284 research outputs found
Tensorizing Neural Networks
Deep neural networks currently demonstrate state-of-the-art performance in
several domains. At the same time, models of this class are very demanding in
terms of computational resources. In particular, a large amount of memory is
required by commonly used fully-connected layers, making it hard to use the
models on low-end devices and stopping the further increase of the model size.
In this paper we convert the dense weight matrices of the fully-connected
layers to the Tensor Train format such that the number of parameters is reduced
by a huge factor and at the same time the expressive power of the layer is
preserved. In particular, for the Very Deep VGG networks we report the
compression factor of the dense weight matrix of a fully-connected layer up to
200000 times leading to the compression factor of the whole network up to 7
times
Learning Compact Recurrent Neural Networks with Block-Term Tensor Decomposition
Recurrent Neural Networks (RNNs) are powerful sequence modeling tools.
However, when dealing with high dimensional inputs, the training of RNNs
becomes computational expensive due to the large number of model parameters.
This hinders RNNs from solving many important computer vision tasks, such as
Action Recognition in Videos and Image Captioning. To overcome this problem, we
propose a compact and flexible structure, namely Block-Term tensor
decomposition, which greatly reduces the parameters of RNNs and improves their
training efficiency. Compared with alternative low-rank approximations, such as
tensor-train RNN (TT-RNN), our method, Block-Term RNN (BT-RNN), is not only
more concise (when using the same rank), but also able to attain a better
approximation to the original RNNs with much fewer parameters. On three
challenging tasks, including Action Recognition in Videos, Image Captioning and
Image Generation, BT-RNN outperforms TT-RNN and the standard RNN in terms of
both prediction accuracy and convergence rate. Specifically, BT-LSTM utilizes
17,388 times fewer parameters than the standard LSTM to achieve an accuracy
improvement over 15.6\% in the Action Recognition task on the UCF11 dataset.Comment: CVPR201
Compact Neural Networks based on the Multiscale Entanglement Renormalization Ansatz
This paper demonstrates a method for tensorizing neural networks based upon
an efficient way of approximating scale invariant quantum states, the
Multi-scale Entanglement Renormalization Ansatz (MERA). We employ MERA as a
replacement for the fully connected layers in a convolutional neural network
and test this implementation on the CIFAR-10 and CIFAR-100 datasets. The
proposed method outperforms factorization using tensor trains, providing
greater compression for the same level of accuracy and greater accuracy for the
same level of compression. We demonstrate MERA layers with 14000 times fewer
parameters and a reduction in accuracy of less than 1% compared to the
equivalent fully connected layers, scaling like O(N).Comment: 8 pages, 2 figure
Beating the Perils of Non-Convexity: Guaranteed Training of Neural Networks using Tensor Methods
Training neural networks is a challenging non-convex optimization problem,
and backpropagation or gradient descent can get stuck in spurious local optima.
We propose a novel algorithm based on tensor decomposition for guaranteed
training of two-layer neural networks. We provide risk bounds for our proposed
method, with a polynomial sample complexity in the relevant parameters, such as
input dimension and number of neurons. While learning arbitrary target
functions is NP-hard, we provide transparent conditions on the function and the
input for learnability. Our training method is based on tensor decomposition,
which provably converges to the global optimum, under a set of mild
non-degeneracy conditions. It consists of simple embarrassingly parallel linear
and multi-linear operations, and is competitive with standard stochastic
gradient descent (SGD), in terms of computational complexity. Thus, we propose
a computationally efficient method with guaranteed risk bounds for training
neural networks with one hidden layer.Comment: The tensor decomposition analysis is expanded, and the analysis of
ridge regression is added for recovering the parameters of last layer of
neural networ
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