A Tensor Decomposition Perspective on Second-order RNNs

Fuente: arXiv
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Autores principales: Lizaire, Maude, Rizvi-Martel, Michael, Hameed, Marawan Gamal Abdel, Rabusseau, Guillaume
Formato: Preprint
Publicado: 2024
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author Lizaire, Maude
Rizvi-Martel, Michael
Hameed, Marawan Gamal Abdel
Rabusseau, Guillaume
author_facet Lizaire, Maude
Rizvi-Martel, Michael
Hameed, Marawan Gamal Abdel
Rabusseau, Guillaume
contents Second-order Recurrent Neural Networks (2RNNs) extend RNNs by leveraging second-order interactions for sequence modelling. These models are provably more expressive than their first-order counterparts and have connections to well-studied models from formal language theory. However, their large parameter tensor makes computations intractable. To circumvent this issue, one approach known as MIRNN consists in limiting the type of interactions used by the model. Another is to leverage tensor decomposition to diminish the parameter count. In this work, we study the model resulting from parameterizing 2RNNs using the CP decomposition, which we call CPRNN. Intuitively, the rank of the decomposition should reduce expressivity. We analyze how rank and hidden size affect model capacity and show the relationships between RNNs, 2RNNs, MIRNNs, and CPRNNs based on these parameters. We support these results empirically with experiments on the Penn Treebank dataset which demonstrate that, with a fixed parameter budget, CPRNNs outperforms RNNs, 2RNNs, and MIRNNs with the right choice of rank and hidden size.
format Preprint
id arxiv_https___arxiv_org_abs_2406_05045
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A Tensor Decomposition Perspective on Second-order RNNs
Lizaire, Maude
Rizvi-Martel, Michael
Hameed, Marawan Gamal Abdel
Rabusseau, Guillaume
Machine Learning
Second-order Recurrent Neural Networks (2RNNs) extend RNNs by leveraging second-order interactions for sequence modelling. These models are provably more expressive than their first-order counterparts and have connections to well-studied models from formal language theory. However, their large parameter tensor makes computations intractable. To circumvent this issue, one approach known as MIRNN consists in limiting the type of interactions used by the model. Another is to leverage tensor decomposition to diminish the parameter count. In this work, we study the model resulting from parameterizing 2RNNs using the CP decomposition, which we call CPRNN. Intuitively, the rank of the decomposition should reduce expressivity. We analyze how rank and hidden size affect model capacity and show the relationships between RNNs, 2RNNs, MIRNNs, and CPRNNs based on these parameters. We support these results empirically with experiments on the Penn Treebank dataset which demonstrate that, with a fixed parameter budget, CPRNNs outperforms RNNs, 2RNNs, and MIRNNs with the right choice of rank and hidden size.
title A Tensor Decomposition Perspective on Second-order RNNs
topic Machine Learning
url https://arxiv.org/abs/2406.05045