However, it is notoriously di fficult to solve in practice, because IPMs memory requirements scale at a demanding rate. Indeed, state-of-the-art SDO solvers such as MOSEK cannot solve constrained instances of Problem (1) with n 250 variables on a standard laptop, and it is optimization folklore that there is a gap between SDOs theoretical and practical tractability. Motivated by the demanding memory requirements of IPMs, a stream of literature studies inexact methods for SDOs, which replace the semidefinite constraint with weaker yet less computationally demanding constraints. This approach was first investigated by Kim and Kojima [13], who observed that relaxing a positive semidefinite constraint to the weaker constraint that all 2 2 minors of a matrix are positive semidefinite yields a second order cone (SOC)-representable outer approximation of the positive semidefinite (PSD) cone. In a related line of work, Krishnan and Mitchell [15] propose applying Kelley [12]'s cutting plane method to generate

Generating point clouds, e.g., molecular structures, in arbitrary rotations, translations, and enumerations remains a challenging task. Meanwhile, neural networks utilizing symmetry invariant layers have been shown to be able to optimize their training objective in a data-efficient way. In this spirit, we present an architecture which allows to produce valid Euclidean distance matrices, which by construction are already invariant under rotation and translation of the described object. Motivated by the goal to generate molecular structures in Cartesian space, we use this architecture to construct a Wasserstein GAN utilizing a permutation invariant critic network. This makes it possible to generate molecular structures in a one-shot fashion by producing Euclidean distance matrices which have a three-dimensional embedding.

Advances in deep neural network (DNN) based molecular property prediction have recently led to the development of models of remarkable accuracy and generalization ability, with graph convolution neural networks (GCNNs) reporting state-of-the-art performance for this task. However, some challenges remain and one of the most important that needs to be fully addressed concerns uncertainty quantification. DNN performance is affected by the volume and the quality of the training samples. Therefore, establishing when and to what extent a prediction can be considered reliable is just as important as outputting accurate predictions, especially when out-of-domain molecules are targeted. Recently, several methods to account for uncertainty in DNNs have been proposed, most of which are based on approximate Bayesian inference. Among these, only a few scale to the large datasets required in applications. Evaluating and comparing these methods has recently attracted great interest, but results are generally fragmented and absent for molecular property prediction. In this paper, we aim to quantitatively compare scalable techniques for uncertainty estimation in GCNNs. We introduce a set of quantitative criteria to capture different uncertainty aspects, and then use these criteria to compare MC-Dropout, deep ensembles, and bootstrapping, both theoretically in a unified framework that separates aleatoric/epistemic uncertainty and experimentally on the QM9 dataset. Our experiments quantify the performance of the different uncertainty estimation methods and their impact on uncertainty-related error reduction. Our findings indicate that ensembling and bootstrapping consistently outperform MC-Dropout, with different context-specific pros and cons. Our analysis also leads to a better understanding of the role of aleatoric/epistemic uncertainty and highlights the challenge posed by out-of-domain uncertainty.

A BSTRACT Designing energy-efficient networks is of critical importance for enabling state-of-the-art deep learning in mobile and edge settings where the computation and energy budgets are highly limited. Recently, Liu et al. (2019b) framed the search of efficient neural architectures into a continuous splitting process: it iteratively splits existing neurons into multiple offsprings to achieve progressive loss minimization, thus finding novel architectures by gradually growing the neural network. However, this method was not specifically tailored for designing energy-efficient networks, and is computationally expensive on large-scale benchmarks. In this work, we substantially improve Liu et al. (2019b) in two significant ways: 1) we incorporate the energy cost of splitting different neurons to better guide the splitting process, thereby discovering more energy-efficient network architectures; 2) we substantially speed up the splitting process of Liu et al. (2019b), which requires expensive eigen-decomposition, by proposing a highly scalable Rayleigh-quotient stochastic gradient algorithm. Our fast algorithm allows us to reduce the computational cost of splitting to the same level of typical back-propagation updates and enables efficient implementation on GPU. Extensive empirical results show that our method can train highly accurate and energy-efficient networks on challenging datasets such as ImageNet, improving a variety of baselines, including the pruning-based methods and expert-designed architectures. 1 I NTRODUCTION Deep neural networks (DNNs) have demonstrated remarkable performance in solving various challenge problems such as image classification (e.g. Simonyan & Zisserman, 2015; He et al., 2016; Huang et al., 2017), object detection (e.g. Although large-scale deep networks have good empirical performance, their large sizes cause slow computation and high energy cost in the inference phase.

Celiac Disease (CD) is a chronic autoimmune disease that affects the small intestine in genetically predisposed children and adults. Gluten exposure triggers an inflammatory cascade which leads to compromised intestinal barrier function. If this enteropathy is unrecognized, this can lead to anemia, decreased bone density, and, in longstanding cases, intestinal cancer. The prevalence of the disorder is 1% in the United States. An intestinal (duodenal) biopsy is considered the "gold standard" for diagnosis. The mild CD might go unnoticed due to non-specific clinical symptoms or mild histologic features. In our current work, we trained a model based on deep residual networks to diagnose CD severity using a histological scoring system called the modified Marsh score. The proposed model was evaluated using an independent set of 120 whole slide images from 15 CD patients and achieved an AUC greater than 0.96 in all classes. These results demonstrate the diagnostic power of the proposed model for CD severity classification using histological images.

With the rising interest in graph representation learning, a variety of approaches have been proposed to effectively capture a graph's properties. While these approaches have improved performance in graph machine learning tasks compared to traditional graph techniques, they are still perceived as techniques with limited insight into the information encoded in these representations. In this work, we explore methods to interpret node embeddings and propose the creation of a robust evaluation framework for comparing graph representation learning algorithms and hyperparameters. We test our methods on graphs with different properties and investigate the relationship between embedding training parameters and the ability of the produced embedding to recover the structure of the original graph in a downstream task.

Towards the challenging problem of semi-supervised node classification, there have been extensive studies. As a frontier, Graph Neural Networks (GNNs) have aroused great interest recently, which update the representation of each node by aggregating information of its neighbors. However, most GNNs have shallow layers with a limited receptive field and may not achieve satisfactory performance especially when the number of labeled nodes is quite small. To address this challenge, we innovatively propose a graph few-shot learning (GFL) algorithm that incorporates prior knowledge learned from auxiliary graphs to improve classification accuracy on the target graph. Specifically, a transferable metric space characterized by a node embedding and a graph-specific prototype embedding function is shared between auxiliary graphs and the target, facilitating the transfer of structural knowledge. Extensive experiments and ablation studies on four real-world graph datasets demonstrate the effectiveness of our proposed model.

Optimal control of stochastic nonlinear dynamical systems is a major challenge in the domain of robot learning. Given the intractability of the global control problem, state-of-the-art algorithms focus on approximate sequential optimization techniques, that heavily rely on heuristics for regularization in order to achieve stable convergence. By building upon the duality between inference and control, we develop the view of Optimal Control as Input Estimation, devising a probabilistic stochastic optimal control formulation that iteratively infers the optimal input distributions by minimizing an upper bound of the control cost. Inference is performed through Expectation Maximization and message passing on a probabilistic graphical model of the dynamical system, and time-varying linear Gaussian feedback controllers are extracted from the joint state-action distribution. This perspective incorporates uncertainty quantification, effective initialization through priors, and the principled regularization inherent to the Bayesian treatment. Moreover, it can be shown that for deterministic linearized systems, our framework derives the maximum entropy linear quadratic optimal control law. We provide a complete and detailed derivation of our probabilistic approach and highlight its advantages in comparison to other deterministic and probabilistic solvers.

Decision support tools that rely on supervised learning require large amounts of expert annotations. Using past radiological reports obtained from hospital archiving systems has many advantages as training data above manual single-class labels: they are expert annotations available in large quantities, covering a population-representative variety of pathologies, and they provide additional context to pathology diagnoses, such as anatomical location and severity. Learning to auto-generate such reports from images present many challenges such as the difficulty in representing and generating long, unstructured textual information, accounting for spelling errors and repetition/redundancy, and the inconsistency across different annotators. We therefore propose to first learn visually-informative medical concepts from raw reports, and, using the concept predictions as image annotations, learn to auto-generate structured reports directly from images. We validate our approach on the OpenI [2] chest x-ray dataset, which consists of frontal and lateral views of chest x-ray images, their corresponding raw textual reports and manual medical subject heading (MeSH ) annotations made by radiologists.

The skip-connections used in residual networks have become a standard architecture choice in deep learning due to the increased training stability and generalization performance with this architecture, although there has been limited theoretical understanding for this improvement. In this work, we analyze overparameterized deep residual networks trained by gradient descent following random initialization, and demonstrate that (i) the class of networks learned by gradient descent constitutes a small subset of the entire neural network function class, and (ii) this subclass of networks is sufficiently large to guarantee small training error. By showing (i) we are able to demonstrate that deep residual networks trained with gradient descent have a small generalization gap between training and test error, and together with (ii) this guarantees that the test error will be small. Our optimization and generalization guarantees require overparameterization that is only logarithmic in the depth of the network, while all known generalization bounds for deep non-residual networks have overparameterization requirements that are at least polynomial in the depth. This provides an explanation for why residual networks are preferable to non-residual ones.