# Exploring the Effect of Basis Rotation on NQS Performance

arXiv: https://arxiv.org/abs/2512.17893 · HTML: https://mlsanity.com/paper/2512.17893/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 55 references that are in the map.
- First posted on arXiv 19 Dec 2025.

## Builds on (most cited first, 12 of 12)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [Revisiting Natural Gradient for Deep Networks](https://mlsanity.com/paper/1301.3584/) (2013)
- [Quantum Natural Gradient](https://mlsanity.com/paper/1909.02108/) (2019)
- [NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems](https://mlsanity.com/paper/2112.10526/) (2021)
- [When can classical neural networks represent quantum states?](https://mlsanity.com/paper/2410.23152/) (2024)
- [Learning ground states of gapped quantum Hamiltonians with Kernel Methods](https://mlsanity.com/paper/2303.08902/) (2023)

## Abstract (arXiv)

Neural Quantum States (NQS) are powerful variational representations of quantum many-body wavefunctions, yet their performance depends sensitively on the chosen basis. Using an exactly solvable one-dimensional Ising model, we show that local basis rotations leave the minimization landscape unchanged while relocating the exact ground state in parameter space. This provides a controlled framework to disentangle representational limitations from optimization-induced trainability effects. This geometric displacement, quantified through information-geometric measures, can steer optimization of shallow architectures toward saddle points and high-curvature regions. As a result, low energy errors may coexist with an incorrect wavefunction structure. By comparing energy and infidelity optimization within the same variational architectures, we show that optimization failure can persist even when the rotated target state remains representable. Our results identify a geometric mechanism contributing to basis dependence in NQS and motivate landscape-aware variational design.