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Computing demands for large scientific experiments, such as the CMS experiment at the CERN LHC, will increase dramatically in the next decades. To complement the future performance increases of software running on central processing units (CPUs), explorations of coprocessor usage in data processing hold great potential and interest. Coprocessors are a class of computer processors that supplement CPUs, often improving the execution of certain functions due to architectural design choices. We explore the approach of Services for Optimized Network Inference on Coprocessors (SONIC) and study the deployment of this as-a-service approach in large-scale data processing. In the studies, we take a data processing workflow of the CMS experiment and run the main workflow on CPUs, while offloading several machine learning (ML) inference tasks onto either remote or local coprocessors, specifically graphics processing units (GPUs). With experiments performed at Google Cloud, the Purdue Tier-2 computing center, and combinations of the two, we demonstrate the acceleration of these ML algorithms individually on coprocessors and the corresponding throughput improvement for the entire workflow. This approach can be easily generalized to different types of coprocessors and deployed on local CPUs without decreasing the throughput performance. We emphasize that the SONIC approach enables high coprocessor usage and enables the portability to run workflows on different types of coprocessors.

Knowing which countries contribute the most to pushing the boundaries of knowledge in science and technology has social and political importance. However, common citation metrics do not adequately measure this contribution. This measure requires more stringent metrics appropriate for the highly influential breakthrough papers that push the boundaries of knowledge, which are very highly cited but very rare. Here I used the recently described Rk index, specifically designed to address this issue. I applied this index to 25 countries and the EU across 10 key research topics, five technological and five biomedical, studying domestic and international collaborative papers independently. In technological topics, the Rk indices of domestic papers show that overall, the USA, China, and the EU are leaders; other countries are clearly behind. The USA is notably ahead of China, and the EU is far behind China. The same approach to biomedical topics shows an overwhelming dominance of the USA and that the EU is ahead of China. The analysis of internationally collaborative papers further demonstrates the US dominance. These results conflict with current country rankings based on less stringent indicators.

In this paper, we develop a new type of Runge--Kutta (RK) discontinuous Galerkin (DG) method for solving hyperbolic conservation laws. Compared with the original RKDG method, the new method features improved compactness and allows simple boundary treatment. The key idea is to hybridize two different spatial operators in an explicit RK scheme, utilizing local projected derivatives for inner RK stages and the usual DG spatial discretization for the final stage only. Limiters are applied only at the final stage for the control of spurious oscillations. We also explore the connections between our method and Lax--Wendroff DG schemes and ADER-DG schemes. Numerical examples are given to confirm that the new RKDG method is as accurate as the original RKDG method, while being more compact, for problems including two-dimensional Euler equations for compressible gas dynamics.

We propose a novel algorithm for the support estimation of partially known Gaussian graphical models that incorporates prior information about the underlying graph. In contrast to classical approaches that provide a point estimate based on a maximum likelihood or a maximum a posteriori criterion using (simple) priors on the precision matrix, we consider a prior on the graph and rely on annealed Langevin diffusion to generate samples from the posterior distribution. Since the Langevin sampler requires access to the score function of the underlying graph prior, we use graph neural networks to effectively estimate the score from a graph dataset (either available beforehand or generated from a known distribution). Numerical experiments demonstrate the benefits of our approach.

The purpose of this paper is to look into how central notions in statistical learning theory, such as realisability, generalise under the assumption that train and test distribution are issued from the same credal set, i.e., a convex set of probability distributions. This can be considered as a first step towards a more general treatment of statistical learning under epistemic uncertainty.

Optimal solutions of combinatorial optimization problems can be sensitive to changes in the cost of one or more elements. Single and set tolerances measure the largest / smallest possible change such that the current solution remains optimal and other solutions become non-optimal for cost changes in one or more elements, respectively. The current definition only applies to subsets of elements. In this paper, we broaden the definition to all elements, for single tolerances, and to all subsets of elements for set tolerances, while proving that key computational and theoretical properties still apply to the new definitions.

We propose a simple empirical representation of expectations such that: For a number of samples above a certain threshold, drawn from any probability distribution with finite fourth-order statistic, the proposed estimator outperforms the empirical average when tested against the actual population, with respect to the quadratic loss. For datasets smaller than this threshold, the result still holds, but for a class of distributions determined by their first four statistics. Our approach leverages the duality between distributionally robust and risk-averse optimization.

We propose a novel methodology to solve a key eigenvalue optimization problem which arises in the contractivity analysis of neural ODEs. When looking at contractivity properties of a one layer weight-tied neural ODE $\dot{u}(t)=\sigma(Au(t)+b)$ (with $u,b \in {\mathbb R}^n$, $A$ is a given $n \times n$ matrix, $\sigma : {\mathbb R} \to {\mathbb R}^+$ denotes an activation function and for a vector $z \in {\mathbb R}^n$, $\sigma(z) \in {\mathbb R}^n$ has to be interpreted entry-wise), we are led to study the logarithmic norm of a set of products of type $D A$, where $D$ is a diagonal matrix such that ${\mathrm{diag}}(D) \in \sigma'({\mathbb R}^n)$. Specifically, given a real number $c$ (usually $c=0$), the problem consists in finding the largest positive interval $\chi\subseteq \mathbb [0,\infty)$ such that the logarithmic norm $\mu(DA) \le c$ for all diagonal matrices $D$ with $D_{ii}\in \chi$. We propose a two-level nested methodology: an inner level where, for a given $\chi$, we compute an optimizer $D^\star(\chi)$ by a gradient system approach, and an outer level where we tune $\chi$ so that the value $c$ is reached by $\mu(D^\star(\chi)A)$. We extend the proposed two-level approach to the general multilayer, and possibly time-dependent, case $\dot{u}(t) = \sigma( A_k(t) \ldots \sigma ( A_{1}(t) u(t) + b_{1}(t) ) \ldots + b_{k}(t) )$ and we propose several numerical examples to illustrate its behaviour, including its stabilizing performance on a one-layer neural ODE applied to the classification of the MNIST handwritten digits dataset.

In this paper we develop a novel neural network model for predicting implied volatility surface. Prior financial domain knowledge is taken into account. A new activation function that incorporates volatility smile is proposed, which is used for the hidden nodes that process the underlying asset price. In addition, financial conditions, such as the absence of arbitrage, the boundaries and the asymptotic slope, are embedded into the loss function. This is one of the very first studies which discuss a methodological framework that incorporates prior financial domain knowledge into neural network architecture design and model training. The proposed model outperforms the benchmarked models with the option data on the S&P 500 index over 20 years. More importantly, the domain knowledge is satisfied empirically, showing the model is consistent with the existing financial theories and conditions related to implied volatility surface.

This paper does not describe a working system. Instead, it presents a single idea about representation which allows advances made by several different groups to be combined into an imaginary system called GLOM. The advances include transformers, neural fields, contrastive representation learning, distillation and capsules. GLOM answers the question: How can a neural network with a fixed architecture parse an image into a part-whole hierarchy which has a different structure for each image? The idea is simply to use islands of identical vectors to represent the nodes in the parse tree. If GLOM can be made to work, it should significantly improve the interpretability of the representations produced by transformer-like systems when applied to vision or language