Modern neural network architectures use structured linear transformations, such as low-rank matrices, sparse matrices, permutations, and the Fourier transform, to improve inference speed and reduce memory usage compared to general linear maps. However, choosing which of the myriad structured transformations to use (and its associated parameterization) is a laborious task that requires trading off speed, space, and accuracy. We consider a different approach: we introduce a family of matrices called kaleidoscope matrices (K-matrices) that provably capture any structured matrix with near-optimal space (parameter) and time (arithmetic operation) complexity. We empirically validate that K-matrices can be automatically learned within end-to-end pipelines to replace hand-crafted procedures, in order to improve model quality. For example, replacing channel shuffles in ShuffleNet improves classification accuracy on ImageNet by up to 5%. K-matrices can also simplify hand-engineered pipelines---we replace filter bank feature computation in speech data preprocessing with a learnable kaleidoscope layer, resulting in only 0.4% loss in accuracy on the TIMIT speech recognition task. In addition, K-matrices can capture latent structure in models: for a challenging permuted image classification task, adding a K-matrix to a standard convolutional architecture can enable learning the latent permutation and improve accuracy by over 8 points. We provide a practically efficient implementation of our approach, and use K-matrices in a Transformer network to attain 36% faster end-to-end inference speed on a language translation task.
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AutoShuffleNet: Learning Permutation Matrices via an Exact Lipschitz Continuous Penalty in Deep Convolutional Neural Networks
ShuffleNet is a state-of-the-art light weight convolutional neural
network architecture. Its basic operations include group, channelwise
convolution and channel shuffling. However, channel shuffling
is manually designed on empirical grounds. Mathematically, shuffling
is a multiplication by a permutation matrix. In this paper, we
propose to automate channel shuffling by learning permutation
matrices in network training. We introduce an exact Lipschitz continuous
non-convex penalty so that it can be incorporated in the
stochastic gradient descent to approximate permutation at high
precision. Exact permutations are obtained by simple rounding at
the end of training and are used in inference. The resulting network,
referred to as AutoShuffleNet, achieved improved classification accuracies
on data from CIFAR-10, CIFAR-100 and ImageNet while
preserving the inference costs of ShuffleNet. In addition, we found
experimentally that the standard convex relaxation of permutation
matrices into stochastic matrices leads to poor performance. We
prove theoretically the exactness (error bounds) in recovering permutation
matrices when our penalty function is zero (very small).
We present examples of permutation optimization through graph
matching and two-layer neural network models where the loss
functions are calculated in closed analytical form. In the examples,
convex relaxation failed to capture permutations whereas our
penalty succeeded.
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- NSF-PAR ID:
- 10158881
- Date Published:
- Journal Name:
- 26th ACM SIGKDD Conference on Knowledge Discovery and Data Mining
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/https://doi.org/10.1145/3394486.3403103
