Understanding Convolutional Neural Networks from Theoretical Perspective via Volterra Convolution

Overview

nnvolterra

Run Code

Compile first: make compile

Run all codes: make all

Test xconv: make npxconv_test

MNIST dataset needs to be downloaded, converted to numpy format, and placed to mnist/ folder.

Train MNIST network: make mnist_train

Test MNIST network: make mnist_try

Hack MNIST network: make mnist_hack

Required

  • python
  • numpy
  • pytorch
  • g++ 9.3.0
  • xelatex [optional]: for mnist_draw.py

About Files

  • xconvlibrary
    • xconvolution.hpp: core lib
    • npxconv.cpp: cpp to python
    • npxconv.py: interface for python
    • npxconv_setup.py: setup
    • npxconv_test.py: test file
  • outer convolution
    • oconv_draw.py: nnfragile and three example images of outer convolution
    • oconv_rank.py: compute rank for outer convolution and neural network to Volterra Convolution
    • oconv_rank_draw.py: draw images from oconv_rank.py
  • mnist hack
    • mnist_module.py: the module
    • mnist_train.py: train this module in training set
    • mnist_try.py: check module in test set
    • mnist_hack.py: try to hack the module
    • mnist_draw.py: slightly draw the hack result
  • other
    • tensordec.py: about tensor decomposition
    • shape_check.py: check shapes

Please Cite

@misc{li2021understanding,
      title={Understanding Convolutional Neural Networks from Theoretical Perspective via Volterra Convolution}, 
      author={Tenghui Li and Guoxu Zhou and Yuning Qiu and Qibin Zhao},
      year={2021},
      eprint={2110.09902},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}
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