Decomposing MLP Activations into Interpretable Features via
  Semi-Nonnegative Matrix Factorization
Authors: name: Or Shafran, name: Atticus Geiger, name: Mor Geva

A central goal for mechanistic interpretability has been to identify the
right units of analysis in large language models (LLMs) that causally explain
their outputs. While early work focused on individual neurons, evidence that
neurons often encode multiple concepts has motivated a shift toward analyzing
directions in activation space. A key question is how to find directions that
capture interpretable features in an unsupervised manner. Current methods rely
on dictionary learning with sparse autoencoders (SAEs), commonly trained over
residual stream activations to learn directions from scratch. However, SAEs
often struggle in causal evaluations and lack intrinsic interpretability, as
their learning is not explicitly tied to the computations of the model. Here,
we tackle these limitations by directly decomposing MLP activations with
semi-nonnegative matrix factorization (SNMF), such that the learned features
are (a) sparse linear combinations of co-activated neurons, and (b) mapped to
their activating inputs, making them directly interpretable. Experiments on
Llama 3.1, Gemma 2 and GPT-2 show that SNMF derived features outperform SAEs
and a strong supervised baseline (difference-in-means) on causal steering,
while aligning with human-interpretable concepts. Further analysis reveals that
specific neuron combinations are reused across semantically-related features,
exposing a hierarchical structure in the MLP's activation space. Together,
these results position SNMF as a simple and effective tool for identifying
interpretable features and dissecting concept representations in LLMs.