The performance of Deep Neural Networks (DNNs) keeps elevating in recent years with increasing network depth and width. To enable DNNs on edge devices like mobile phones, researchers proposed several network compression methods including pruning, quantization and factorization. Among the factorization-based approaches, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a pre-trained model by low-rank decomposition; however, small approximation errors in parameters can ripple a large prediction loss. As a result, performance usually drops significantly and a sophisticated fine-tuning is required to recover accuracy. We argue that it is not optimal to separate low-rank approximation from training. Unlike previous works, this paper integrates low rank approximation and regularization into the training. We propose Trained Rank Pruning (TRP), which iterates low rank approximation and training. TRP maintains the capacity of original network while imposes low-rank constraints during training. A stochastic sub-gradient descent optimized nuclear regularization is utilized to further encourage low rank in TRP. The TRP trained network has low-rank structure in nature, and can be approximated with negligible performance loss, eliminating fine-tuning after low rank approximation. The methods are comprehensively evaluated on CIFAR-10 and ImageNet, outperforming previous compression methods using low rank approximation.
The focus of this paper is speeding up the evaluation of convolutional neural networks. While delivering impressive results across a range of computer vision and machine learning tasks, these networks are computationally demanding, limiting their deployability. Convolutional layers generally consume the bulk of the processing time, and so in this work we present two simple schemes for drastically speeding up these layers. This is achieved by exploiting cross-channel or filter redundancy to construct a low rank basis of filters that are rank-1 in the spatial domain. Our methods are architecture agnostic, and can be easily applied to existing CPU and GPU convolutional frameworks for tuneable speedup performance. We demonstrate this with a real world network designed for scene text character recognition, showing a possible 2.5x speedup with no loss in accuracy, and 4.5x speedup with less than 1 drop in accuracy, still achieving state-of-the-art on standard benchmarks. We present techniques for speeding up the test-time evaluation of large convolutional networks, designed for object recognition tasks. These models deliver impressive accuracy, but each image evaluation requires millions of floating point operations, making their deployment on smartphones and Internet-scale clusters problematic. The computation is dominated by the convolution operations in the lower layers of the model. We exploit the redundancy present within the convolutional filters to derive approximations that significantly reduce the required computation. Using large state-of-the-art models, we demonstrate speedups of convolutional layers on both CPU and GPU by a factor of 2 x, while keeping the accuracy within 1 of the original model. Depthwise separable convolution has shown great efficiency in network design, but requires time-consuming training procedure with full training-set available. This paper first analyzes the mathematical relationship between regular convolutions and depthwise separable convolutions, and proves that the former one could be approximated with the latter one in closed form. We show depthwise separable convolutions are principal components of regular convolutions. And then we propose network decoupling (ND), a training-free method to accelerate convolutional neural networks (CNNs) by transferring pre-trained CNN models into the MobileNet-like depthwise separable convolution structure, with a promising speedup yet negligible accuracy loss. We further verify through experiments that the proposed method is orthogonal to other training-free methods like channel decomposition, spatial decomposition, etc. Combining the proposed method with them will bring even larger CNN speedup. For instance, ND itself achieves about 2X speedup for the widely used VGG16, and combined with other methods, it reaches 3.7X speedup with graceful accuracy degradation. We demonstrate that ND is widely applicable to classification networks like ResNet, and object detection network like SSD300. 