mlsanityData to 14 Oct 2026

Rethinking LLM Training through Information Geometry and Quantum Metrics

arXiv 2506.15830 ↗First posted 18 Jun 2025cs.CL quant-phcited by 3

On the map: LLM reasoning → Reinforcement learning for reasoning

Abstract (arXiv)

Optimization in large language models (LLMs) unfolds over high-dimensional parameter spaces with non-Euclidean structure. Information geometry frames this landscape using the Fisher information metric, enabling more principled learning via natural gradient descent. Though often impractical, this geometric lens clarifies phenomena such as sharp minima, generalization, and observed scaling laws. We argue that curvature-based approaches deepen our understanding of LLM training. Finally, we speculate on quantum analogies based on the Fubini-Study metric and Quantum Fisher Information, hinting at efficient optimization in quantum-enhanced systems.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning. Builds on 5 of its 17 references that are in the map. First posted on arXiv 18 Jun 2025.

Builds on

5 of 17 references.

References · 5

  1. 2020Scaling Laws for Neural Language Modelscited by 6,586
  2. 2022Training Compute-Optimal Large Language Modelscited by 3,019
  3. 2016Optimization Methods for Large-Scale Machine Learningcited by 1,150
  4. 2015Optimizing Neural Networks with Kronecker-factored Approximate Curvaturecited by 796
  5. 2018Supervised learning with quantum enhanced feature spacescited by 665

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026TopoCurate:Modeling Interaction Topology for Tool-Use Agent Trainingcited by 4
  2. 2026Towards Understanding the Power and Limits of the Muon Optimizer: A River-Valley Perspectivecited by 2
  3. 2026Hessian Spectral Analysis at Foundation Model Scalecited by 1

Similar, not cited

Close in wording, no citation either way

  1. 2025Large Language Model Scaling Laws for Neural Quantum States in Quantum Chemistry
  2. 2026Aligning Quantum Operators with Large Language Models
  3. 2025Superpositional Gradient Descent: Harnessing Quantum Principles for Model Training
  4. 2026LLMs as Noisy Channels: A Shannon Perspective on Model Capacity and Scaling Laws
  5. 2026The Blessing of Dimensionality in LLM Fine-tuning: A Variance-Curvature Perspective
  6. 2026Towards a Data-Parameter Correspondence for LLMs: A Preliminary Discussion
  7. 2025Compute-Optimal LLMs Provably Generalize Better With Scale
  8. 2026SIGMA: Scalable Spectral Insights for LLM Model Collapse