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Register a new userCompressing Neural Networks: Towards Determining the Optimal Layer-wise Decomposition
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Added by
Lucas Liebenwein
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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We present a novel global compression framework for deep neural networks that automatically analyzes each layer to identify the optimal per-layer compression ratio, while simultaneously achieving the desired overall compression. Our algorithm hinges on the idea of compressing each convolutional (or fully-connected) layer by slicing its channels into multiple groups and decomposing each group via low-rank decomposition. At the core of our algorithm is the derivation of layer-wise error bounds from the Eckart Young Mirsky theorem. We then leverage these bounds to frame the compression problem as an optimization problem where we wish to minimize the maximum compression error across layers and propose an efficient algorithm towards a solution. Our experiments indicate that our method outperforms existing low-rank compression approaches across a wide range of networks and data sets. We believe that our results open up new avenues for future research into the global performance-size trade-offs of modern neural networks. Our code is available at https://github.com/lucaslie/torchprune.
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Safety concerns on the deep neural networks (DNNs) have been raised when they are applied to critical sectors. In this paper, we define safety risks by requesting the alignment of the networks decision with human perception. To enable a general methodology for quantifying safety risks, we define a generic safety property and instantiate it to express various safety risks. For the quantification of risks, we take the maximum radius of safe norm balls, in which no safety risk exists. The computation of the maximum safe radius is reduced to the computation of their respective Lipschitz metrics - the quantities to be computed. In addition to the known adversarial example, reachability example, and invariant example, in this paper we identify a new class of risk - uncertainty example - on which humans can tell easily but the network is unsure. We develop an algorithm, inspired by derivative-free optimization techniques and accelerated by tensor-based parallelization on GPUs, to support efficient computation of the metrics. We perform evaluations on several benchmark neural networks, including ACSC-Xu, MNIST, CIFAR-10, and ImageNet networks. The experiments show that, our method can achieve competitive performance on safety quantification in terms of the tightness and the efficiency of computation. Importantly, as a generic approach, our method can work with a broad class of safety risks and without restrictions on the structure of neural networks.
Studying the implicit regularization effect of the nonlinear training dynamics of neural networks (NNs) is important for understanding why over-parameterized neural networks often generalize well on real dataset. Empirically, for two-layer NN, existing works have shown that input weights of hidden neurons (the input weight of a hidden neuron consists of the weight from its input layer to the hidden neuron and its bias term) condense on isolated orientations with a small initialization. The condensation dynamics implies that NNs can learn features from the training data with a network configuration effectively equivalent to a much smaller network during the training. In this work, we show that the multiple roots of activation function at origin (referred as ``multiplicity) is a key factor for understanding the condensation at the initial stage of training. Our experiments of multilayer networks suggest that the maximal number of condensed orientations is twice the multiplicity of the activation function used. Our theoretical analysis of two-layer networks confirms experiments for two cases, one is for the activation function of multiplicity one, which contains many common activation functions, and the other is for the one-dimensional input. This work makes a step towards understanding how small initialization implicitly leads NNs to condensation at initial training stage, which lays a foundation for the future study of the nonlinear dynamics of NNs and its implicit regularization effect at a later stage of training.
We propose a new algorithm to learn a one-hidden-layer convolutional neural network where both the convolutional weights and the outputs weights are parameters to be learned. Our algorithm works for a general class of (potentially overlapping) patches, including commonly used structures for computer vision tasks. Our algorithm draws ideas from (1) isotonic regression for learning neural networks and (2) landscape analysis of non-convex matrix factorization problems. We believe these findings may inspire further development in designing provable algorithms for learning neural networks and other complex models.
As the complexity of deep neural networks (DNNs) trend to grow to absorb the increasing sizes of data, memory and energy consumption has been receiving more and more attentions for industrial applications, especially on mobile devices. This paper presents a novel structure based on functional hashing to compress DNNs, namely FunHashNN. For each entry in a deep net, FunHashNN uses multiple low-cost hash functions to fetch values in the compression space, and then employs a small reconstruction network to recover that entry. The reconstruction network is plugged into the whole network and trained jointly. FunHashNN includes the recently proposed HashedNets as a degenerated case, and benefits from larger value capacity and less reconstruction loss. We further discuss extensions with dual space hashing and multi-hops. On several benchmark datasets, FunHashNN demonstrates high compression ratios with little loss on prediction accuracy.
Neural networks are increasingly applied to support decision making in safety-critical applications (like autonomous cars, unmanned aerial vehicles and face recognition based authentication). While many impressive static verification techniques have been proposed to tackle the correctness problem of neural networks, it is possible that static verification may never be sufficiently scalable to handle real-world neural networks. In this work, we propose a runtime verification method to ensure the correctness of neural networks. Given a neural network and a desirable safety property, we adopt state-of-the-art static verification techniques to identify strategically locations to introduce additional gates which correct neural network behaviors at runtime. Experiment results show that our approach effectively generates neural networks which are guaranteed to satisfy the properties, whilst being consistent with the original neural network most of the time.
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