标题： 通过信息几何和量子度量重新思考大语言模型训练 显示英文标题

标题： Rethinking LLM Training through Information Geometry and Quantum Metrics

摘要： 大型语言模型（LLMs）中的优化是在具有非欧几里得结构的高维参数空间中展开的。 信息几何使用费舍尔信息度量来描述这一景观，通过自然梯度下降实现更合理的学习。 尽管通常不切实际，但这种几何视角阐明了尖锐极小值、泛化和观察到的缩放定律等现象。 我们认为，考虑曲率的方法加深了我们对LLM训练的理解。 最后，我们基于Fubini-Study度量和量子费舍尔信息提出了量子类比，暗示了在量子增强系统中的高效优化。 显示英文摘要

摘要： 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.