Resistive random-access memory (RRAM) is widely recognized as a promising emerging hardware platform for deep neural networks (DNNs). Yet, due to manufacturing limitations, current RRAM devices are highly susceptible to hardware defects, which poses a significant challenge to their practical applicability. In this paper, we present a machine learning technique that enables the deployment of defect-prone RRAM accelerators for DNN applications, without necessitating modifying the hardware, retraining of the neural network, or implementing additional detection circuitry/logic. The key idea involves incorporating a drop-connect inspired approach during the training phase of a DNN, where random subsets of weights are selected to emulate fault effects (e.g., set to zero to mimic stuck-at-1 faults), thereby equipping the DNN with the ability to learn and adapt to RRAM defects with the corresponding fault rates. Our results demonstrate the viability of the dropconnect approach, coupled with various algorithm and system-level design and trade-off considerations. We show that, even in the presence of high defect rates (e.g., up to 30%), the degradation of DNN accuracy can be as low as less than 1% compared to that of the fault-free version, while incurring minimal system-level runtime/energy costs.

We develop an approach to efficiently grow neural networks, within which parameterization and optimization strategies are designed by considering their effects on the training dynamics. Unlike existing growing methods, which follow simple replication heuristics or utilize auxiliary gradient-based local optimization, we craft a parameterization scheme which dynamically stabilizes weight, activation, and gradient scaling as the architecture evolves, and maintains the inference functionality of the network. To address the optimization difficulty resulting from imbalanced training effort distributed to subnetworks fading in at different growth phases, we propose a learning rate adaption mechanism that rebalances the gradient contribution of these separate subcomponents. Experiments show that our method achieves comparable or better accuracy than training large fixed-size models, while saving a substantial portion of the original training computation budget. We demonstrate that these gains translate into real wall-clock training speedups.

We study the problem of training deep networks while quantizing parameters and activations into low-precision numeric representations, a setting central to reducing energy consumption and inference time of deployed models. We propose a method that learns different precisions, as measured by bits in numeric representations, for different weights in a neural network, yielding a heterogeneous allocation of bits across parameters. Learning precisions occurs alongside learning weight values, using a strategy derived from a novel framework wherein the intractability of optimizing discrete precisions is approximated by training per-parameter noise magnitudes. We broaden this framework to also encompass learning precisions for hidden state activations, simultaneously with weight precisions and values. Our approach exposes the objective of constructing a low-precision inference-efficient model to the entirety of the training process. Experiments show that it finds highly heterogeneous precision assignments for CNNs trained on CIFAR and ImageNet, improving upon previous state-of-the-art quantization methods. Our improvements extend to the challenging scenario of learning reduced-precision GANs.

We study image segmentation from an information-theoretic perspective, proposing a novel adversarial method that performs unsupervised segmentation by partitioning images into maximally independent sets. More specifically, we group image pixels into foreground and background, with the goal of minimizing predictability of one set from the other. An easily computed loss drives a greedy search process to maximize inpainting error over these partitions. Our method does not involve training deep networks, is computationally cheap, class-agnostic, and even applicable in isolation to a single unlabeled image. Experiments demonstrate that it achieves a new state-of-the-art in unsupervised segmentation quality, while being substantially faster and more general than competing approaches.1

From a simplified analysis of adaptive methods, we derive AvaGrad, a new optimizer which outperforms SGD on vision tasks when its adaptability is properly tuned. We observe that the power of our method is partially explained by a decoupling of learning rate and adaptability, greatly simplifying hyperparameter search. In light of this observation, we demonstrate that, against conventional wisdom, Adam can also outperform SGD on vision tasks, as long as the coupling between its learning rate and adaptability is taken into account. In practice, AvaGrad matches the best results, as measured by generalization accuracy, delivered by any existing optimizer (SGD or adaptive) across image classification (CIFAR, ImageNet) and character-level language modelling (Penn Treebank) tasks. When training GANs, AvaGrad improves upon existing optimizers.1

A recent line of work studies overparametrized neural networks in the “kernel regime,” i.e. when during training the network behaves as a kernelized linear predictor, and thus, training with gradient descent has the effect of finding the corresponding minimum RKHS norm solution. This stands in contrast to other studies which demonstrate how gradient descent on overparametrized networks can induce rich implicit biases that are not RKHS norms. Building on an observation by \citet{chizat2018note}, we show how the \textbf{\textit{scale of the initialization}} controls the transition between the “kernel” (aka lazy) and “rich” (aka active) regimes and affects generalization properties in multilayer homogeneous models. We provide a complete and detailed analysis for a family of simple depth-$D$ linear networks that exhibit an interesting and meaningful transition between the kernel and rich regimes, and highlight an interesting role for the \emph{width} of the models. We further demonstrate this transition empirically for matrix factorization and multilayer non-linear networks.

The search for efficient, sparse deep neural network models is most prominently performed by pruning: training a dense, overparameterized network and removing parameters, usually via following a manually-crafted heuristic. Additionally, the recent Lottery Ticket Hypothesis conjectures that, for a typically-sized neural network, it is possible to find small sub-networks which, when trained from scratch on a comparable budget, match the performance of the original dense counterpart. We revisit fundamental aspects of pruning algorithms, pointing out missing ingredients in previous approaches, and develop a method, Continuous Sparsification, which searches for sparse networks based on a novel approximation of an intractable $\ell_0$ regularization. We compare against dominant heuristic-based methods on pruning as well as ticket search -- finding sparse subnetworks that can be successfully re-trained from an early iterate. Empirical results show that we surpass the state-of-the-art for both objectives, across models and datasets, including VGG trained on CIFAR-10 and ResNet-50 trained on ImageNet. In addition to setting a new standard for pruning, Continuous Sparsification also offers fast parallel ticket search, opening doors to new applications of the Lottery Ticket Hypothesis.

We provide a detailed study on the implicit bias of gradient descent when optimizing loss functions with strictly monotone tails, such as the logistic loss, over separable datasets. We look at two basic questions: (a) what are the conditions on the tail of the loss function under which gradient descent converges in the direction of the $L_2$ maximum-margin separator? (b) how does the rate of margin convergence depend on the tail of the loss function and the choice of the step size? We show that for a large family of super-polynomial tailed losses, gradient descent iterates on linear networks of any depth converge in the direction of $L_2$ maximum-margin solution, while this does not hold for losses with heavier tails. Within this family, for simple linear models we show that the optimal rates with fixed step size is indeed obtained for the commonly used exponentially tailed losses such as logistic loss. However, with a fixed step size the optimal convergence rate is extremely slow as $1/\log(t)$, as also proved in Soudry et al (2018). For linear models with exponential loss, we further prove that the convergence rate could be improved to $\log (t) /\sqrt{t}$ by using aggressive step sizes that compensates for the rapidly vanishing gradients. Numerical results suggest this method might be useful for deep networks.

We consider the question of what functions can be captured by ReLU networks with an unbounded number of units (infinite width), but where the overall network Euclidean norm (sum of squares of all weights in the system, except for an unregularized bias term for each unit) is bounded; or equivalently what is the minimal norm required to approximate a given function. For functions $f:\mathbb R \rightarrow\mathbb R$ and a single hidden layer, we show that the minimal network norm for representing $f$ is $\max(\int \lvert f”(x) \rvert \mathrm{d} x, \lvert f’(-\infty) + f’(+\infty) \rvert)$, and hence the minimal norm fit for a sample is given by a linear spline interpolation.

We propose a Las Vegas transformation of Markov Chain Monte Carlo (MCMC) estimators of Restricted Boltzmann Machines (RBMs). We denote our approach Markov Chain Las Vegas (MCLV). MCLV gives statistical guarantees in exchange for random running times. MCLV uses a stopping set built from the training data and has maximum number of Markov chain steps K (referred as MCLV-K). We present a MCLV-K gradient estimator (LVS-K) for RBMs and explore the correspondence and differences between LVS-K and Contrastive Divergence (CD-K), with LVS-K significantly outperforming CD-K training RBMs over the MNIST dataset, indicating MCLV to be a promising direction in learning generative models.