Training a Tucker Model With Shared Factors: a Riemannian Optimization Approach

Ivan Peshekhonov, Aleksey Arzhantsev, Maxim Rakhuba
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:3304-3312, 2024.

Abstract

Factorization of a matrix into a product of two rectangular factors, is a classic tool in various machine learning applications. Tensor factorizations generalize this concept to more than two dimensions. In applications, where some of the tensor dimensions have the same size or encode the same objects (e.g., knowledge graphs with entity-relation-entity 3D tensors), it can also be beneficial for the respective factors to be shared. In this paper, we consider a well-known Tucker tensor factorization and study its properties under the shared factor constraint. We call it a shared-factor Tucker factorization (SF-Tucker). Since sharing factors breaks polylinearity of classical tensor factorizations, common optimization schemes such as alternating least squares become inapplicable. Nevertheless, as we show in this paper, a set of fixed-rank SF-Tucker tensors preserves a Riemannian manifold structure. Therefore, we develop efficient algorithms for the main ingredients of Riemannian optimization on the SF-Tucker manifold and implement a Riemannian optimization method with momentum. We showcase the benefits of our approach on several machine learning tasks including knowledge graph completion and compression of neural networks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-peshekhonov24a, title = { Training a {T}ucker Model With Shared Factors: a {R}iemannian Optimization Approach }, author = {Peshekhonov, Ivan and Arzhantsev, Aleksey and Rakhuba, Maxim}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {3304--3312}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/peshekhonov24a/peshekhonov24a.pdf}, url = {https://proceedings.mlr.press/v238/peshekhonov24a.html}, abstract = { Factorization of a matrix into a product of two rectangular factors, is a classic tool in various machine learning applications. Tensor factorizations generalize this concept to more than two dimensions. In applications, where some of the tensor dimensions have the same size or encode the same objects (e.g., knowledge graphs with entity-relation-entity 3D tensors), it can also be beneficial for the respective factors to be shared. In this paper, we consider a well-known Tucker tensor factorization and study its properties under the shared factor constraint. We call it a shared-factor Tucker factorization (SF-Tucker). Since sharing factors breaks polylinearity of classical tensor factorizations, common optimization schemes such as alternating least squares become inapplicable. Nevertheless, as we show in this paper, a set of fixed-rank SF-Tucker tensors preserves a Riemannian manifold structure. Therefore, we develop efficient algorithms for the main ingredients of Riemannian optimization on the SF-Tucker manifold and implement a Riemannian optimization method with momentum. We showcase the benefits of our approach on several machine learning tasks including knowledge graph completion and compression of neural networks. } }
Endnote
%0 Conference Paper %T Training a Tucker Model With Shared Factors: a Riemannian Optimization Approach %A Ivan Peshekhonov %A Aleksey Arzhantsev %A Maxim Rakhuba %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-peshekhonov24a %I PMLR %P 3304--3312 %U https://proceedings.mlr.press/v238/peshekhonov24a.html %V 238 %X Factorization of a matrix into a product of two rectangular factors, is a classic tool in various machine learning applications. Tensor factorizations generalize this concept to more than two dimensions. In applications, where some of the tensor dimensions have the same size or encode the same objects (e.g., knowledge graphs with entity-relation-entity 3D tensors), it can also be beneficial for the respective factors to be shared. In this paper, we consider a well-known Tucker tensor factorization and study its properties under the shared factor constraint. We call it a shared-factor Tucker factorization (SF-Tucker). Since sharing factors breaks polylinearity of classical tensor factorizations, common optimization schemes such as alternating least squares become inapplicable. Nevertheless, as we show in this paper, a set of fixed-rank SF-Tucker tensors preserves a Riemannian manifold structure. Therefore, we develop efficient algorithms for the main ingredients of Riemannian optimization on the SF-Tucker manifold and implement a Riemannian optimization method with momentum. We showcase the benefits of our approach on several machine learning tasks including knowledge graph completion and compression of neural networks.
APA
Peshekhonov, I., Arzhantsev, A. & Rakhuba, M.. (2024). Training a Tucker Model With Shared Factors: a Riemannian Optimization Approach . Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:3304-3312 Available from https://proceedings.mlr.press/v238/peshekhonov24a.html.

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