Generalized hetero-associative neural networks
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908386997567488 |
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| author | Agliari, Elena Alessandrelli, Andrea Barra, Adriano Centonze, Martino Salomone Ricci-Tersenghi, Federico |
| author_facet | Agliari, Elena Alessandrelli, Andrea Barra, Adriano Centonze, Martino Salomone Ricci-Tersenghi, Federico |
| contents | Auto-associative neural networks (e.g., the Hopfield model implementing the standard Hebbian prescription) serve as a foundational framework for pattern recognition and associative memory in statistical mechanics. However, their hetero-associative counterparts, though less explored, exhibit even richer computational capabilities. In this work, we examine a straightforward extension of Kosko's Bidirectional Associative Memory (BAM), introducing a Three-directional Associative Memory (TAM), that is a tripartite neural network equipped with generalized Hebbian weights. Through both analytical approaches (using replica-symmetric statistical mechanics) and computational methods (via Monte Carlo simulations), we derive phase diagrams within the space of control parameters, revealing a region where the network can successfully perform pattern recognition as well as other tasks tasks. In particular, it can achieve pattern disentanglement, namely, when presented with a mixture of patterns, the network can recover the original patterns. Furthermore, the system is capable of retrieving Markovian sequences of patterns and performing generalized frequency modulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08151 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized hetero-associative neural networks Agliari, Elena Alessandrelli, Andrea Barra, Adriano Centonze, Martino Salomone Ricci-Tersenghi, Federico Disordered Systems and Neural Networks Auto-associative neural networks (e.g., the Hopfield model implementing the standard Hebbian prescription) serve as a foundational framework for pattern recognition and associative memory in statistical mechanics. However, their hetero-associative counterparts, though less explored, exhibit even richer computational capabilities. In this work, we examine a straightforward extension of Kosko's Bidirectional Associative Memory (BAM), introducing a Three-directional Associative Memory (TAM), that is a tripartite neural network equipped with generalized Hebbian weights. Through both analytical approaches (using replica-symmetric statistical mechanics) and computational methods (via Monte Carlo simulations), we derive phase diagrams within the space of control parameters, revealing a region where the network can successfully perform pattern recognition as well as other tasks tasks. In particular, it can achieve pattern disentanglement, namely, when presented with a mixture of patterns, the network can recover the original patterns. Furthermore, the system is capable of retrieving Markovian sequences of patterns and performing generalized frequency modulation. |
| title | Generalized hetero-associative neural networks |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2409.08151 |