust tool for analyzing feature dynamics. It proposes a solution to the problem of polysemanticity, where features represent multiple unrelated concepts, complicating model interpretation. By aligning features across layers, the paper advances our understanding of neural network behavior, offering potential improvements in transparency and explainability.

Experimental Results

The validation using the Gemma 2 model showed improved matching quality due to the parameter folding technique. Features were observed to persist over several layers, supporting the hypothesis of feature similarity across layers. The use of Mean Squared Error (MSE) in evaluating feature matching provided quantifiable metrics that support the method's efficacy.

Future Prospects

This paper opens avenues for further research into feature alignment methods applicable to various models beyond Gemma 2. Potential expansions could explore the integration of these methods with other interpretability tools to enhance model transparency further. The assumption of optimal parameter choice also suggests room for optimization to achieve better matching performance in different network architectures.

Conclusion

The paper presents a substantial contribution to the field of neural network interpretability by introducing SAE Match. Through the development of data-free methods and parameter folding, it offers a refined approach to understanding how features evolve across model layers. This advancement paves the way for deeper insights into network dynamics, aiding in their responsible deployment in complex applications. Future work can build on these findings to generalize across different architectures, enhancing interpretability tools across the AI landscape.