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We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation property of this type of networks, both methods extend the extreme learning machine (ELM) approach from low to high dimensions. With the first method the unknown solution field in $d$ dimensions is represented by a randomized feed-forward neural network, in which the hidden-layer parameters are randomly assigned and fixed while the output-layer parameters are trained. The PDE and the boundary/initial conditions, as well as the continuity conditions (for the local variant of the method), are enforced on a set of random interior/boundary collocation points. The resultant linear or nonlinear algebraic system, through its least squares solution, provides the trained values for the network parameters. With the second method the high-dimensional PDE problem is reformulated through a constrained expression based on an Approximate variant of the Theory of Functional Connections (A-TFC), which avoids the exponential growth in the number of terms of TFC as the dimension increases. The free field function in the A-TFC constrained expression is represented by a randomized neural network and is trained by a procedure analogous to the first method. We present ample numerical simulations for a number of high-dimensional linear/nonlinear stationary/dynamic PDEs to demonstrate their performance. These methods can produce accurate solutions to high-dimensional PDEs, in particular with their errors reaching levels not far from the machine accuracy for relatively lower dimensions. Compared with the physics-informed neural network (PINN) method, the current method is both cost-effective and more accurate for high-dimensional PDEs.

Until high-fidelity quantum computers with a large number of qubits become widely available, classical simulation remains a vital tool for algorithm design, tuning, and validation. We present a simulator for the Quantum Approximate Optimization Algorithm (QAOA). Our simulator is designed with the goal of reducing the computational cost of QAOA parameter optimization and supports both CPU and GPU execution. Our central observation is that the computational cost of both simulating the QAOA state and computing the QAOA objective to be optimized can be reduced by precomputing the diagonal Hamiltonian encoding the problem. We reduce the time for a typical QAOA parameter optimization by eleven times for $n = 26$ qubits compared to a state-of-the-art GPU quantum circuit simulator based on cuQuantum. Our simulator is available on GitHub: //github.com/jpmorganchase/QOKit

Performing a Bayesian inference on large spatio-temporal models requires extracting inverse elements of large sparse precision matrices for marginal variances. Although direct matrix factorizations can be used for the inversion, such methods fail to scale well for distributed problems when run on large computing clusters. On the contrary, Krylov subspace methods for the selected inversion have been gaining traction. We propose a parallel hybrid approach based on domain decomposition, which extends the Rao-Blackwellized Monte Carlo estimator for distributed precision matrices. Our approach exploits the strength of Krylov subspace methods as global solvers and efficiency of direct factorizations as base case solvers to compute the marginal variances using a divide-and-conquer strategy. By introducing subdomain overlaps, one can achieve a greater accuracy at an increased computational effort with little to no additional communication. We demonstrate the speed improvements on both simulated models and a massive US daily temperature data.

An idealized, though simplistic, view of the referring expression production and grounding process in (situated) dialogue assumes that a speaker must merely appropriately specify their expression so that the target referent may be successfully identified by the addressee. However, referring in conversation is a collaborative process that cannot be aptly characterized as an exchange of minimally-specified referring expressions. Concerns have been raised regarding assumptions made by prior work on visually-grounded dialogue that reveal an oversimplified view of conversation and the referential process. We address these concerns by introducing a collaborative image ranking task, a grounded agreement game we call "A Game Of Sorts". In our game, players are tasked with reaching agreement on how to rank a set of images given some sorting criterion through a largely unrestricted, role-symmetric dialogue. By putting emphasis on the argumentation in this mixed-initiative interaction, we collect discussions that involve the collaborative referential process. We describe results of a small-scale data collection experiment with the proposed task. All discussed materials, which includes the collected data, the codebase, and a containerized version of the application, are publicly available.

Bayesian probabilistic numerical methods for numerical integration offer significant advantages over their non-Bayesian counterparts: they can encode prior information about the integrand, and can quantify uncertainty over estimates of an integral. However, the most popular algorithm in this class, Bayesian quadrature, is based on Gaussian process models and is therefore associated with a high computational cost. To improve scalability, we propose an alternative approach based on Bayesian neural networks which we call Bayesian Stein networks. The key ingredients are a neural network architecture based on Stein operators, and an approximation of the Bayesian posterior based on the Laplace approximation. We show that this leads to orders of magnitude speed-ups on the popular Genz functions benchmark, and on challenging problems arising in the Bayesian analysis of dynamical systems, and the prediction of energy production for a large-scale wind farm.

Individual modules of programmable matter participate in their system's collective behavior by expending energy to perform actions. However, not all modules may have access to the external energy source powering the system, necessitating a local and distributed strategy for supplying energy to modules. In this work, we present a general energy distribution framework for the canonical amoebot model of programmable matter that transforms energy-agnostic algorithms into energy-constrained ones with equivalent behavior and an $\mathcal{O}(n^2)$-round runtime overhead -- even under an unfair adversary -- provided the original algorithms satisfy certain conventions. We then prove that existing amoebot algorithms for leader election (ICDCN 2023) and shape formation (Distributed Computing, 2023) are compatible with this framework and show simulations of their energy-constrained counterparts, demonstrating how other unfair algorithms can be generalized to the energy-constrained setting with relatively little effort. Finally, we show that our energy distribution framework can be composed with the concurrency control framework for amoebot algorithms (Distributed Computing, 2023), allowing algorithm designers to focus on the simpler energy-agnostic, sequential setting but gain the general applicability of energy-constrained, asynchronous correctness.

We propose a novel unsupervised object localization method that allows us to explain the predictions of the model by utilizing self-supervised pre-trained models without additional finetuning. Existing unsupervised and self-supervised object localization methods often utilize class-agnostic activation maps or self-similarity maps of a pre-trained model. Although these maps can offer valuable information for localization, their limited ability to explain how the model makes predictions remains challenging. In this paper, we propose a simple yet effective unsupervised object localization method based on representer point selection, where the predictions of the model can be represented as a linear combination of representer values of training points. By selecting representer points, which are the most important examples for the model predictions, our model can provide insights into how the model predicts the foreground object by providing relevant examples as well as their importance. Our method outperforms the state-of-the-art unsupervised and self-supervised object localization methods on various datasets with significant margins and even outperforms recent weakly supervised and few-shot methods.

Variational inference, such as the mean-field (MF) approximation, requires certain conjugacy structures for efficient computation. These can impose unnecessary restrictions on the viable prior distribution family and further constraints on the variational approximation family. In this work, we introduce a general computational framework to implement MF variational inference for Bayesian models, with or without latent variables, using the Wasserstein gradient flow (WGF), a modern mathematical technique for realizing a gradient flow over the space of probability measures. Theoretically, we analyze the algorithmic convergence of the proposed approaches, providing an explicit expression for the contraction factor. We also strengthen existing results on MF variational posterior concentration from a polynomial to an exponential contraction, by utilizing the fixed point equation of the time-discretized WGF. Computationally, we propose a new constraint-free function approximation method using neural networks to numerically realize our algorithm. This method is shown to be more precise and efficient than traditional particle approximation methods based on Langevin dynamics.

The accurate and interpretable prediction of future events in time-series data often requires the capturing of representative patterns (or referred to as states) underpinning the observed data. To this end, most existing studies focus on the representation and recognition of states, but ignore the changing transitional relations among them. In this paper, we present evolutionary state graph, a dynamic graph structure designed to systematically represent the evolving relations (edges) among states (nodes) along time. We conduct analysis on the dynamic graphs constructed from the time-series data and show that changes on the graph structures (e.g., edges connecting certain state nodes) can inform the occurrences of events (i.e., time-series fluctuation). Inspired by this, we propose a novel graph neural network model, Evolutionary State Graph Network (EvoNet), to encode the evolutionary state graph for accurate and interpretable time-series event prediction. Specifically, Evolutionary State Graph Network models both the node-level (state-to-state) and graph-level (segment-to-segment) propagation, and captures the node-graph (state-to-segment) interactions over time. Experimental results based on five real-world datasets show that our approach not only achieves clear improvements compared with 11 baselines, but also provides more insights towards explaining the results of event predictions.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.