ABSTRACT We propose convex relaxations for convolutional neural nets with one hidden layer where the output weights are fixed. For convex activation functions such as rectified linear units, the relaxations are convex second order cone programs which can be solved very efficiently. We prove that the relaxation recovers the global minimum under a planted model assumption, given sufficiently many training samples from a Gaussian distribution. We also identify a phase transition phenomenon in recovering the global minimum for the relaxation. Index Terms -- Convolutional neural networks, convex relaxations, linear programming, deep learning 1. INTRODUCTION Convolutional neural networks (CNNs) have been extremely successful across many domains in machine learning and computer vision [14, 15].

Neural Networks (NN) have been proposed in the past as an effective means for both modeling and control of systems with very complex dynamics. However, despite the extensive research, NN-based controllers have not been adopted by the industry for safety critical systems. The primary reason is that systems with learning based controllers are notoriously hard to test and verify. Even harder is the analysis of such systems against system-level specifications. In this paper, we provide a gradient based method for searching the input space of a closed-loop control system in order to find adversarial samples against some system-level requirements. Our experimental results show that combined with randomized search, our method outperforms Simulated Annealing optimization.

Designing RNA molecules has garnered recent interest in medicine, synthetic biology, biotechnology and bioinformatics since many functional RNA molecules were shown to be involved in regulatory processes for transcription, epigenetics and translation. Since an RNA's function depends on its structural properties, the RNA Design problem is to find an RNA sequence that folds into a specified secondary structure. Here, we propose a new algorithm for the RNA Design problem, dubbed LEARNA. LEARNA uses deep reinforcement learning to train a policy network to sequentially design an entire RNA sequence given a specified secondary target structure. By meta-learning across 8000 different RNA target structures for one hour on 20 cores, our extension Meta-LEARNA constructs an RNA Design policy that can be applied out of the box to solve novel RNA target structures. Methodologically, for what we believe to be the first time, we jointly optimize over a rich space of neural architectures for the policy network, the hyperparameters of the training procedure and the formulation of the decision process. Comprehensive empirical results on two widely-used RNA secondary structure design benchmarks, as well as a third one that we introduce, show that our approach achieves new state-of-the-art performance on all benchmarks while also being orders of magnitudes faster in reaching the previous state-of-the-art performance. In an ablation study, we analyze the importance of our method's different components.

The high computational and parameter complexity of neural networks makes their training very slow and difficult to deploy on energy and storage-constrained computing systems. Many network complexity reduction techniques have been proposed including fixed-point implementation. However, a systematic approach for designing full fixed-point training and inference of deep neural networks remains elusive. We describe a precision assignment methodology for neural network training in which all network parameters, i.e., activations and weights in the feedforward path, gradients and weight accumulators in the feedback path, are assigned close to minimal precision. The precision assignment is derived analytically and enables tracking the convergence behavior of the full precision training, known to converge a priori. Thus, our work leads to a systematic methodology of determining suitable precision for fixed-point training. The near optimality (minimality) of the resulting precision assignment is validated empirically for four networks on the CIFAR-10, CIFAR-100, and SVHN datasets. The complexity reduction arising from our approach is compared with other fixed-point neural network designs.

The impact of the maximally possible batch size (for the better runtime) on performance of graphic processing units (GPU) and tensor processing units (TPU) during training and inference phases is investigated. The numerous runs of the selected deep neural network (DNN) were performed on the standard MNIST and Fashion-MNIST datasets. The significant speedup was obtained even for extremely low-scale usage of Google TPUv2 units (8 cores only) in comparison to the quite powerful GPU NVIDIA Tesla K80 card with the speedup up to 10x for training stage (without taking into account the overheads) and speedup up to 2x for prediction stage (with and without taking into account overheads). The precise speedup values depend on the utilization level of TPUv2 units and increase with the increase of the data volume under processing, but for the datasets used in this work (MNIST and Fashion-MNIST with images of sizes 28x28) the speedup was observed for batch sizes >512 images for training phase and >40 000 images for prediction phase. It should be noted that these results were obtained without detriment to the prediction accuracy and loss that were equal for both GPU and TPU runs up to the 3rd significant digit for MNIST dataset, and up to the 2nd significant digit for Fashion-MNIST dataset.

The low displacement rank (LDR) framework for structured matrices represents a matrix through two displacement operators and a low-rank residual. Existing use of LDR matrices in deep learning has applied fixed displacement operators encoding forms of shift invariance akin to convolutions. We introduce a rich class of LDR matrices with more general displacement operators, and explicitly learn over both the operators and the low-rank component. This class generalizes several previous constructions while preserving compression and efficient computation. We prove bounds on the VC dimension of multi-layer neural networks with structured weight matrices and show empirically that our compact parameterization can reduce the sample complexity of learning. When replacing weight layers in fully-connected, convolutional, and recurrent neural networks for image classification and language modeling tasks, our new classes exceed the accuracy of existing compression approaches, and on some tasks even outperform general unstructured layers while using more than 20x fewer parameters.

This paper addresses the problem of manipulating images using natural language description. Our task aims to semantically modify visual attributes of an object in an image according to the text describing the new visual appearance. Although existing methods synthesize images having new attributes, they do not fully preserve text-irrelevant contents of the original image. In this paper, we propose the text-adaptive generative adversarial network (TAGAN) to generate semantically manipulated images while preserving text-irrelevant contents. The key to our method is the text-adaptive discriminator that creates word level local discriminators according to input text to classify fine-grained attributes independently. With this discriminator, the generator learns to generate images where only regions that correspond to the given text is modified. Experimental results show that our method outperforms existing methods on CUB and Oxford-102 datasets, and our results were mostly preferred on a user study. Extensive analysis shows that our method is able to effectively disentangle visual attributes and produce pleasing outputs.

This paper addresses the problem of manipulating images using natural language description. Our task aims to semantically modify visual attributes of an object in an image according to the text describing the new visual appearance. Although existing methods synthesize images having new attributes, they do not fully preserve text-irrelevant contents of the original image. In this paper, we propose the text-adaptive generative adversarial network (TAGAN) to generate semantically manipulated images while preserving text-irrelevant contents. The key to our method is the text-adaptive discriminator that creates word level local discriminators according to input text to classify fine-grained attributes independently. With this discriminator, the generator learns to generate images where only regions that correspond to the given text is modified. Experimental results show that our method outperforms existing methods on CUB and Oxford-102 datasets, and our results were mostly preferred on a user study. Extensive analysis shows that our method is able to effectively disentangle visual attributes and produce pleasing outputs.

Learning in small sample regimes is among the most remarkable features of the human perceptual system. This ability is related to robustness to transformations, which is acquired through visual experience in the form of weak- or self-supervision during development. We explore the idea of allowing artificial systems to learn representations of visual stimuli through weak supervision prior to downstream supervised tasks. We introduce a novel loss function for representation learning using unlabeled image sets and video sequences, and experimentally demonstrate that these representations support one-shot learning and reduce the sample complexity of multiple recognition tasks. We establish the existence of a trade-off between the sizes of weakly supervised, automatically obtained from video sequences, and fully supervised data sets. Our results suggest that equivalence sets other than class labels, which are abundant in unlabeled visual experience, can be used for self-supervised learning of semantically relevant image embeddings.

The ever-increasing number of parameters in deep neural networks poses challenges for memory-limited applications. Regularize-and-prune methods aim at meeting these challenges by sparsifying the network weights. In this context we quantify the output sensitivity to the parameters (i.e. their relevance to the network output) and introduce a regularization term that gradually lowers the absolute value of parameters with low sensitivity. Thus, a very large fraction of the parameters approach zero and are eventually set to zero by simple thresholding. Our method surpasses most of the recent techniques both in terms of sparsity and error rates. In some cases, the method reaches twice the sparsity obtained by other techniques at equal error rates.