Disentangling Representations in Restricted Boltzmann Machines without Adversaries
A goal of unsupervised machine learning is to build representations of complex high-dimensional data, with simple relations to their properties. Such disentangled representations make it easier to interpret the significant latent factors of variation in the data, as well as to generate new data with...
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| Vydané v: | Physical review. X Ročník 13; číslo 2; s. 021003 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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01.04.2023
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| ISSN: | 2160-3308, 2160-3308 |
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| Abstract | A goal of unsupervised machine learning is to build representations of complex high-dimensional data, with simple relations to their properties. Such disentangled representations make it easier to interpret the significant latent factors of variation in the data, as well as to generate new data with desirable features. The methods for disentangling representations often rely on an adversarial scheme, in which representations are tuned to avoid discriminators from being able to reconstruct information about the data properties (labels). Unfortunately, adversarial training is generally difficult to implement in practice. Here we propose a simple, effective way of disentangling representations without any need to train adversarial discriminators and apply our approach to Restricted Boltzmann Machines, one of the simplest representation-based generative models. Our approach relies on the introduction of adequate constraints on the weights during training, which allows us to concentrate information about labels on a small subset of latent variables. The effectiveness of the approach is illustrated with four examples: the CelebA dataset of facial images, the two-dimensional Ising model, the MNIST dataset of handwritten digits, and the taxonomy of protein families. In addition, we show how our framework allows for analytically computing the cost, in terms of the log-likelihood of the data, associated with the disentanglement of their representations. |
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| AbstractList | A goal of unsupervised machine learning is to build representations of complex high-dimensional data, with simple relations to their properties. Such disentangled representations make it easier to interpret the significant latent factors of variation in the data, as well as to generate new data with desirable features. The methods for disentangling representations often rely on an adversarial scheme, in which representations are tuned to avoid discriminators from being able to reconstruct information about the data properties (labels). Unfortunately, adversarial training is generally difficult to implement in practice. Here we propose a simple, effective way of disentangling representations without any need to train adversarial discriminators and apply our approach to Restricted Boltzmann Machines, one of the simplest representation-based generative models. Our approach relies on the introduction of adequate constraints on the weights during training, which allows us to concentrate information about labels on a small subset of latent variables. The effectiveness of the approach is illustrated with four examples: the CelebA dataset of facial images, the two-dimensional Ising model, the MNIST dataset of handwritten digits, and the taxonomy of protein families. In addition, we show how our framework allows for analytically computing the cost, in terms of the log-likelihood of the data, associated with the disentanglement of their representations. |
| ArticleNumber | 021003 |
| Author | Monasson, Rémi Fernandez-de-Cossio-Diaz, Jorge Cocco, Simona |
| Author_xml | – sequence: 1 givenname: Jorge orcidid: 0000-0002-4476-805X surname: Fernandez-de-Cossio-Diaz fullname: Fernandez-de-Cossio-Diaz, Jorge – sequence: 2 givenname: Simona orcidid: 0000-0002-1852-7789 surname: Cocco fullname: Cocco, Simona – sequence: 3 givenname: Rémi orcidid: 0000-0002-4459-0204 surname: Monasson fullname: Monasson, Rémi |
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| Cites_doi | 10.1109/MSP.2012.2211477 10.1103/PhysRev.65.117 10.1103/PhysRevB.100.064304 10.1070/SM1967v001n04ABEH001994 10.1088/1361-6633/aa9965 10.1016/S0092-8674(00)81100-9 10.1017/CBO9781139164542 10.1017/CBO9780511810800 10.1140/epjb/e2006-00209-7 10.1038/nrm2178 10.1103/PhysRevE.99.032113 10.7554/eLife.39397 10.1103/PhysRevLett.118.138301 10.1146/annurev.neuro.25.112701.142909 10.1093/oso/9780198517962.001.0001 10.1103/PhysRevE.100.032128 10.1103/PhysRevResearch.2.043390 10.1073/pnas.1111471108 10.1093/nar/gky995 10.1093/nar/29.3.638 10.21468/SciPostPhys.8.5.074 10.1371/journal.pcbi.1007544 10.7551/mitpress/4175.001.0001 10.1093/nar/gkab314 10.1016/S0896-6273(00)81205-2 10.1038/s41587-022-01307-0 10.1093/nar/gkaa1100 10.1088/1742-5468/ac98a7 10.1016/j.cels.2020.11.005 10.1111/j.1742-4658.2008.06411.x 10.1038/s41592-022-01488-1 10.1103/RevModPhys.77.579 10.1109/TIP.2019.2916751 10.1016/j.cpc.2020.107518 10.1088/1751-8121/ab7d00 |
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| SubjectTerms | Computer Science Constraints Cost analysis Datasets Discriminators Handwriting Image reconstruction Ising model Labels Machine learning Neural networks Physics Representations Taxonomy Training Two dimensional models Unsupervised learning |
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| Title | Disentangling Representations in Restricted Boltzmann Machines without Adversaries |
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