Nonequilibrium Thermodynamics of Associative Memory Continuous-Time Recurrent Neural Networks
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911265856684032 |
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| author | Aguilera, Miguel De Martino, Daniele Garashchuk, Ivan Sinelshchikov, Dmitry |
| author_facet | Aguilera, Miguel De Martino, Daniele Garashchuk, Ivan Sinelshchikov, Dmitry |
| contents | Continuous-Time Recurrent Neural Networks (CTRNNs) have been widely used for their capacity to model complex temporal behaviour. However, their internal dynamics often remain difficult to interpret. In this paper, we propose a new class of CTRNNs based on Hopfield-like associative memories with asymmetric couplings. This model combines the expressive power of associative memories with a tractable mathematical formalism to characterize fluctuations in nonequilibrium dynamics. We show that this mathematical description allows us to directly compute the evolution of its macroscopic observables (the encoded features), as well as the instantaneous entropy and entropy dissipation of the system, thereby offering a bridge between dynamical systems descriptions of low-dimensional observables and the statistical mechanics of large nonequilibrium networks. Our results suggest that these nonequilibrium associative CTRNNs can serve as more interpretable models for complex sequence-encoding networks. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_11150 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonequilibrium Thermodynamics of Associative Memory Continuous-Time Recurrent Neural Networks Aguilera, Miguel De Martino, Daniele Garashchuk, Ivan Sinelshchikov, Dmitry Disordered Systems and Neural Networks Statistical Mechanics Chaotic Dynamics Continuous-Time Recurrent Neural Networks (CTRNNs) have been widely used for their capacity to model complex temporal behaviour. However, their internal dynamics often remain difficult to interpret. In this paper, we propose a new class of CTRNNs based on Hopfield-like associative memories with asymmetric couplings. This model combines the expressive power of associative memories with a tractable mathematical formalism to characterize fluctuations in nonequilibrium dynamics. We show that this mathematical description allows us to directly compute the evolution of its macroscopic observables (the encoded features), as well as the instantaneous entropy and entropy dissipation of the system, thereby offering a bridge between dynamical systems descriptions of low-dimensional observables and the statistical mechanics of large nonequilibrium networks. Our results suggest that these nonequilibrium associative CTRNNs can serve as more interpretable models for complex sequence-encoding networks. |
| title | Nonequilibrium Thermodynamics of Associative Memory Continuous-Time Recurrent Neural Networks |
| topic | Disordered Systems and Neural Networks Statistical Mechanics Chaotic Dynamics |
| url | https://arxiv.org/abs/2511.11150 |