Learning with springs and sticks
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912555461509120 |
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| author | Calderón, Luis Mantilla Aspuru-Guzik, Alán |
| author_facet | Calderón, Luis Mantilla Aspuru-Guzik, Alán |
| contents | Learning is a physical process. Here, we aim to study a simple dynamical system composed of springs and sticks capable of arbitrarily approximating any continuous function. The main idea of our work is to use the sticks to mimic a piecewise-linear approximation of the given function, use the potential energy of springs to encode a desired mean squared error loss function, and converge to a minimum-energy configuration via dissipation. We apply the proposed simulation system to regression tasks and show that its performance is comparable to that of multi-layer perceptrons. In addition, we study the thermodynamic properties of the system and find a relation between the free energy change of the system and its ability to learn an underlying data distribution. We empirically find a \emph{thermodynamic learning barrier} for the system caused by the fluctuations of the environment, whereby the system cannot learn if its change in free energy hits such a barrier. We believe this simple model can help us better understand learning systems from a physical point of view. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_19015 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning with springs and sticks Calderón, Luis Mantilla Aspuru-Guzik, Alán Machine Learning Learning is a physical process. Here, we aim to study a simple dynamical system composed of springs and sticks capable of arbitrarily approximating any continuous function. The main idea of our work is to use the sticks to mimic a piecewise-linear approximation of the given function, use the potential energy of springs to encode a desired mean squared error loss function, and converge to a minimum-energy configuration via dissipation. We apply the proposed simulation system to regression tasks and show that its performance is comparable to that of multi-layer perceptrons. In addition, we study the thermodynamic properties of the system and find a relation between the free energy change of the system and its ability to learn an underlying data distribution. We empirically find a \emph{thermodynamic learning barrier} for the system caused by the fluctuations of the environment, whereby the system cannot learn if its change in free energy hits such a barrier. We believe this simple model can help us better understand learning systems from a physical point of view. |
| title | Learning with springs and sticks |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2508.19015 |