The Gaussian-Multinoulli Restricted Boltzmann Machine: A Potts Model Extension of the GRBM
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917326396325888 |
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| author | Kapasi, Nikhil Elfouly, Mohamed Whitehead, William Theogarajan, Luke |
| author_facet | Kapasi, Nikhil Elfouly, Mohamed Whitehead, William Theogarajan, Luke |
| contents | Many real-world tasks, from associative memory to symbolic reasoning, benefit from discrete, structured representations that standard continuous latent models can struggle to express. We introduce the Gaussian-Multinoulli Restricted Boltzmann Machine (GM-RBM), a generative energy-based model that extends the Gaussian-Bernoulli RBM (GB-RBM) by replacing binary hidden units with q-state categorical (Potts) units, yielding a richer latent state space for multivalued concepts. We provide a self-contained derivation of the energy, conditional distributions, and learning rules, and detail practical training choices (contrastive divergence with temperature annealing and intra-slot diversity constraints) that avoid state collapse. To separate architectural effects from sheer latent capacity, we evaluate under both capacity-matched and parameter-matched setups, comparing GM-RBM with GB-RBM configured to have the same number of possible latent assignments. On analogical recall and structured memory benchmarks, GM-RBM achieves competitive, and in several regimes improved, recall at equal capacity with comparable training cost, despite using only Gibbs updates. The discrete q-ary formulation is also amenable to efficient implementation. These results clarify when categorical hidden units provide a simple, scalable alternative to binary latents for discrete inference within tractable RBMs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11635 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Gaussian-Multinoulli Restricted Boltzmann Machine: A Potts Model Extension of the GRBM Kapasi, Nikhil Elfouly, Mohamed Whitehead, William Theogarajan, Luke Machine Learning Many real-world tasks, from associative memory to symbolic reasoning, benefit from discrete, structured representations that standard continuous latent models can struggle to express. We introduce the Gaussian-Multinoulli Restricted Boltzmann Machine (GM-RBM), a generative energy-based model that extends the Gaussian-Bernoulli RBM (GB-RBM) by replacing binary hidden units with q-state categorical (Potts) units, yielding a richer latent state space for multivalued concepts. We provide a self-contained derivation of the energy, conditional distributions, and learning rules, and detail practical training choices (contrastive divergence with temperature annealing and intra-slot diversity constraints) that avoid state collapse. To separate architectural effects from sheer latent capacity, we evaluate under both capacity-matched and parameter-matched setups, comparing GM-RBM with GB-RBM configured to have the same number of possible latent assignments. On analogical recall and structured memory benchmarks, GM-RBM achieves competitive, and in several regimes improved, recall at equal capacity with comparable training cost, despite using only Gibbs updates. The discrete q-ary formulation is also amenable to efficient implementation. These results clarify when categorical hidden units provide a simple, scalable alternative to binary latents for discrete inference within tractable RBMs. |
| title | The Gaussian-Multinoulli Restricted Boltzmann Machine: A Potts Model Extension of the GRBM |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2505.11635 |