Abstract--Improving performance of deep learning models and reducing their training times are ongoing challenges in deep neural networks. There are several approaches proposed to address these challenges one of which is to increase the depth of the neural networks. Such deeper networks not only increase training times, but also suffer from vanishing gradients problem while training. In this work, we propose gradient amplification approach for training deep learning models to prevent vanishing gradients and also develop a training strategy to enable or disable gradient amplification method across several epochs with different learning rates. We perform experiments on VGG-19 and resnet (Resnet-18 and Resnet-34) models, and study the impact of amplification parameters on these models in detail. Our proposed approach improves performance of these deep learning models even at higher learning rates, thereby allowing these models to achieve higher performance with reduced training time.

In this paper, we consider large-scale finite-sum nonconvex problems arising from machine learning. Since the Hessian is often a summation of a relative cheap and accessible part and an expensive or even inaccessible part, a stochastic quasi-Newton matrix is constructed using partial Hessian information as much as possible. By further exploiting the low-rank structures based on the Nystr\"om approximation, the computation of the quasi-Newton direction is affordable. To make full use of the gradient estimation, we also develop an extra-step strategy for this framework. Global convergence to stationary point in expectation and local suplinear convergence rate are established under some mild assumptions. Numerical experiments on logistic regression, deep autoencoder networks and deep learning problems show that the efficiency of our proposed method is at least comparable with the state-of-the-art methods.

This paper compares two different types of data-driven control methods, representing model-based and model-free approaches. One is a recently proposed method - Deep Koopman Representation for Control (DKRC), which utilizes a deep neural network to map an unknown nonlinear dynamical system to a high-dimensional linear system, which allows for employing state-of-the-art control strategy. The other one is a classic model-free control method based on an actor-critic architecture - Deep Deterministic Policy Gradient (DDPG), which has been proved to be effective in various dynamical systems. The comparison is carried out in OpenAI Gym, which provides multiple control environments for benchmark purposes. Two examples are provided for comparison, i.e., classic Inverted Pendulum and Lunar Lander Continuous Control. From the results of the experiments, we compare these two methods in terms of control strategies and the effectiveness under various initialization conditions. We also examine the learned dynamic model from DKRC with the analytical model derived from the Euler-Lagrange Linearization method, which demonstrates the accuracy in the learned model for unknown dynamics from a data-driven sample-efficient approach.

Deep neural networks (DNNs) are inherently susceptible to adversarial attacks even under black-box settings, in which the adversary only has query access to the target models. In practice, while it may be possible to effectively detect such attacks (e.g., observing massive similar but non-identical queries), it is often challenging to exactly infer the adversary intent (e.g., the target class of the adversarial example the adversary attempts to craft) especially during early stages of the attacks, which is crucial for performing effective deterrence and remediation of the threats in many scenarios. In this paper, we present AdvMind, a new class of estimation models that infer the adversary intent of black-box adversarial attacks in a robust and prompt manner. Specifically, to achieve robust detection, AdvMind accounts for the adversary adaptiveness such that her attempt to conceal the target will significantly increase the attack cost (e.g., in terms of the number of queries); to achieve prompt detection, AdvMind proactively synthesizes plausible query results to solicit subsequent queries from the adversary that maximally expose her intent. Through extensive empirical evaluation on benchmark datasets and state-of-the-art black-box attacks, we demonstrate that on average AdvMind detects the adversary intent with over 75% accuracy after observing less than 3 query batches and meanwhile increases the cost of adaptive attacks by over 60%. We further discuss the possible synergy between AdvMind and other defense methods against black-box adversarial attacks, pointing to several promising research directions.

Deep neural networks have achieved human-level accuracy on almost all perceptual benchmarks. It is interesting that these advances were made using two ideas that are decades old: (a) an artificial neuron based on a linear summator and (b) SGD training. However, there are important metrics beyond accuracy: computational efficiency and stability against adversarial perturbations. In this paper, we propose two closely connected methods to improve these metrics on contour recognition tasks: (a) a novel model of an artificial neuron, a "strong neuron," with low hardware requirements and inherent robustness against adversarial perturbations and (b) a novel constructive training algorithm that generates sparse networks with $O(1)$ connections per neuron. We demonstrate the feasibility of our approach through experiments on SVHN and GTSRB benchmarks. We achieved an impressive 10x-100x reduction in operations count (10x when compared with other sparsification approaches, 100x when compared with dense networks) and a substantial reduction in hardware requirements (8-bit fixed-point math was used) with no reduction in model accuracy. Superior stability against adversarial perturbations (exceeding that of adversarial training) was achieved without any counteradversarial measures, relying on the robustness of strong neurons alone. We also proved that constituent blocks of our strong neuron are the only activation functions with perfect stability against adversarial attacks.

Many state-of-the-art results in domains such as NLP and computer vision have been obtained by scaling up the number of parameters in existing models. However, the weight parameters and intermediate outputs of these large models often do not fit in the main memory of a single accelerator device; this means that it is necessary to use multiple accelerators to train large models, which is challenging to do in a time-efficient way. In this work, we propose PipeDream-2BW, a system that performs memory-efficient pipeline parallelism, a hybrid form of parallelism that combines data and model parallelism with input pipelining. Our system uses a novel pipelining and weight gradient coalescing strategy, combined with the double buffering of weights, to ensure high throughput, low memory footprint, and weight update semantics similar to data parallelism. In addition, PipeDream-2BW automatically partitions the model over the available hardware resources, while being cognizant of constraints such as compute capabilities, memory capacities, and interconnect topologies, and determines when to employ existing memory-savings techniques, such as activation recomputation, that trade off extra computation for lower memory footprint. PipeDream-2BW is able to accelerate the training of large language models with up to 2.5 billion parameters by up to 6.9x compared to optimized baselines.

Attention and self-attention mechanisms, inspired by cognitive processes, are now central to state-of-the-art deep learning on sequential tasks. However, most recent progress hinges on heuristic approaches with limited understanding of attention's role in model optimization and computation, and rely on considerable memory and computational resources that scale poorly. In this work, we present a formal analysis of how self-attention affects gradient propagation in recurrent networks, and prove that it mitigates the problem of vanishing gradients when trying to capture long-term dependencies. Building on these results, we propose a relevancy screening mechanism, inspired by the cognitive process of memory consolidation, that allows for a scalable use of sparse self-attention with recurrence. While providing guarantees to avoid vanishing gradients, we use simple numerical experiments to demonstrate the tradeoffs in performance and computational resources by efficiently balancing attention and recurrence. Based on our results, we propose a concrete direction of research to improve scalability of attentive networks.

Invertible neural networks (INNs) have been used to design generative models, implement memory-saving gradient computation, and solve inverse problems. In this work, we show that commonly-used INN architectures suffer from exploding inverses and are thus prone to becoming numerically non-invertible. Across a wide range of INN use-cases, we reveal failures including the non-applicability of the change-of-variables formula on in- and out-of-distribution (OOD) data, incorrect gradients for memory-saving backprop, and the inability to sample from normalizing flow models. We further derive bi-Lipschitz properties of atomic building blocks of common architectures. These insights into the stability of INNs then provide ways forward to remedy these failures. For tasks where local invertibility is sufficient, like memory-saving backprop, we propose a flexible and efficient regularizer. For problems where global invertibility is necessary, such as applying normalizing flows on OOD data, we show the importance of designing stable INN building blocks.

Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a priori information within Gaussian process regression to supplement limited data and regularize the behavior of the model. We provide an overview and survey of several classes of Gaussian process constraints, including positivity or bound constraints, monotonicity and convexity constraints, differential equation constraints provided by linear PDEs, and boundary condition constraints. We compare the strategies behind each approach as well as the differences in implementation, concluding with a discussion of the computational challenges introduced by constraints.

Despite its success in a wide range of applications, characterizing the generalization properties of stochastic gradient descent (SGD) in non-convex deep learning problems is still an important challenge. While modeling the trajectories of SGD via stochastic differential equations (SDE) under heavy-tailed gradient noise has recently shed light over several peculiar characteristics of SGD, a rigorous treatment of the generalization properties of such SDEs in a learning theoretical framework is still missing. Aiming to bridge this gap, in this paper, we prove generalization bounds for SGD under the assumption that its trajectories can be well-approximated by a Feller process, which defines a rich class of Markov processes that include several recent SDE representations (both Brownian or heavy-tailed) as its special case. We show that the generalization error can be controlled by the Hausdorff dimension of the trajectories, which is intimately linked to the tail behavior of the driving process. Our results imply that heavier-tailed processes should achieve better generalization; hence, the tail-index of the process can be used as a notion of ``capacity metric''. We support our theory with experiments on deep neural networks illustrating that the proposed capacity metric accurately estimates the generalization error, and it does not necessarily grow with the number of parameters unlike the existing capacity metrics in the literature.