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Rethinking LLM Training through Information Geometry and Quantum Metrics

18 June 2025
Riccardo Di Sipio
ArXiv (abs)PDFHTML
Main:7 Pages
1 Figures
Bibliography:2 Pages
Abstract

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-aware 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.

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@article{sipio2025_2506.15830,
  title={ Rethinking LLM Training through Information Geometry and Quantum Metrics },
  author={ Riccardo Di Sipio },
  journal={arXiv preprint arXiv:2506.15830},
  year={ 2025 }
}
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