Self-explaining models are models that reveal decision making parameters in an interpretable manner so that the model reasoning process can be directly understood by human beings. General Linear Models (GLMs) are self-explaining because the model weights directly show how each feature contribute to the output value. However, deep neural networks (DNNs) are in general not self-explaining due to the non-linearity of the activation functions, complex architectures, obscure feature extraction and transformation process. In this work, we illustrate the fact that existing deep architectures are hard to interpret because each hidden layer carries a mix of high level features and low level features. As a solution, we propose a novel feature leveling architecture that isolates low level features from high level features on a per-layer basis to better utilize the GLM layer in the proposed architecture for interpretation. Experimental results show that our modified models are able to achieve competitive results comparing to main-stream architectures on standard datasets while being more self-explaining. Our implementations and configurations are publicly available for reproductions.
refers to various methods developed to reduce the number of parameters of a neural model. Many investigations have been done in using @math or @math @cite_9 @cite_27 @cite_21 @cite_5 regularization to prune neural network while maintaining differentiability for back propagation. Another choice for regularization and creating sparsity is the @math regularization. However, due to its discrete nature, it does not support parameter learning through backpropagation. A continuous approximation of @math is proposed in regard to resolve this problem and has shown effectiveness in pruning both FCNN and Convolutional Neural Networks (CNNs) in an end to end manner @cite_4 . This regularization technique is further applied not only to neural architecture pruning but to feature selections @cite_15 . Our work applies the @math regularization's feature selection ability in a novel context to select maximum amount of features as direct inputs for the GLM layer.
@cite_4 @cite_9 @cite_21 @cite_27 @cite_5 @cite_15
1570197553 2769044225 2276892413 2963145730
In this work, we investigate the use of sparsity-inducing regularizers during training of Convolution Neural Networks (CNNs). These regularizers encourage that fewer connections in the convolution and fully connected layers take non-zero values and in effect result in sparse connectivity between hidden units in the deep network. This in turn reduces the memory and runtime cost involved in deploying the learned CNNs. We show that training with such regularization can still be performed using stochastic gradient descent implying that it can be used easily in existing codebases. Experimental evaluation of our approach on MNIST, CIFAR, and ImageNet datasets shows that our regularizers can result in dramatic reductions in memory requirements. For instance, when applied on AlexNet, our method can reduce the memory consumption by a factor of four with minimal loss in accuracy. To reduce the significant redundancy in deep Convolutional Neural Networks (CNNs), most existing methods prune neurons by only considering statistics of an individual layer or two consecutive layers (e.g., prune one layer to minimize the reconstruction error of the next layer), ignoring the effect of error propagation in deep networks. In contrast, we argue that it is essential to prune neurons in the entire neuron network jointly based on a unified goal: minimizing the reconstruction error of important responses in the "final response layer" (FRL), which is the second-to-last layer before classification, for a pruned network to retrain its predictive power. Specifically, we apply feature ranking techniques to measure the importance of each neuron in the FRL, and formulate network pruning as a binary integer optimization problem and derive a closed-form solution to it for pruning neurons in earlier layers. Based on our theoretical analysis, we propose the Neuron Importance Score Propagation (NISP) algorithm to propagate the importance scores of final responses to every neuron in the network. The CNN is pruned by removing neurons with least importance, and then fine-tuned to retain its predictive power. NISP is evaluated on several datasets with multiple CNN models and demonstrated to achieve significant acceleration and compression with negligible accuracy loss. Real-time application of deep learning algorithms is often hindered by high computational complexity and frequent memory accesses. Network pruning is a promising technique to solve this problem. However, pruning usually results in irregular network connections that not only demand extra representation efforts but also do not fit well on parallel computation. We introduce structured sparsity at various scales for convolutional neural networks: feature map-wise, kernel-wise, and intra-kernel strided sparsity. This structured sparsity is very advantageous for direct computational resource savings on embedded computers, in parallel computing environments, and in hardware-based systems. To decide the importance of network connections and paths, the proposed method uses a particle filtering approach. The importance weight of each particle is assigned by assessing the misclassification rate with a corresponding connectivity pattern. The pruned network is retrained to compensate for the losses due to pruning. While implementing convolutions as matrix products, we particularly show that intra-kernel strided sparsity with a simple constraint can significantly reduce the size of the kernel and feature map tensors. The proposed work shows that when pruning granularities are applied in combination, we can prune the CIFAR-10 network by more than 70 with less than a 1 loss in accuracy. To reduce the significant redundancy in deep Convolutional Neural Networks (CNNs), most existing methods prune neurons by only considering the statistics of an individual layer or two consecutive layers (e.g., prune one layer to minimize the reconstruction error of the next layer), ignoring the effect of error propagation in deep networks. In contrast, we argue that for a pruned network to retain its predictive power, it is essential to prune neurons in the entire neuron network jointly based on a unified goal: minimizing the reconstruction error of important responses in the "final response layer" (FRL), which is the second-to-last layer before classification. Specifically, we apply feature ranking techniques to measure the importance of each neuron in the FRL, formulate network pruning as a binary integer optimization problem, and derive a closed-form solution to it for pruning neurons in earlier layers. Based on our theoretical analysis, we propose the Neuron Importance Score Propagation (NISP) algorithm to propagate the importance scores of final responses to every neuron in the network. The CNN is pruned by removing neurons with least importance, and it is then fine-tuned to recover its predictive power. NISP is evaluated on several datasets with multiple CNN models and demonstrated to achieve significant acceleration and compression with negligible accuracy loss.