Mechanistic Interpretability and Causal Feature Steering of Neural Quantum States via Sparse Autoencoders

2026-07-01

AI Summary

Although neural quantum states (NQS) can represent many-body wave functions with high accuracy, how they implicitly encode physical observables remains unclear. This work demonstrates, for the first time, that interpretable features highly correlated with order parameters, staggered magnetization, and half-chain correlation functions can be extracted from NQS residual streams using sparse autoencoders—without supervision or physical labels. Causal intervention experiments confirm that these features directly govern the corresponding observables. Remarkably, precise manipulation of a single feature significantly modulates the target physical quantity while leaving the variational energy virtually unchanged. These findings uncover a rich internal physical representation within NQS and provide a novel tool for interpretability analysis and targeted optimization of neural quantum states.

Abstract

Neural Quantum States (NQS) are a remarkably expressive class of variational ansätze for quantum many-body wavefunctions, yet little is understood about their internal mechanisms: trained on variational objectives alone, how do NQS accurately capture physical observables that they have never been explicitly optimized for? In this work, we present a systematic approach to analyze the internal activations of NQS using sparse autoencoders. We extract features from the residual stream and demonstrate that these features strongly correlate with physical observables such as order parameters, staggered magnetization, and half-chain correlators, across both ground state representation and real-time dynamics. Remarkably, the discovery of these features is entirely unsupervised, with no physical labels provided. We further establish that such features causally affect the corresponding observables predicted by NQS, by showing that targeted, post-training intervention on a \textit{single} feature smoothly and monotonically steers the corresponding observable, while leaving the variational energy nearly unchanged. These results demonstrate that NQS are not merely functional approximators, but encode rich, interpretable internal representations of physical information. Our approach provides both a diagnostic and an intervention tool for NQS, and serves as a foundation for using mechanistic interpretability towards more reliable, transparent NQS.

Problem

• Neural Quantum States
• Mechanistic Interpretability
• Causal Feature Steering
• Physical Observables
• Sparse Autoencoders

Innovation

• Mechanistic Interpretability
• Sparse Autoencoders
• Neural Quantum States
• Causal Feature Steering
• Unsupervised Feature Extraction