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- W3136231202 abstract "The restricted Boltzmann machine is a basic machine learning tool able in principle to model the distribution of some arbitrary dataset. Its standard training procedure appears however delicate and obscure in many respects. We bring some new insights on it by considering the situation where the data have low intrinsic dimension, offering the possibility of an exact treatment, illustrated with simple study cases where the standard training is observed to fail. The reason for this failure is clarified thanks to a Coulomb interactions reformulation of the model where the hidden features are uniformly charged hyperplanes interacting repulsively with point-like charges representing the data. This leads us to consider a convex relaxation of the original optimization problem thereby resulting in a unique solution, obtained in precise numerical form in $d=1,2$ while a constrained linear regression solution is conjectured on the basis of an information theory argument." @default.
- W3136231202 created "2021-03-29" @default.
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- W3136231202 date "2021-09-06" @default.
- W3136231202 modified "2023-09-25" @default.
- W3136231202 title "Exact Training of Restricted Boltzmann Machines on Intrinsically Low Dimensional Data" @default.
- W3136231202 hasPublicationYear "2021" @default.
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