Existing methods for reducing the computational burden of neural networks at run-time, such as parameter pruning or dynamic computational path selection, focus solely on improving computational efficiency during inference. On the other hand, in this work, we propose a novel method which reduces the memory footprint and number of computing operations required for training and inference. Our framework efficiently integrates pruning as part of the training procedure by exploring and tracking the relative importance of convolutional channels. At each training step, we select only a subset of highly salient channels to execute according to the combinatorial upper confidence bound algorithm, and run a forward and backward pass only on these activated channels, hence learning their parameters. Consequently, we enable the efficient discovery of compact models. We validate our approach empirically on state-of-the-art CNNs - VGGNet, ResNet and DenseNet, and on several image classification datasets. Results demonstrate our framework for dynamic channel execution reduces computational cost up to 4x and parameter count up to 9x, thus reducing the memory and computational demands for discovering and training compact neural network models.
is applied after training an initial network in order to eliminate model parameters, therefore making inference less computationally intensive, and decreasing model size and memory footprint. One approach is non-structured pruning which dates back to Optimal Brain Damage @cite_27 . More recently, Han @cite_20 propose to prune individual weights with small magnitude, and Srinivas and Babu @cite_7 propose to remove redundant neurons iteratively. The issue with non-structured pruning is that it requires specialized hardware @cite_24 . Structured pruning @cite_32 @cite_5 @cite_26 @cite_30 @cite_16 @cite_23 ,on the other hand, does not require dedicated libraries hardware as it prunes whole filters, channels of convolutional kernels or even layers, based on some importance criteria. Other post-processing techniques to achieve compact network models include knowledge distillation @cite_4 @cite_28 , weight quantization @cite_3 @cite_0 , low-rank approximation of weights @cite_33 @cite_22 .
@cite_30 @cite_26 @cite_4 @cite_33 @cite_7 @cite_22 @cite_28 @cite_32 @cite_3 @cite_24 @cite_0 @cite_27 @cite_23 @cite_5 @cite_16 @cite_20
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A very simple way to improve the performance of almost any machine learning algorithm is to train many different models on the same data and then to average their predictions. Unfortunately, making predictions using a whole ensemble of models is cumbersome and may be too computationally expensive to allow deployment to a large number of users, especially if the individual models are large neural nets. Caruana and his collaborators have shown that it is possible to compress the knowledge in an ensemble into a single model which is much easier to deploy and we develop this approach further using a different compression technique. We achieve some surprising results on MNIST and we show that we can significantly improve the acoustic model of a heavily used commercial system by distilling the knowledge in an ensemble of models into a single model. We also introduce a new type of ensemble composed of one or more full models and many specialist models which learn to distinguish fine-grained classes that the full models confuse. Unlike a mixture of experts, these specialist models can be trained rapidly and in parallel. Abstract: 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 is competitive with previous approaches, leading to higher obtained CPU speedups at the cost of lower accuracy drops for the smaller of the two networks. Thus, 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 @math increase of the overall top-5 classification error. Deep Neural nets (NNs) with millions of parameters are at the heart of many state-of-the-art computer vision systems today. However, recent works have shown that much smaller models can achieve similar levels of performance. In this work, we address the problem of pruning parameters in a trained NN model. Instead of removing individual weights one at a time as done in previous works, we remove one neuron at a time. We show how similar neurons are redundant, and propose a systematic way to remove them. Unlike previous works, our pruning method does not require access to any training validation data. Channel pruning is one of the predominant approaches for deep model compression. Existing pruning methods either (i) train from scratch with sparsity constraints on channels, or (ii) minimize the reconstruction error between the pre-trained feature maps and the compressed ones. Both strategies suffer from limitations: the former kind is computationally expensive and difficult to converge, whilst the latter kind optimizes the reconstruction error but ignores the discriminative power of channels. To overcome these drawbacks, we investigate a simple-yet-effective method, named discrimination-aware channel pruning (DCP), which seeks to select those channels that really contribute to discriminative power. To this end, we introduce additional losses into the network to increase the discriminative power of intermediate layers. We then propose to select the most discriminative channels for each layer, where both an additional loss and the reconstruction error are considered. Last, we propose a greedy algorithm to make channel selection and parameter optimization in an iterative way. Extensive experiments demonstrate the effectiveness of our method. For example, on ILSVRC-12, our pruned ResNet-50 with 30 reduction of channels even outperforms the original model by 0.39 in top-1 accuracy. We propose two efficient approximations to standard convolutional neural networks: Binary-Weight-Networks and XNOR-Networks. In Binary-Weight-Networks, the filters are approximated with binary values resulting in 32 ( ) memory saving. In XNOR-Networks, both the filters and the input to convolutional layers are binary. XNOR-Networks approximate convolutions using primarily binary operations. This results in 58 ( ) faster convolutional operations (in terms of number of the high precision operations) and 32 ( ) memory savings. XNOR-Nets offer the possibility of running state-of-the-art networks on CPUs (rather than GPUs) in real-time. Our binary networks are simple, accurate, efficient, and work on challenging visual tasks. We evaluate our approach on the ImageNet classification task. The classification accuracy with a Binary-Weight-Network version of AlexNet is the same as the full-precision AlexNet. We compare our method with recent network binarization methods, BinaryConnect and BinaryNets, and outperform these methods by large margins on ImageNet, more than (16 , ) in top-1 accuracy. Our code is available at: http: allenai.org plato xnornet. State-of-the-art deep neural networks (DNNs) have hundreds of millions of connections and are both computationally and memory intensive, making them difficult to deploy on embedded systems with limited hardware resources and power budgets. While custom hardware helps the computation, fetching weights from DRAM is two orders of magnitude more expensive than ALU operations, and dominates the required power. Previously proposed 'Deep Compression' makes it possible to fit large DNNs (AlexNet and VGGNet) fully in on-chip SRAM. This compression is achieved by pruning the redundant connections and having multiple connections share the same weight. We propose an energy efficient inference engine (EIE) that performs inference on this compressed network model and accelerates the resulting sparse matrix-vector multiplication with weight sharing. Going from DRAM to SRAM gives EIE 120× energy saving; Exploiting sparsity saves 10×; Weight sharing gives 8×; Skipping zero activations from ReLU saves another 3×. Evaluated on nine DNN benchmarks, EIE is 189× and 13× faster when compared to CPU and GPU implementations of the same DNN without compression. EIE has a processing power of 102 GOPS working directly on a compressed network, corresponding to 3 TOPS on an uncompressed network, and processes FC layers of AlexNet at 1.88×104 frames sec with a power dissipation of only 600mW. It is 24,000× and 3,400× more energy efficient than a CPU and GPU respectively. Compared with DaDianNao, EIE has 2.9×, 19× and 3× better throughput, energy efficiency and area efficiency. We have used information-theoretic ideas to derive a class of practical and nearly optimal schemes for adapting the size of a neural network. By removing unimportant weights from a network, several improvements can be expected: better generalization, fewer training examples required, and improved speed of learning and or classification. The basic idea is to use second-derivative information to make a tradeoff between network complexity and training set error. Experiments confirm the usefulness of the methods on a real-world application. Neural networks are both computationally intensive and memory intensive, making them difficult to deploy on embedded systems. Also, conventional networks fix the architecture before training starts; as a result, training cannot improve the architecture. To address these limitations, we describe a method to reduce the storage and computation required by neural networks by an order of magnitude without affecting their accuracy by learning only the important connections. Our method prunes redundant connections using a three-step method. First, we train the network to learn which connections are important. Next, we prune the unimportant connections. Finally, we retrain the network to fine tune the weights of the remaining connections. On the ImageNet dataset, our method reduced the number of parameters of AlexNet by a factor of 9x, from 61 million to 6.7 million, without incurring accuracy loss. Similar experiments with VGG-16 found that the total number of parameters can be reduced by 13x, from 138 million to 10.3 million, again with no loss of accuracy.