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Register a new userDeep Neural Networks with Trainable Activations and Controlled Lipschitz Constant
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We introduce a variational framework to learn the activation functions of deep neural networks. Our aim is to increase the capacity of the network while controlling an upper-bound of the actual Lipschitz constant of the input-output relation. To that end, we first establish a global bound for the Lipschitz constant of neural networks. Based on the obtained bound, we then formulate a variational problem for learning activation functions. Our variational problem is infinite-dimensional and is not computationally tractable. However, we prove that there always exists a solution that has continuous and piecewise-linear (linear-spline) activations. This reduces the original problem to a finite-dimensional minimization where an l1 penalty on the parameters of the activations favors the learning of sparse nonlinearities. We numerically compare our scheme with standard ReLU network and its variations, PReLU and LeakyReLU and we empirically demonstrate the practical aspects of our framework.
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This paper addresses a challenging problem - how to reduce energy consumption without incurring performance drop when deploying deep neural networks (DNNs) at the inference stage. In order to alleviate the computation and storage burdens, we propose a novel dataflow-based joint quantization approach with the hypothesis that a fewer number of quantization operations would incur less information loss and thus improve the final performance. It first introduces a quantization scheme with efficient bit-shifting and rounding operations to represent network parameters and activations in low precision. Then it restructures the network architectures to form unified modules for optimization on the quantized model. Extensive experiments on ImageNet and KITTI validate the effectiveness of our model, demonstrating that state-of-the-art results for various tasks can be achieved by this quantized model. Besides, we designed and synthesized an RTL model to measure the hardware costs among various quantization methods. For each quantization operation, it reduces area cost by about 15 times and energy consumption by about 9 times, compared to a strong baseline.
Deep neural networks are considered to be state of the art models in many offline machine learning tasks. However, their performance and generalization abilities in online learning tasks are much less understood. Therefore, we focus on online learning and tackle the challenging problem where the underlying process is stationary and ergodic and thus removing the i.i.d. assumption and allowing observations to depend on each other arbitrarily. We prove the generalization abilities of Lipschitz regularized deep neural networks and show that by using those networks, a convergence to the best possible prediction strategy is guaranteed.
The distribution of a neural networks latent representations has been successfully used to detect out-of-distribution (OOD) data. This work investigates whether this distribution moreover correlates with a models epistemic uncertainty, thus indicates its ability to generalise to novel inputs. We first empirically verify that epistemic uncertainty can be identified with the surprise, thus the negative log-likelihood, of observing a particular latent representation. Moreover, we demonstrate that the output-conditional distribution of hidden representations also allows quantifying aleatoric uncertainty via the entropy of the predictive distribution. We analyse epistemic and aleatoric uncertainty inferred from the representations of different layers and conclude that deeper layers lead to uncertainty with similar behaviour as established - but computationally more expensive - methods (e.g. deep ensembles). While our approach does not require modifying the training process, we follow prior work and experiment with an additional regularising loss that increases the information in the latent representations. We find that this leads to improved OOD detection of epistemic uncertainty at the cost of ambiguous calibration close to the data distribution. We verify our findings on both classification and regression models.
We introduce a method to train Binarized Neural Networks (BNNs) - neural networks with binary weights and activations at run-time. At training-time the binary weights and activations are used for computing the parameters gradients. During the forward pass, BNNs drastically reduce memory size and accesses, and replace most arithmetic operations with bit-wise operations, which is expected to substantially improve power-efficiency. To validate the effectiveness of BNNs we conduct two sets of experiments on the Torch7 and Theano frameworks. On both, BNNs achieved nearly state-of-the-art results over the MNIST, CIFAR-10 and SVHN datasets. Last but not least, we wrote a binary matrix multiplication GPU kernel with which it is possible to run our MNIST BNN 7 times faster than with an unoptimized GPU kernel, without suffering any loss in classification accuracy. The code for training and running our BNNs is available on-line.
ShuffleNet is a state-of-the-art light weight convolutional neural network architecture. Its basic operations include group, channel-wise convolution and channel shuffling. However, channel shuffling is manually designed empirically. Mathematically, shuffling is a multiplication by a permutation matrix. In this paper, we propose to automate channel shuffling by learning permutation matrices in network training. We introduce an exact Lipschitz continuous non-convex penalty so that it can be incorporated in the stochastic gradient descent to approximate permutation at high precision. Exact permutations are obtained by simple rounding at the end of training and are used in inference. The resulting network, referred to as AutoShuffleNet, achieved improved classification accuracies on CIFAR-10 and ImageNet data sets. In addition, we found experimentally that the standard convex relaxation of permutation matrices into stochastic matrices leads to poor performance. We prove theoretically the exactness (error bounds) in recovering permutation matrices when our penalty function is zero (very small). We present examples of permutation optimization through graph matching and two-layer neural network models where the loss functions are calculated in closed analytical form. In the examples, convex relaxation failed to capture permutations whereas our penalty succeeded.
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