aiqbench analysis
This research formalizes feature interactions in crosscoders, offering a differentiable loss penalty that significantly improves reconstruction efficiency and sparsity. By enabling semantically meaningful clustering and detecting significant interactions in sleeper agents, the work provides a rigorous mathematical foundation for mechanistic interpretability. These advances are critical for building more transparent and reliable model explanations without sacrificing performance.
Interactions Between Crosscoder Features: A Compact Proofs Perspective
arXiv:2606.09940v1 Announce Type: new 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 interaction between crosscoder features and provide an explicit expression for the interaction term in the Multi-Layer Perceptron (MLP) layers. We then provide three 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 https://github.com/chainik1125/crosscoders-feature-interactions/tree/arxiv.
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 interaction between crosscoder features and provide an explicit expression for the interaction term in the Multi-Layer Perceptron (MLP) layers. We then provide three 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 this https URL.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2606.09940 [cs.LG]
(or arXiv:2606.09940v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.09940 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 283 words
Related coverage
Beyond Belief Nesting: Rethinking Higher-Order Theory of Mind in Large Language Models
arXiv · Oct 14, 2026
On the Diverse Dynamical Behaviors Arising in Deep Linear Transformers
arXiv · Jul 22, 2026
TruthSplit: Operationalizing Conditional Validity in Arguments Through Multi-Perspective Reasoning
arXiv · Jun 9, 2026
Infant simulator with an embodied caregiver: Generating infant-perspective touch and vision during social interaction
arXiv · Oct 6, 2026