Convergence of energy-based learning in linear resistive networks
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917224137097216 |
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| author | Huijzer, Anne-Men Chaffey, Thomas Besselink, Bart van Waarde, Henk J. |
| author_facet | Huijzer, Anne-Men Chaffey, Thomas Besselink, Bart van Waarde, Henk J. |
| contents | Energy-based learning algorithms are alternatives to backpropagation and are well-suited to distributed implementations in analog electronic devices. However, a rigorous theory of convergence is lacking. We make a first step in this direction by analysing a particular energybased learning algorithm, Contrastive Learning, applied to a network of linear adjustable resistors. It is shown that, in this setup, Contrastive Learning is equivalent to projected gradient descent on a convex function with Lipschitz continuous gradient, giving a guarantee of convergence of the algorithm for a range of stepsizes. This convergence result is then extended to a stochastic variant of Contrastive Learning. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_00349 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence of energy-based learning in linear resistive networks Huijzer, Anne-Men Chaffey, Thomas Besselink, Bart van Waarde, Henk J. Optimization and Control Machine Learning Neural and Evolutionary Computing Systems and Control 65K10, 68T05, 93B30, 93D99 Energy-based learning algorithms are alternatives to backpropagation and are well-suited to distributed implementations in analog electronic devices. However, a rigorous theory of convergence is lacking. We make a first step in this direction by analysing a particular energybased learning algorithm, Contrastive Learning, applied to a network of linear adjustable resistors. It is shown that, in this setup, Contrastive Learning is equivalent to projected gradient descent on a convex function with Lipschitz continuous gradient, giving a guarantee of convergence of the algorithm for a range of stepsizes. This convergence result is then extended to a stochastic variant of Contrastive Learning. |
| title | Convergence of energy-based learning in linear resistive networks |
| topic | Optimization and Control Machine Learning Neural and Evolutionary Computing Systems and Control 65K10, 68T05, 93B30, 93D99 |
| url | https://arxiv.org/abs/2503.00349 |