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This work focuses on developing methods for approximating the solution operators of a class of parametric partial differential equations via neural operators. Neural operators have several challenges, including the issue of generating appropriate training data, cost-accuracy trade-offs, and nontrivial hyperparameter tuning. The unpredictability of the accuracy of neural operators impacts their applications in downstream problems of inference, optimization, and control. A framework based on the linear variational problem that gives the correction to the prediction furnished by neural operators is considered based on earlier work in JCP 486 (2023) 112104. The operator, called Residual-based Error Corrector Operator or simply Corrector Operator, associated with the corrector problem is analyzed further. Numerical results involving a nonlinear reaction-diffusion model in two dimensions with PCANet-type neural operators show almost two orders of increase in the accuracy of approximations when neural operators are corrected using the correction scheme. Further, topology optimization involving a nonlinear reaction-diffusion model is considered to highlight the limitations of neural operators and the efficacy of the correction scheme. Optimizers with neural operator surrogates are seen to make significant errors (as high as 80 percent). However, the errors are much lower (below 7 percent) when neural operators are corrected.

We propose an efficient semi-Lagrangian characteristic mapping method for solving the one+one-dimensional Vlasov-Poisson equations with high precision on a coarse grid. The flow map is evolved numerically and exponential resolution in linear time is obtained. Global third-order convergence in space and time is shown and conservation properties are assessed. For benchmarking, we consider linear and nonlinear Landau damping and the two-stream instability. We compare the results with a Fourier pseudo-spectral method. The extreme fine-scale resolution features are illustrated showing the method's capabilities to efficiently treat filamentation in fusion plasma simulations.

We revisit the problem of efficiently learning the underlying parameters of Ising models from data. Current algorithmic approaches achieve essentially optimal sample complexity when given i.i.d. samples from the stationary measure and the underlying model satisfies "width" bounds on the total $\ell_1$ interaction involving each node. We show that a simple existing approach based on node-wise logistic regression provably succeeds at recovering the underlying model in several new settings where these assumptions are violated: (1) Given dynamically generated data from a wide variety of local Markov chains, like block or round-robin dynamics, logistic regression recovers the parameters with optimal sample complexity up to $\log\log n$ factors. This generalizes the specialized algorithm of Bresler, Gamarnik, and Shah [IEEE Trans. Inf. Theory'18] for structure recovery in bounded degree graphs from Glauber dynamics. (2) For the Sherrington-Kirkpatrick model of spin glasses, given $\mathsf{poly}(n)$ independent samples, logistic regression recovers the parameters in most of the known high-temperature regime via a simple reduction to weaker structural properties of the measure. This improves on recent work of Anari, Jain, Koehler, Pham, and Vuong [ArXiv'23] which gives distribution learning at higher temperature. (3) As a simple byproduct of our techniques, logistic regression achieves an exponential improvement in learning from samples in the M-regime of data considered by Dutt, Lokhov, Vuffray, and Misra [ICML'21] as well as novel guarantees for learning from the adversarial Glauber dynamics of Chin, Moitra, Mossel, and Sandon [ArXiv'23]. Our approach thus significantly generalizes the elegant analysis of Wu, Sanghavi, and Dimakis [Neurips'19] without any algorithmic modification.

While large language models (LLMs) already achieve strong performance on standard generic summarization benchmarks, their performance on more complex summarization task settings is less studied. Therefore, we benchmark LLMs on instruction controllable text summarization, where the model input consists of both a source article and a natural language requirement for the desired summary characteristics. To this end, we curate an evaluation-only dataset for this task setting and conduct human evaluation on 5 LLM-based summarization systems. We then benchmark LLM-based automatic evaluation for this task with 4 different evaluation protocols and 11 LLMs, resulting in 40 evaluation methods in total. Our study reveals that instruction controllable text summarization remains a challenging task for LLMs, since (1) all LLMs evaluated still make factual and other types of errors in their summaries; (2) all LLM-based evaluation methods cannot achieve a strong alignment with human annotators when judging the quality of candidate summaries; (3) different LLMs show large performance gaps in summary generation and evaluation. We make our collected benchmark, InstruSum, publicly available to facilitate future research in this direction.

By composing graphical models with deep learning architectures, we learn generative models with the strengths of both frameworks. The structured variational autoencoder (SVAE) inherits structure and interpretability from graphical models, and flexible likelihoods for high-dimensional data from deep learning, but poses substantial optimization challenges. We propose novel algorithms for learning SVAEs, and are the first to demonstrate the SVAE's ability to handle multimodal uncertainty when data is missing by incorporating discrete latent variables. Our memory-efficient implicit differentiation scheme makes the SVAE tractable to learn via gradient descent, while demonstrating robustness to incomplete optimization. To more rapidly learn accurate graphical model parameters, we derive a method for computing natural gradients without manual derivations, which avoids biases found in prior work. These optimization innovations enable the first comparisons of the SVAE to state-of-the-art time series models, where the SVAE performs competitively while learning interpretable and structured discrete data representations.

Phase transitions, characterized by abrupt shifts between macroscopic patterns of organization, are ubiquitous in complex systems. Despite considerable research in the physical and natural sciences, the empirical study of this phenomenon in societal systems is relatively underdeveloped. The goal of this study is to explore whether the dynamics of collective civil unrest can be plausibly characterized as a sequence of recurrent phase shifts, with each phase having measurable and identifiable latent characteristics. Building on previous efforts to characterize civil unrest as a self-organized critical system, we introduce a macro-level statistical model of civil unrest and evaluate its plausibility using a comprehensive dataset of civil unrest events in 170 countries from 1946 to 2017. Our findings demonstrate that the macro-level phase model effectively captures the characteristics of civil unrest data from diverse countries globally and that universal mechanisms may underlie certain aspects of the dynamics of civil unrest. We also introduce a scale to quantify a country's long-term unrest per unit of time and show that civil unrest events tend to cluster geographically, with the magnitude of civil unrest concentrated in specific regions. Our approach has the potential to identify and measure phase transitions in various collective human phenomena beyond civil unrest, contributing to a better understanding of complex social systems.

A mixture of multivariate Poisson-log normal factor analyzers is introduced by imposing constraints on the covariance matrix, which resulted in flexible models for clustering purposes. In particular, a class of eight parsimonious mixture models based on the mixtures of factor analyzers model are introduced. Variational Gaussian approximation is used for parameter estimation, and information criteria are used for model selection. The proposed models are explored in the context of clustering discrete data arising from RNA sequencing studies. Using real and simulated data, the models are shown to give favourable clustering performance. The GitHub R package for this work is available at //github.com/anjalisilva/mixMPLNFA and is released under the open-source MIT license.

The problem of optimizing discrete phases in a reconfigurable intelligent surface (RIS) to maximize the received power at a user equipment is addressed. Necessary and sufficient conditions to achieve this maximization are given. These conditions are employed in an algorithm to achieve the maximization. New versions of the algorithm are given that are proven to achieve convergence in N or fewer steps whether the direct link is completely blocked or not, where N is the number of the RIS elements, whereas previously published results achieve this in KN or 2N number of steps where K is the number of discrete phases, e.g., [1], [2]. Thus, for a discrete-phase RIS, the techniques presented in this paper achieve the optimum received power in the smallest number of steps published in the literature. In addition, in each of those N steps, the techniques presented in this paper determine only one or a small number of phase shifts with a simple elementwise update rule, which result in a substantial reduction of computation time, as compared to the algorithms in the literature, e.g., [2], [3].

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.

We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.