Understanding the underlying mechanisms that enable the empirical successes of deep neural networks is essential for further improving their performance and explaining such networks. Towards this goal, a specific question is how to explain the "surprising" behavior of the same over-parametrized deep neural networks that can generalize well on real datasets and at the same time "memorize" training samples when the labels are randomized. In this paper, we demonstrate that deep ReLU networks generalize from training samples to new points via piece-wise linear interpolation. We provide a quantified analysis on the generalization ability of a deep ReLU network: Given a fixed point $\mathbf{x}$ and a fixed direction in the input space $\mathcal{S}$, there is always a segment such that any point on the segment will be classified the same as the fixed point $\mathbf{x}$. We call this segment the $generalization \ interval$. We show that the generalization intervals of a ReLU network behave similarly along pairwise directions between samples of the same label in both real and random cases on the MNIST and CIFAR-10 datasets. This result suggests that the same interpolation mechanism is used in both cases. Additionally, for datasets using real labels, such networks provide a good approximation of the underlying manifold in the data, where the changes are much smaller along tangent directions than along normal directions. On the other hand, however, for datasets with random labels, generalization intervals along mid-lines of triangles with the same label are much smaller than those on the datasets with real labels, suggesting different behaviors along other directions. Our systematic experiments demonstrate for the first time that such deep neural networks generalize through the same interpolation and explain the differences between their performance on datasets with real and random labels.

Event sequences can be modeled by temporal point processes (TPPs) to capture their asynchronous and probabilistic nature. We contribute an intensity-free framework that directly models the point process as a non-parametric distribution by utilizing normalizing flows. This approach is capable of capturing highly complex temporal distributions and does not rely on restrictive parametric forms. Comparisons with state-of-the-art baseline models on both synthetic and challenging real-life datasets show that the proposed framework is effective at modeling the stochasticity of discrete event sequences.

While deep learning has been incredibly successful in modeling tasks with large, carefully curated labeled datasets, its application to problems with limited labeled data remains a challenge. The aim of the present work is to improve the label efficiency of large neural networks operating on audio data through a combination of multitask learning and self-supervised learning on unlabeled data. We trained an end-to-end audio feature extractor based on WaveNet that feeds into simple, yet versatile task-specific neural networks. We describe several easily implemented self-supervised learning tasks that can operate on any large, unlabeled audio corpus. We demonstrate that, in scenarios with limited labeled training data, one can significantly improve the performance of three different supervised classification tasks individually by up to 6% through simultaneous training with these additional self-supervised tasks. We also show that incorporating data augmentation into our multitask setting leads to even further gains in performance.

The usability and practicality of any machine learning (ML) applications are largely influenced by two critical but hard-to-attain factors: low latency and low cost. Unfortunately, achieving low latency and low cost is very challenging when ML depends on real-world data that are highly distributed and rapidly growing (e.g., data collected by mobile phones and video cameras all over the world). Such real-world data pose many challenges in communication and computation. For example, when training data are distributed across data centers that span multiple continents, communication among data centers can easily overwhelm the limited wide-area network bandwidth, leading to prohibitively high latency and high cost. In this dissertation, we demonstrate that the latency and cost of ML on highly-distributed and rapidly-growing data can be improved by one to two orders of magnitude by designing ML systems that exploit the characteristics of ML algorithms, ML model structures, and ML training/serving data. We support this thesis statement with three contributions. First, we design a system that provides both low-latency and low-cost ML serving (inferencing) over large-scale and continuously-growing datasets, such as videos. Second, we build a system that makes ML training over geo-distributed datasets as fast as training within a single data center. Third, we present a first detailed study and a system-level solution on a fundamental and largely overlooked problem: ML training over non-IID (i.e., not independent and identically distributed) data partitions (e.g., facial images collected by cameras varies according to the demographics of each camera's location).

We propose a novel discrete-time dynamical system-based framework for achieving adversarial robustness in machine learning models. Our algorithm is originated from robust optimization, which aims to find the saddle point of a min-max optimization problem in the presence of uncertainties. The robust learning problem is formulated as a robust optimization problem, and we introduce a discrete-time algorithm based on a saddle-point dynamical system (SDS) to solve this problem. Under the assumptions that the cost function is convex and uncertainties enter concavely in the robust learning problem, we analytically show that using a diminishing step-size, the stochastic version of our algorithm, SSDS converges asymptotically to the robust optimal solution. The algorithm is deployed for the training of adversarially robust deep neural networks. Although such training involves highly non-convex non-concave robust optimization problems, empirical results show that the algorithm can achieve significant robustness for deep learning. We compare the performance of our SSDS model to other state-of-the-art robust models, e.g., trained using the projected gradient descent (PGD)-training approach. From the empirical results, we find that SSDS training is computationally inexpensive (compared to PGD-training) while achieving comparable performances. SSDS training also helps robust models to maintain a relatively high level of performance for clean data as well as under black-box attacks.

The Poisson equation is commonly encountered in engineering, including in computational fluid dynamics where it is needed to compute corrections to the pressure field. We propose a novel fully convolutional neural network (CNN) architecture to infer the solution of the Poisson equation on a 2D Cartesian grid of varying size and spacing given the right hand side term, arbitrary Dirichlet boundary conditions and grid parameters which provides unprecendented versatility in this application. The boundary conditions are handled using a novel approach by decomposing the original Poisson problem into a homogeneous Poisson problem plus four inhomogeneous Laplace sub-problems. The model is trained using a novel loss function approximating the continuous $L^p$ norm between the prediction and the target. Analytical test cases indicate that our CNN architecture is capable of predicting the correct solution of a Poisson problem with mean percentage errors of 15% and promises improvements in wall-clock runtimes for large problems. Furthermore, even when predicting on meshes denser than previously encountered, our model demonstrates encouraging capacity to reproduce the correct solution profile.

The field of high-energy physics (HEP), along with many scientific disciplines, is currently experiencing a dramatic influx of new methodologies powered by modern machine learning techniques. Over the last few years, a growing body of HEP literature has focused on identifying promising applications of deep learning in particular, and more recently these techniques are starting to be realized in an increasing number of experimental measurements. The overall conclusion from this impressive and extensive set of studies is that rarer and more complex physics signatures can be identified with the new set of powerful tools from deep learning. However, there is an unstudied systematic risk associated with combining the traditional HEP workflow and deep learning with high-dimensional data. In particular, calibrating and validating the response of deep neural networks is in general not experimentally feasible, and therefore current methods may be biased in ways that are not covered by current uncertainty estimates. By borrowing ideas from AI safety, we illustrate these potential issues and propose a method to bound the size of unaccounted for uncertainty. In addition to providing a pragmatic diagnostic, this work will hopefully begin a dialogue within the community about the robust application of deep learning to experimental analyses.

In this work, we investigate semi-supervised learning (SSL) for image classification using adversarial training. Previous results have illustrated that generative adversarial networks (GANs) can be used for multiple purposes. Triple-GAN, which aims to jointly optimize model components by incorporating three players, generates suitable image-label pairs to compensate for the lack of labeled data in SSL with improved benchmark performance. Conversely, Bad (or complementary) GAN, optimizes generation to produce complementary data-label pairs and force a classifier's decision boundary to lie between data manifolds. Although it generally outperforms Triple-GAN, Bad GAN is highly sensitive to the amount of labeled data used for training. Unifying these two approaches, we present unified-GAN (UGAN), a novel framework that enables a classifier to simultaneously learn from both good and bad samples through adversarial training. We perform extensive experiments on various datasets and demonstrate that UGAN: 1) achieves state-of-the-art performance among other deep generative models, and 2) is robust to variations in the amount of labeled data used for training.

The problem of attribution is concerned with identifying the parts of an input that are responsible for a model's output. An important family of attribution methods is based on measuring the effect of perturbations applied to the input. In this paper, we discuss some of the shortcomings of existing approaches to perturbation analysis and address them by introducing the concept of extremal perturbations, which are theoretically grounded and interpretable. We also introduce a number of technical innovations to compute extremal perturbations, including a new area constraint and a parametric family of smooth perturbations, which allow us to remove all tunable hyper-parameters from the optimization problem. We analyze the effect of perturbations as a function of their area, demonstrating excellent sensitivity to the spatial properties of the deep neural network under stimulation. We also extend perturbation analysis to the intermediate layers of a network. This application allows us to identify the salient channels necessary for classification, which, when visualized using feature inversion, can be used to elucidate model behavior. Lastly, we introduce TorchRay, an interpretability library built on PyTorch.

In many real-world deployments of machine learning systems, data arrive piecemeal. These learning scenarios may be passive, where data arrive incrementally due to structural properties of the problem (e.g., daily financial data) or active, where samples are selected according to a measure of their quality (e.g., experimental design). In both of these cases, we are building a sequence of models that incorporate an increasing amount of data. We would like each of these models in the sequence to be performant and take advantage of all the data that are available to that point. Conventional intuition suggests that when solving a sequence of related optimization problems of this form, it should be possible to initialize using the solution of the previous iterate---to "warm start" the optimization rather than initialize from scratch---and see reductions in wall-clock time. However, in practice this warm-starting seems to yield poorer generalization performance than models that have fresh random initializations, even though the final training losses are similar. While it appears that some hyperparameter settings allow a practitioner to close this generalization gap, they seem to only do so in regimes that damage the wall-clock gains of the warm start. Nevertheless, it is highly desirable to be able to warm-start neural network training, as it would dramatically reduce the resource usage associated with the construction of performant deep learning systems. In this work, we take a closer look at this empirical phenomenon and try to understand when and how it occurs. Although the present investigation did not lead to a solution, we hope that a thorough articulation of the problem will spur new research that may lead to improved methods that consume fewer resources during training.