Interactions between crosscoder features: a compact proofs perspective

ICLR 2026 Conference Submission17900 Authors

Keywords: Sparse autoencoders, compact proofs, interpretability, formal verification

TL;DR: We show how a crosscoder can be used to derive a compact proof of model performance and use that to derive a measure of interactions between crosscoder features.

Abstract: Dictionary learning methods like Sparse Autoencoders (SAEs) and crosscoders attempt to explain a model by decomposing its activations into independent features. Interactions between features hence induce errors in the reconstruction. We formalize this intuition via compact proofs and make five contributions. First, we show how, \textit{in principle}, a compact proof of model performance can be constructed using a crosscoder. Second, we show that an error term arising in this proof can naturally be interpreted as a measure of inteaction between crosscoder features and provide an explicit expression for the interaction term in the Multi-Layer Perceptron (MLP) layers. We then provide two applications of this new interaction measure. In our third contribution we show that the interaction term itself can be used as a differentiable loss penalty. Applying this penalty, we can achieve ``computationally sparse" crosscoders that retain $60\%$ of MLP performance when only keeping a single feature at each datapoint and neuron, compared to $10\%$ in standard crosscoders. We then show that clustering according to our interaction measure provides semantically meaningful feature clusters, and finally that sleeper agents have significant interactions. Code is available at the following anonymous repository: \url{https://anonymous.4open.science/r/anon_crosscoders-2F77/}.

Primary Area: interpretability and explainable AI

Submission Number: 17900