# Adiabatic Fine-Tuning of Neural Quantum States Enables Detection of Phase Transitions in Weight Space

arXiv: https://arxiv.org/abs/2503.17140 · HTML: https://mlsanity.com/paper/2503.17140/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 22 references that are in the map.
- First posted on arXiv 21 Mar 2025.

## Builds on (most cited first, 7 of 7)

- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networks](https://mlsanity.com/paper/2110.06296/) (2021)
- [Predicting Neural Network Accuracy from Weights](https://mlsanity.com/paper/2002.11448/) (2020)
- [Classifying the classifier: dissecting the weight space of neural networks](https://mlsanity.com/paper/2002.05688/) (2020)
- [Towards Scalable and Versatile Weight Space Learning](https://mlsanity.com/paper/2406.09997/) (2024)
- [Discovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networks](https://mlsanity.com/paper/2003.04299/) (2020)
- [Explainable Representation Learning of Small Quantum States](https://mlsanity.com/paper/2306.05694/) (2023)

## Built on by (most cited first, 3 of 3)

- [Mechanistic Interpretability and Causal Feature Steering of Neural Quantum States via Sparse Autoencoders](https://mlsanity.com/paper/2607.01336/) (2026)
- [Why is topology hard to learn?](https://mlsanity.com/paper/2509.26261/) (2025)
- [Apparent Compression, Real Stability: The Intrinsic Dimension of Learning a Quantum Wavefunction](https://mlsanity.com/paper/2609.33193/) (2026)

## Abstract (arXiv)

Neural quantum states (NQS) have emerged as a powerful tool for approximating quantum wavefunctions using deep learning. While these models achieve remarkable accuracy, understanding how they encode physical information remains an open challenge. In this work, we introduce adiabatic fine-tuning, a scheme that trains NQS across a phase diagram, leading to strongly correlated weight representations across different models. This correlation in weight space enables the detection of phase transitions in quantum systems by analyzing the trained network weights alone. We validate our approach on the transverse field Ising model and the J1-J2 Heisenberg model, demonstrating that phase transitions manifest as distinct structures in weight space. Our results establish a connection between physical phase transitions and the geometry of neural network parameters, opening new directions for the interpretability of machine learning models in physics.