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Stable tensor neural networks for efficient deep learning.

Elizabeth Newman1, Lior Horesh2, Haim Avron3

  • 1Department of Mathematics, Emory University, Atlanta, GA, United States.

Frontiers in Big Data
|June 14, 2024
PubMed
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Tensor neural networks (t-NNs) offer efficient deep learning for complex data. These networks leverage tensor representations to reduce parameters, improving speed and memory for high-dimensional function approximation.

Area of Science:

  • Computational Mathematics
  • Deep Learning
  • Tensor Computations

Background:

  • Deep neural networks (DNNs) are effective high-dimensional function approximators.
  • Tensors naturally arise in deep learning as data, weights, and features, often causing computational bottlenecks.
  • Efficient parameterization is crucial for training DNNs on complex, multidimensional data.

Purpose of the Study:

  • To propose tensor neural networks (t-NNs) for efficient DNN parameterization.
  • To leverage tensor representations and processing for high-dimensional data learning.
  • To extend existing DNN frameworks, like stable neural networks, to a multidimensional tensor context.

Main Methods:

  • Developed tensor neural networks (t-NNs) as an extension of fully-connected networks.
Keywords:
deep learningimage classificationinverse problemsmachine learningtensor algebra

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  • Utilized matrix-mimetic tensor-tensor products to maintain algebraic properties and capture correlations.
  • Extended the framework of stable neural networks, interpreting DNNs as differential equation discretizations.

    • Main Results:

    • t-NNs enable efficient training in a reduced, powerful parameter space.
    • Demonstrated parametric advantages of t-NNs in dimensionality reduction (autoencoders) and classification tasks.
    • Empirical validation on MNIST and CIFAR-10 benchmark imaging datasets using fully-connected and stable t-NN variants.

    Conclusions:

    • t-NNs provide an efficient and powerful approach for deep learning with high-dimensional, multiway data.
    • The proposed tensor-based methods address computational bottlenecks in DNNs.
    • t-NNs offer a promising direction for advancing deep learning architectures and applications.