High-dimensional representations often have a lower dimensional underlying structure. This is particularly the case in many decision making settings. For example, when the representation of actions is generated from a deep neural network, it is reasonable to expect a low-rank structure whereas conventional structures like sparsity are not valid anymore. Subspace recovery methods, such as Principle Component Analysis (PCA) can find the underlying low-rank structures in the feature space and reduce the complexity of the learning tasks. In this work, we propose Projected Stochastic Linear Bandit (PSLB), an algorithm for high dimensional stochastic linear bandits (SLB) when the representation of actions has an underlying low-dimensional subspace structure. PSLB deploys PCA based projection to iteratively find the low rank structure in SLBs. We show that deploying projection methods assures dimensionality reduction and results in a tighter regret upper bound that is in terms of the dimensionality of the subspace and its properties, rather than the dimensionality of the ambient space. We modify the image classification task into the SLB setting and empirically show that, when a pre-trained DNN provides the high dimensional feature representations, deploying PSLB results in significant reduction of regret and faster convergence to an accurate model compared to state-of-art algorithm.

Unsupervised and semi-supervised learning are important problems that are especially challenging with complex data like natural images. Progress on these problems would accelerate if we had access to appropriate generative models under which to pose the associated inference tasks. Inspired by the success of Convolutional Neural Networks (CNNs) for supervised prediction in images, we design the Neural Rendering Model (NRM), a new probabilistic generative model whose inference calculations correspond to those in a given CNN architecture. The NRM uses the given CNN to design the prior distribution in the probabilistic model. Furthermore, the NRM generates images from coarse to finer scales. It introduces a small set of latent variables at each level, and enforces dependencies among all the latent variables via a conjugate prior distribution. This conjugate prior yields a new regularizer based on paths rendered in the generative model for training CNNs-the Rendering Path Normalization (RPN). We demonstrate that this regularizer improves generalization, both in theory and in practice. In addition, likelihood estimation in the NRM yields training losses for CNNs, and inspired by this, we design a new loss termed as the Max-Min cross entropy which outperforms the traditional cross-entropy loss for object classification. The Max-Min cross entropy suggests a new deep network architecture, namely the Max-Min network, which can learn from less labeled data while maintaining good prediction performance. Our experiments demonstrate that the NRM with the RPN and the Max-Min architecture exceeds or matches the-state-of-art on benchmarks including SVHN, CIFAR10, and CIFAR100 for semi-supervised and supervised learning tasks.

Training neural networks on large datasets can be accelerated by distributing the workload over a network of machines. As datasets grow ever larger, networks of hundreds or thousands of machines become economically viable. The time cost of communicating gradients limits the effectiveness of using such large machine counts, as may the increased chance of network faults. We explore a particularly simple algorithm for robust, communication-efficient learning---signSGD. Workers transmit only the sign of their gradient vector to a server, and the overall update is decided by a majority vote. This algorithm uses $32\times$ less communication per iteration than full-precision, distributed SGD. Under natural conditions verified by experiment, we prove that signSGD converges in the large and mini-batch settings, establishing convergence for a parameter regime of Adam as a byproduct. We model adversaries as those workers who may compute a stochastic gradient estimate and manipulate it, but may not coordinate with other adversaries. Aggregating sign gradients by majority vote means that no individual worker has too much power. We prove that unlike SGD, majority vote is robust when up to 50% of workers behave adversarially. On the practical side, we built our distributed training system in Pytorch. Benchmarking against the state of the art collective communications library (NCCL), our framework---with the parameter server housed entirely on one machine---led to a 25% reduction in time for training resnet50 on Imagenet when using 15 AWS p3.2xlarge machines.

Often models that operate on source code consume ASTs by linearizing them (usually with a depth-first traversal) (Amodio et al., 2017; Liu et al., 2017; Li et al., 2017), but they can also be processed by deep learning models that take graphs as input, as in White et al. (2016) and Chen et al. (2018) who use Recursive Neural Networks (RveNNs) (Goller & Kuchler, 1996) on ASTs. RveNNs are models that operate on tree-topology graphs, and have been used extensively for language modeling (Socher et al., 2013) and on domains similar to source code, like mathematical expressions (Zaremba et al., 2014; Arabshahi et al., 2018). They can be considered a special case of Message Passing Neural Networks (MPNNs) in the framework of Gilmer et al. (2017): in this analogy RveNNs are to Belief Propagation as MPNNs are to Loopy Belief Propagation. They can also be considered a special case of Graph Networks in the framework of Battaglia et al. (2018). ASTs also serve as a natural basis for models that generate code as output, as in Maddison & Tarlow (2014), Yin & Neubig (2017), Rabinovich et al. (2017), Chen et al. (2018), and Brockschmidt et al. (2018).

Training large neural networks requires distributing learning across multiple workers, where the cost of communicating gradients can be a significant bottleneck. signSGD alleviates this problem by transmitting just the sign of each minibatch stochastic gradient. We prove that it can get the best of both worlds: compressed gradients and SGD-level convergence rate. The relative $\ell_1/\ell_2$ geometry of gradients, noise and curvature informs whether signSGD or SGD is theoretically better suited to a particular problem. On the practical side we find that the momentum counterpart of signSGD is able to match the accuracy and convergence speed of Adam on deep Imagenet models. We extend our theory to the distributed setting, where the parameter server uses majority vote to aggregate gradient signs from each worker enabling 1-bit compression of worker-server communication in both directions. Using a theorem by Gauss we prove that majority vote can achieve the same reduction in variance as full precision distributed SGD. Thus, there is great promise for sign-based optimisation schemes to achieve fast communication and fast convergence. Code to reproduce experiments is to be found at https://github.com/jxbz/signSGD.

We introduce Probabilistic FastText, a new model for word embeddings that can capture multiple word senses, sub-word structure, and uncertainty information. In particular, we represent each word with a Gaussian mixture density, where the mean of a mixture component is given by the sum of n-grams. This representation allows the model to share statistical strength across sub-word structures (e.g. Latin roots), producing accurate representations of rare, misspelt, or even unseen words. Moreover, each component of the mixture can capture a different word sense. Probabilistic FastText outperforms both FastText, which has no probabilistic model, and dictionary-level probabilistic embeddings, which do not incorporate subword structures, on several word-similarity benchmarks, including English RareWord and foreign language datasets. We also achieve state-of-art performance on benchmarks that measure ability to discern different meanings. Thus, the proposed model is the first to achieve multi-sense representations while having enriched semantics on rare words.

Knowledge distillation (KD) consists of transferring knowledge from one machine learning model (the teacher}) to another (the student). Commonly, the teacher is a high-capacity model with formidable performance, while the student is more compact. By transferring knowledge, one hopes to benefit from the student's compactness. %we desire a compact model with performance close to the teacher's. We study KD from a new perspective: rather than compressing models, we train students parameterized identically to their teachers. Surprisingly, these {Born-Again Networks (BANs), outperform their teachers significantly, both on computer vision and language modeling tasks. Our experiments with BANs based on DenseNets demonstrate state-of-the-art performance on the CIFAR-10 (3.5%) and CIFAR-100 (15.5%) datasets, by validation error. Additional experiments explore two distillation objectives: (i) Confidence-Weighted by Teacher Max (CWTM) and (ii) Dark Knowledge with Permuted Predictions (DKPP). Both methods elucidate the essential components of KD, demonstrating a role of the teacher outputs on both predicted and non-predicted classes. We present experiments with students of various capacities, focusing on the under-explored case where students overpower teachers. Our experiments show significant advantages from transferring knowledge between DenseNets and ResNets in either direction.

Neural networks are known to be vulnerable to adversarial examples. Carefully chosen perturbations to real images, while imperceptible to humans, induce misclassification and threaten the reliability of deep learning systems in the wild. To guard against adversarial examples, we take inspiration from game theory and cast the problem as a minimax zero-sum game between the adversary and the model. In general, for such games, the optimal strategy for both players requires a stochastic policy, also known as a mixed strategy. In this light, we propose Stochastic Activation Pruning (SAP), a mixed strategy for adversarial defense. SAP prunes a random subset of activations (preferentially pruning those with smaller magnitude) and scales up the survivors to compensate. We can apply SAP to pretrained networks, including adversarially trained models, without fine-tuning, providing robustness against adversarial examples. Experiments demonstrate that SAP confers robustness against attacks, increasing accuracy and preserving calibration.

Developing efficient and guaranteed nonconvex algorithms has been an important challenge in modern machine learning. Algorithms with good empirical performance such as stochastic gradient descent often lack theoretical guarantees. In this paper, we analyze the class of homotopy or continuation methods for global optimization of nonconvex functions. These methods start from an objective function that is efficient to optimize (e.g. convex), and progressively modify it to obtain the required objective, and the solutions are passed along the homotopy path. For the challenging problem of tensor PCA, we prove global convergence of the homotopy method in the "high noise" regime. The signal-to-noise requirement for our algorithm is tight in the sense that it matches the recovery guarantee for the best degree-4 sum-of-squares algorithm. In addition, we prove a phase transition along the homotopy path for tensor PCA. This allows to simplify the homotopy method to a local search algorithm, viz., tensor power iterations, with a specific initialization and a noise injection procedure, while retaining the theoretical guarantees.

Tensor decomposition is positioned to be a pervasive tool in the era of big data. In this paper, we resolve many of the key algorithmic questions regarding robustness, memory efficiency, and differential privacy of tensor decomposition. We propose simple variants of the tensor power method which enjoy these strong properties. We propose the first streaming method with a linear memory requirement. Moreover, we present a noise calibrated tensor power method with efficient privacy guarantees. At the heart of all these guarantees lies a careful perturbation analysis derived in this paper which improves up on the existing results significantly.