Compressing Neural Networks Using Tensor Networks with Exponentially Fewer Variational Parameters
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866918029375307776 |
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| author | Qing, Yong Li, Ke Zhou, Peng-Fei Ran, Shi-Ju |
| author_facet | Qing, Yong Li, Ke Zhou, Peng-Fei Ran, Shi-Ju |
| contents | Neural network (NN) designed for challenging machine learning tasks is in general a highly nonlinear mapping that contains massive variational parameters. High complexity of NN, if unbounded or unconstrained, might unpredictably cause severe issues including \R{overfitting}, loss of generalization power, and unbearable cost of hardware. In this work, we propose a general compression scheme that significantly reduces the variational parameters of NN's, despite of their specific types (linear, convolutional, \textit{etc}), by encoding them to deep \R{automatically differentiable} tensor network (ADTN) that contains exponentially-fewer free parameters. Superior compression performance of our scheme is demonstrated on several widely-recognized NN's (FC-2, LeNet-5, AlextNet, ZFNet and VGG-16) and datasets (MNIST, CIFAR-10 and CIFAR-100). For instance, we compress two linear layers in VGG-16 with approximately $10^{7}$ parameters to two ADTN's with just 424 parameters, improving the testing accuracy on CIFAR-10 from $90.17\%$ to $91.74\%$. We argue that the deep structure of ADTN is an essential reason for the remarkable compression performance of ADTN, compared to existing compression schemes that are mainly based on tensor decompositions/factorization and shallow tensor networks. Our work suggests deep TN as an exceptionally efficient mathematical structure for representing the variational parameters of NN's, which exhibits superior compressibility over the commonly-used matrices and multi-way arrays. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06058 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Compressing Neural Networks Using Tensor Networks with Exponentially Fewer Variational Parameters Qing, Yong Li, Ke Zhou, Peng-Fei Ran, Shi-Ju Machine Learning Artificial Intelligence Neural network (NN) designed for challenging machine learning tasks is in general a highly nonlinear mapping that contains massive variational parameters. High complexity of NN, if unbounded or unconstrained, might unpredictably cause severe issues including \R{overfitting}, loss of generalization power, and unbearable cost of hardware. In this work, we propose a general compression scheme that significantly reduces the variational parameters of NN's, despite of their specific types (linear, convolutional, \textit{etc}), by encoding them to deep \R{automatically differentiable} tensor network (ADTN) that contains exponentially-fewer free parameters. Superior compression performance of our scheme is demonstrated on several widely-recognized NN's (FC-2, LeNet-5, AlextNet, ZFNet and VGG-16) and datasets (MNIST, CIFAR-10 and CIFAR-100). For instance, we compress two linear layers in VGG-16 with approximately $10^{7}$ parameters to two ADTN's with just 424 parameters, improving the testing accuracy on CIFAR-10 from $90.17\%$ to $91.74\%$. We argue that the deep structure of ADTN is an essential reason for the remarkable compression performance of ADTN, compared to existing compression schemes that are mainly based on tensor decompositions/factorization and shallow tensor networks. Our work suggests deep TN as an exceptionally efficient mathematical structure for representing the variational parameters of NN's, which exhibits superior compressibility over the commonly-used matrices and multi-way arrays. |
| title | Compressing Neural Networks Using Tensor Networks with Exponentially Fewer Variational Parameters |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2305.06058 |