In "The papers for ICLR 2015 are now open for discussion !" I mentioned a few papers that Nuit Blanche had featured recently and that were up for review at ICLR 2015. Here is another one that aims at using tensor reduction for reducing the time it takes to perform computation with convolutional neural networks:

Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decomposition by Vadim Lebedev, Yaroslav Ganin, Maksim Rakhuba, Ivan Oseledets, Victor Lempitsky

We propose a simple two-step approach for speeding up convolution layers within large convolutional neural networks based on tensor decomposition and discriminative fine-tuning. Given a layer, we use non-linear least squares to compute a low-rank CP-decomposition of the 4D convolution kernel tensor into a sum of a small number of rank-one tensors. At the second step, this decomposition is used to replace the original convolutional layer with a sequence of four convolutional layers with small kernels. After such replacement, the entire network is fine-tuned on the training data using standard backpropagation process.

We evaluate this approach on two CNNs and show that it yields larger CPU speedups at the cost of lower accuracy drops compared to previous approaches. For the 36-class character classification CNN, our approach obtains a 8.5x CPU speedup of the whole network with only minor accuracy drop (1% from 91% to 90%). For the standard ImageNet architecture (AlexNet), the approach speeds up the second convolution layer by a factor of 4x at the cost of 1% increase of the overall top-5 classification error.

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