Geometric Learning Dynamics
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917339500380160 |
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| author | Vanchurin, Vitaly |
| author_facet | Vanchurin, Vitaly |
| contents | We present a unified geometric framework for modeling learning dynamics in physical, biological, and machine learning systems. The theory reveals three fundamental regimes, each emerging from the power-law relationship $g \propto κ^α$ between the metric tensor $g$ in the space of trainable variables and the noise covariance matrix $κ$. The quantum regime corresponds to $α= 1$ and describes Schrödinger-like dynamics that emerges from a discrete shift symmetry. The efficient learning regime corresponds to $α= \tfrac{1}{2}$ and describes very fast machine learning algorithms. The equilibration regime corresponds to $α= 0$ and describes classical models of biological evolution. We argue that the emergence of the intermediate regime $α= \tfrac{1}{2}$ is a key mechanism underlying the emergence of biological complexity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14728 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric Learning Dynamics Vanchurin, Vitaly Machine Learning Populations and Evolution Quantum Physics We present a unified geometric framework for modeling learning dynamics in physical, biological, and machine learning systems. The theory reveals three fundamental regimes, each emerging from the power-law relationship $g \propto κ^α$ between the metric tensor $g$ in the space of trainable variables and the noise covariance matrix $κ$. The quantum regime corresponds to $α= 1$ and describes Schrödinger-like dynamics that emerges from a discrete shift symmetry. The efficient learning regime corresponds to $α= \tfrac{1}{2}$ and describes very fast machine learning algorithms. The equilibration regime corresponds to $α= 0$ and describes classical models of biological evolution. We argue that the emergence of the intermediate regime $α= \tfrac{1}{2}$ is a key mechanism underlying the emergence of biological complexity. |
| title | Geometric Learning Dynamics |
| topic | Machine Learning Populations and Evolution Quantum Physics |
| url | https://arxiv.org/abs/2504.14728 |