Neural plasticity is an important functionality of human brain, in which number of neurons and synapses can shrink or expand in response to stimuli throughout the span of life. We model this dynamic learning process as an @math -norm regularized binary optimization problem, in which each unit of a neural network (e.g., weight, neuron or channel, etc.) is attached with a stochastic binary gate, whose parameters determine the level of activity of a unit in the network. At the beginning, only a small portion of binary gates (therefore the corresponding neurons) are activated, while the remaining neurons are in a hibernation mode. As the learning proceeds, some neurons might be activated or deactivated if doing so can be justified by the cost-benefit tradeoff measured by the @math -norm regularized objective. As the training gets mature, the probability of transition between activation and deactivation will diminish until a final hardening stage. We demonstrate that all of these learning dynamics can be modulated by a single parameter @math seamlessly. Our neural plasticity network (NPN) can prune or expand a network depending on the initial capacity of network provided by the user; it also unifies dropout (when @math ), traditional training of DNNs (when @math ) and interpolates between these two. To the best of our knowledge, this is the first learning framework that unifies network sparsification and network expansion in an end-to-end training pipeline. Extensive experiments on synthetic dataset and multiple image classification benchmarks demonstrate the superior performance of NPN. We show that both network sparsification and network expansion can yield compact models of similar architectures and of similar predictive accuracies that are close to or sometimes even higher than baseline networks. We plan to release our code to facilitate the research in this area.
Compared to network sparsification, network expansion is a relatively less explored area. There are few existing works that can dynamically increase the capacity of network during training. For example, DNC @cite_16 sequentially adds neurons one at a time to the hidden layers of network until the desired approximation accuracy is achieved. @cite_17 proposes to train a denoising autoencoder (DAE) by adding in new neurons and later merging them with other neurons to prevent redundancy. For convolutional networks, @cite_18 proposes to widen or deepen a pretrained network for better knowledge transfer. Recently, a boosting-style method named AdaNet @cite_25 is used to adaptively grow the structure while learning the weights. However, all these approaches either only add neurons or add remove neurons manually. In contrast, our NPN can add or remove (deactivate) neurons during training as needed without human intervention, and is an end-to-end unified framework for network sparsification and expansion.
@cite_18 @cite_16 @cite_25 @cite_17
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Abstract Although deep neural networks (DNNs) are being a revolutionary power to open up the AI era, the notoriously huge hardware overhead has challenged their applications. Recently, several binary and ternary networks, in which the costly multiply-accumulate operations can be replaced by accumulations or even binary logic operations, make the on-chip training of DNNs quite promising. Therefore there is a pressing need to build an architecture that could subsume these networks under a unified framework that achieves both higher performance and less overhead. To this end, two fundamental issues are yet to be addressed. The first one is how to implement the back propagation when neuronal activations are discrete. The second one is how to remove the full-precision hidden weights in the training phase to break the bottlenecks of memory computation consumption. To address the first issue, we present a multi-step neuronal activation discretization method and a derivative approximation technique that enable the implementing the back propagation algorithm on discrete DNNs. While for the second issue, we propose a discrete state transition (DST) methodology to constrain the weights in a discrete space without saving the hidden weights. Through this way, we build a unified framework that subsumes the binary or ternary networks as its special cases, and under which a heuristic algorithm is provided at the website https: github.com AcrossV Gated-XNOR . More particularly, we find that when both the weights and activations become ternary values, the DNNs can be reduced to sparse binary networks, termed as gated XNOR networks (GXNOR-Nets) since only the event of non-zero weight and non-zero activation enables the control gate to start the XNOR logic operations in the original binary networks. This promises the event-driven hardware design for efficient mobile intelligence. We achieve advanced performance compared with state-of-the-art algorithms. Furthermore, the computational sparsity and the number of states in the discrete space can be flexibly modified to make it suitable for various hardware platforms. Recent work has shown deep neural networks (DNNs) to be highly susceptible to well-designed, small perturbations at the input layer, or so-called adversarial examples. Taking images as an example, such distortions are often imperceptible, but can result in 100 mis-classification for a state of the art DNN. We study the structure of adversarial examples and explore network topology, pre-processing and training strategies to improve the robustness of DNNs. We perform various experiments to assess the removability of adversarial examples by corrupting with additional noise and pre-processing with denoising autoencoders (DAEs). We find that DAEs can remove substantial amounts of the adversarial noise. How- ever, when stacking the DAE with the original DNN, the resulting network can again be attacked by new adversarial examples with even smaller distortion. As a solution, we propose Deep Contractive Network, a model with a new end-to-end training procedure that includes a smoothness penalty inspired by the contractive autoencoder (CAE). This increases the network robustness to adversarial examples, without a significant performance penalty. Given an existing trained neural network, it is often desirable to learn new capabilities without hindering performance of those already learned. Existing approaches either learn sub-optimal solutions, require joint training, or incur a substantial increment in the number of parameters for each added domain, typically as many as the original network. We propose a method called (DAN) that constrains newly learned filters to be linear combinations of existing ones. DANs precisely preserve performance on the original domain, require a fraction (typically 13 , dependent on network architecture) of the number of parameters compared to standard fine-tuning procedures and converge in less cycles of training to a comparable or better level of performance. When coupled with standard network quantization techniques, we further reduce the parameter cost to around 3 of the original with negligible or no loss in accuracy. The learned architecture can be controlled to switch between various learned representations, enabling a single network to solve a task from multiple different domains. We conduct extensive experiments showing the effectiveness of our method on a range of image classification tasks and explore different aspects of its behavior. Due to deep cascades of nonlinear units, deep neural networks (DNNs) can automatically learn non-local generalization priors from data and have achieved high performance in various applications. However, such properties have also opened a door for adversaries to generate the so-called adversarial examples to fool DNNs. Specifically, adversaries can inject small perturbations to the input data and therefore decrease the performance of deep neural networks significantly. Even worse, these adversarial examples have the transferability to attack a black-box model based on finite queries without knowledge of the target model. Therefore, we aim to empirically compare different defensive strategies against various adversary models and analyze the cross-model efficiency for these robust learners. We conclude that the adversarial retraining framework also has the transferability, which can defend adversarial examples without requiring prior knowledge of the adversary models. We compare the general adversarial retraining framework with the state-of-the-art robust deep neural networks, such as distillation, autoencoder stacked with classifier (AEC), and our improved version, IAEC, to evaluate their robustness as well as the vulnerability in terms of the distortion required to mislead the learner. Our experimental results show that the adversarial retraining framework can defend most of the adversarial examples notably and consistently without adding additional vulnerabilities or performance penalty to the original model.