Learning disentangled representations via product manifold projection

Marco Fumero, Luca Cosmo, Simone Melzi, Emanuele Rodola
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:3530-3540, 2021.

Abstract

We propose a novel approach to disentangle the generative factors of variation underlying a given set of observations. Our method builds upon the idea that the (unknown) low-dimensional manifold underlying the data space can be explicitly modeled as a product of submanifolds. This definition of disentanglement gives rise to a novel weakly-supervised algorithm for recovering the unknown explanatory factors behind the data. At training time, our algorithm only requires pairs of non i.i.d. data samples whose elements share at least one, possibly multidimensional, generative factor of variation. We require no knowledge on the nature of these transformations, and do not make any limiting assumption on the properties of each subspace. Our approach is easy to implement, and can be successfully applied to different kinds of data (from images to 3D surfaces) undergoing arbitrary transformations. In addition to standard synthetic benchmarks, we showcase our method in challenging real-world applications, where we compare favorably with the state of the art.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-fumero21a, title = {Learning disentangled representations via product manifold projection}, author = {Fumero, Marco and Cosmo, Luca and Melzi, Simone and Rodola, Emanuele}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {3530--3540}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/fumero21a/fumero21a.pdf}, url = {https://proceedings.mlr.press/v139/fumero21a.html}, abstract = {We propose a novel approach to disentangle the generative factors of variation underlying a given set of observations. Our method builds upon the idea that the (unknown) low-dimensional manifold underlying the data space can be explicitly modeled as a product of submanifolds. This definition of disentanglement gives rise to a novel weakly-supervised algorithm for recovering the unknown explanatory factors behind the data. At training time, our algorithm only requires pairs of non i.i.d. data samples whose elements share at least one, possibly multidimensional, generative factor of variation. We require no knowledge on the nature of these transformations, and do not make any limiting assumption on the properties of each subspace. Our approach is easy to implement, and can be successfully applied to different kinds of data (from images to 3D surfaces) undergoing arbitrary transformations. In addition to standard synthetic benchmarks, we showcase our method in challenging real-world applications, where we compare favorably with the state of the art.} }
Endnote
%0 Conference Paper %T Learning disentangled representations via product manifold projection %A Marco Fumero %A Luca Cosmo %A Simone Melzi %A Emanuele Rodola %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-fumero21a %I PMLR %P 3530--3540 %U https://proceedings.mlr.press/v139/fumero21a.html %V 139 %X We propose a novel approach to disentangle the generative factors of variation underlying a given set of observations. Our method builds upon the idea that the (unknown) low-dimensional manifold underlying the data space can be explicitly modeled as a product of submanifolds. This definition of disentanglement gives rise to a novel weakly-supervised algorithm for recovering the unknown explanatory factors behind the data. At training time, our algorithm only requires pairs of non i.i.d. data samples whose elements share at least one, possibly multidimensional, generative factor of variation. We require no knowledge on the nature of these transformations, and do not make any limiting assumption on the properties of each subspace. Our approach is easy to implement, and can be successfully applied to different kinds of data (from images to 3D surfaces) undergoing arbitrary transformations. In addition to standard synthetic benchmarks, we showcase our method in challenging real-world applications, where we compare favorably with the state of the art.
APA
Fumero, M., Cosmo, L., Melzi, S. & Rodola, E.. (2021). Learning disentangled representations via product manifold projection. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:3530-3540 Available from https://proceedings.mlr.press/v139/fumero21a.html.

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