Apparent Compression, Real Stability: The Intrinsic Dimension of Learning a Quantum Wavefunction

arXiv:2609.33193 · cs.LG, quant-ph · Submitted 2026-09-27 · Read on arXiv

cs.LG, quant-ph

Submitted: 2026-09-27

Updated: 2026-09-27

Terminology

• Intrinsic Dimension — 13× in this paper · explained in 2 episodes
• Fine-Tuning — 9× in this paper · explained in 5 episodes
• Frustration — 7× in this paper · explained in 2 episodes
• Accuracy — 5× in this paper · explained in 1 episode
• Scaling Laws — 4× in this paper · explained in 4 episodes
• Adaptation — 3× in this paper · explained in 1 episode
• Phase Transitions — 3× in this paper · explained in 2 episodes
• Alignment — 2× in this paper · explained in 1 episode
• Benchmark — 2× in this paper · explained in 2 episodes
• Interpretability — 2× in this paper · explained in 15 episodes
• Latent Space — 2× in this paper · explained in 7 episodes
• Variational Monte Carlo (VMC) — 2× in this paper · explained in 2 episodes
• Ablation — 1× in this paper · explained in 1 episode
• Generalization — 1× in this paper · explained in 13 episodes
• Hypernetwork — 1× in this paper · explained in 2 episodes
• Neural Network Approximation — 1× in this paper · explained in 2 episodes
• Parameter-Efficient Fine-Tuning — 1× in this paper · explained in 2 episodes
• Pruning — 1× in this paper · explained in 4 episodes
• Quantum Geometric Tensor (QGT) — 1× in this paper · explained in 2 episodes
• Reinforcement Learning — 1× in this paper · explained in 4 episodes

Sources

• Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning
• Connectivity determines the capability of sparse neural network quantum states
• Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• NetKet: A Machine Learning Toolkit for Many-Body Quantum Systems
• Empowering deep neural quantum states through efficient optimization
• Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States
• Efficiency of neural quantum states in light of the quantum geometric tensor
• Towards Interpretability of Neural Quantum States
• The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks
• Adiabatic Fine-Tuning of Neural Quantum States Enables Detection of Phase Transitions in Weight Space
• LoRA: Low-Rank Adaptation of Large Language Models
• How many degrees of freedom do we need to train deep networks: a loss landscape perspective
• Measuring the Intrinsic Dimension of Objective Landscapes
• Unsupervised learning universal critical behavior via the intrinsic dimension
• Improving neural network performance for solving quantum sign structure
• Geometry of learning neural quantum states
• Fine-tuning Neural Network Quantum States
• A simple linear algebra identity to optimize Large-Scale Neural Network Quantum States
• Scaling Laws for Neural-Network Quantum States

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