{"ID":2878111,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.19015","arxiv_id":"2508.19015","title":"Learning with springs and sticks","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2508.19015","url_pdf":"https://arxiv.org/pdf/2508.19015v1","authors":"[\"Luis Mantilla Calderón\",\"Alán Aspuru-Guzik\"]","published":"2025-08-26T13:26:26Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}