Mechanistic Permutability: Match Features Across Layers
Authors: name: Nikita Balagansky, name: Ian Maksimov, name: Daniil Gavrilov
Organization: T-Tech

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 language model, 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.