Stochastic Parameter Decomposition
This work addresses a bottleneck in mechanistic interpretability by improving the practicality of linear parameter decomposition methods, though it is incremental in scaling existing approaches.
The paper tackles the computational cost and hyperparameter sensitivity of Attribution-based Parameter Decomposition (APD) in linear parameter decomposition for neural networks by introducing Stochastic Parameter Decomposition (SPD), which is shown to be more scalable and robust, enabling decomposition of slightly larger and more complex models.
A key step in reverse engineering neural networks is to decompose them into simpler parts that can be studied in relative isolation. Linear parameter decomposition -- a framework that has been proposed to resolve several issues with current decomposition methods -- decomposes neural network parameters into a sum of sparsely used vectors in parameter space. However, the current main method in this framework, Attribution-based Parameter Decomposition (APD), is impractical on account of its computational cost and sensitivity to hyperparameters. In this work, we introduce \textit{Stochastic Parameter Decomposition} (SPD), a method that is more scalable and robust to hyperparameters than APD, which we demonstrate by decomposing models that are slightly larger and more complex than was possible to decompose with APD. We also show that SPD avoids other issues, such as shrinkage of the learned parameters, and better identifies ground truth mechanisms in toy models. By bridging causal mediation analysis and network decomposition methods, this demonstration opens up new research possibilities in mechanistic interpretability by removing barriers to scaling linear parameter decomposition methods to larger models. We release a library for running SPD and reproducing our experiments at https://github.com/goodfire-ai/spd/tree/spd-paper.