Bilinear MLPs enable weight-based mechanistic interpretability

This is the official code repository for the above paper [link].

Abstract

A mechanistic understanding of how MLPs do computation in deep neural networks remains elusive. Current interpretability work can extract features from hidden activations over an input dataset but generally cannot explain how MLP weights construct features. One challenge is that element-wise nonlinearities introduce higher-order interactions and make it difficult to trace computations through the MLP layer. In this paper, we analyze bilinear MLPs, a type of Gated Linear Unit (GLU) without any element-wise nonlinearity that nevertheless achieves competitive performance. Bilinear MLPs can be fully expressed in terms of linear operations using a third-order tensor, allowing flexible analysis of the weights. Analyzing the spectra of bilinear MLP weights using eigendecomposition reveals interpretable low-rank structure across toy tasks, image classification, and language modeling. We use this understanding to craft adversarial examples, uncover overfitting, and identify small language model circuits directly from the weights alone. Our results demonstrate that bilinear layers serve as an interpretable drop-in replacement for current activation functions and that weight-based interpretability is viable for understanding deep-learning models.

Installation

Install uv, then:

uv sync

This creates a virtual environment and installs all dependencies.

Run scripts and notebooks with, or just select the venv kernel in VSCode:

uv run python <script.py>

Tutorials

The tutorial folder contains a series of notebooks, aimed at beginners or people who simply learn quicker by looking at code. These documents cover weight-based interpretability from the ground up and provide a step-by-step guide on how to think about bilinear layers. The document covers our results on image models and language models.

The tutorials are currently in beta and may be on the short side, if you have any suggestions or critique, let me (@tdooms) know.