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Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting finite-sum structure, which generically arises in empirical variants of learning problems in these contexts. Further, methods with computable approximation errors are highly desirable, as they provide verifiable exit criteria. Motivated by these applications, we study finite-sum monotone inclusion problems, which model broad classes of equilibrium problems. Our main contributions are variants of the classical Halpern iteration that employ variance reduction to obtain improved complexity guarantees in which $n$ component operators in the finite sum are ``on average'' either cocoercive or Lipschitz continuous and monotone, with parameter $L$. The resulting oracle complexity of our methods, which provide guarantees for the last iterate and for a (computable) operator norm residual, is $\widetilde{\mathcal{O}}( n + \sqrt{n}L\varepsilon^{-1})$, which improves upon existing methods by a factor up to $\sqrt{n}$. This constitutes the first variance reduction-type result for general finite-sum monotone inclusions and for more specific problems such as convex-concave optimization when operator norm residual is the optimality measure. We further argue that, up to poly-logarithmic factors, this complexity is unimprovable in the monotone Lipschitz setting; i.e., the provided result is near-optimal.

Counterfactual explanations play an important role in detecting bias and improving the explainability of data-driven classification models. A counterfactual explanation (CE) is a minimal perturbed data point for which the decision of the model changes. Most of the existing methods can only provide one CE, which may not be achievable for the user. In this work we derive an iterative method to calculate robust CEs, i.e. CEs that remain valid even after the features are slightly perturbed. To this end, our method provides a whole region of CEs allowing the user to choose a suitable recourse to obtain a desired outcome. We use algorithmic ideas from robust optimization and prove convergence results for the most common machine learning methods including logistic regression, decision trees, random forests, and neural networks. Our experiments show that our method can efficiently generate globally optimal robust CEs for a variety of common data sets and classification models.

Obtaining the solutions of partial differential equations based on various machine learning methods has drawn more and more attention in the fields of scientific computation and engineering applications. In this work, we first propose a coupled Extreme Learning Machine (called CELM) method incorporated with the physical laws to solve a class of fourth-order biharmonic equations by reformulating it into two well-posed Poisson problems. In addition, some activation functions including tangent, gauss, sine, and trigonometric (sin+cos) functions are introduced to assess our CELM method. Notably, the sine and trigonometric functions demonstrate a remarkable ability to effectively minimize the approximation error of the CELM model. In the end, several numerical experiments are performed to study the initializing approaches for both the weights and biases of the hidden units in our CELM model and explore the required number of hidden units. Numerical results show the proposed CELM algorithm is high-precision and efficient to address the biharmonic equation in both regular and irregular domains.

Providing personalized assistance at scale is a long-standing challenge for computing educators, but a new generation of tools powered by large language models (LLMs) offers immense promise. Such tools can, in theory, provide on-demand help in large class settings and be configured with appropriate guardrails to prevent misuse and mitigate common concerns around learner over-reliance. However, the deployment of LLM-powered tools in authentic classroom settings is still rare, and very little is currently known about how students will use them in practice and what type of help they will seek. To address this, we examine students' use of an innovative LLM-powered tool that provides on-demand programming assistance without revealing solutions directly. We deployed the tool for 12 weeks in an introductory computer and data science course ($n = 52$), collecting more than 2,500 queries submitted by students throughout the term. We manually categorized all student queries based on the type of assistance sought, and we automatically analyzed several additional query characteristics. We found that most queries requested immediate help with programming assignments, whereas fewer requests asked for help on related concepts or for deepening conceptual understanding. Furthermore, students often provided minimal information to the tool, suggesting this is an area in which targeted instruction would be beneficial. We also found that students who achieved more success in the course tended to have used the tool more frequently overall. Lessons from this research can be leveraged by programming educators and institutions who plan to augment their teaching with emerging LLM-powered tools.

Shared autonomy methods, where a human operator and a robot arm work together, have enabled robots to complete a range of complex and highly variable tasks. Existing work primarily focuses on one human sharing autonomy with a single robot. By contrast, in this paper we present an approach for multi-robot shared autonomy that enables one operator to provide real-time corrections across two coordinated robots completing the same task in parallel. Sharing autonomy with multiple robots presents fundamental challenges. The human can only correct one robot at a time, and without coordination, the human may be left idle for long periods of time. Accordingly, we develop an approach that aligns the robot's learned motions to best utilize the human's expertise. Our key idea is to leverage Learning from Demonstration (LfD) and time warping to schedule the motions of the robots based on when they may require assistance. Our method uses variability in operator demonstrations to identify the types of corrections an operator might apply during shared autonomy, leverages flexibility in how quickly the task was performed in demonstrations to aid in scheduling, and iteratively estimates the likelihood of when corrections may be needed to ensure that only one robot is completing an action requiring assistance. Through a preliminary study, we show that our method can decrease the scheduled time spent sanding by iteratively estimating the times when each robot could need assistance and generating an optimized schedule that allows the operator to provide corrections to each robot during these times.

Robustness in machine learning is commonly studied in the adversarial setting, yet real-world noise (such as measurement noise) is random rather than adversarial. Model behavior under such noise is captured by average-case robustness, i.e., the probability of obtaining consistent predictions in a local region around an input. However, the na\"ive approach to computing average-case robustness based on Monte-Carlo sampling is statistically inefficient, especially for high-dimensional data, leading to prohibitive computational costs for large-scale applications. In this work, we develop the first analytical estimators to efficiently compute average-case robustness of multi-class discriminative models. These estimators linearize models in the local region around an input and analytically compute the robustness of the resulting linear models. We show empirically that these estimators efficiently compute the robustness of standard deep learning models and demonstrate these estimators' usefulness for various tasks involving robustness, such as measuring robustness bias and identifying dataset samples that are vulnerable to noise perturbation. In doing so, this work not only proposes a new framework for robustness, but also makes its computation practical, enabling the use of average-case robustness in downstream applications.

Robots performing human-scale manipulation tasks require an extensive amount of knowledge about their surroundings in order to perform their actions competently and human-like. In this work, we investigate the use of virtual reality technology as an implementation for robot environment modeling, and present a technique for translating scene graphs into knowledge bases. To this end, we take advantage of the Universal Scene Description (USD) format which is an emerging standard for the authoring, visualization and simulation of complex environments. We investigate the conversion of USD-based environment models into Knowledge Graph (KG) representations that facilitate semantic querying and integration with additional knowledge sources.

In reliable decision-making systems based on machine learning, models have to be robust to distributional shifts or provide the uncertainty of their predictions. In node-level problems of graph learning, distributional shifts can be especially complex since the samples are interdependent. To evaluate the performance of graph models, it is important to test them on diverse and meaningful distributional shifts. However, most graph benchmarks considering distributional shifts for node-level problems focus mainly on node features, while structural properties are also essential for graph problems. In this work, we propose a general approach for inducing diverse distributional shifts based on graph structure. We use this approach to create data splits according to several structural node properties: popularity, locality, and density. In our experiments, we thoroughly evaluate the proposed distributional shifts and show that they can be quite challenging for existing graph models. We also reveal that simple models often outperform more sophisticated methods on the considered structural shifts. Finally, our experiments provide evidence that there is a trade-off between the quality of learned representations for the base classification task under structural distributional shift and the ability to separate the nodes from different distributions using these representations.

Ising machines are a form of quantum-inspired processing-in-memory computer which has shown great promise for overcoming the limitations of traditional computing paradigms while operating at a fraction of the energy use. The process of designing Ising machines is known as the reverse Ising problem. Unfortunately, this problem is in general computationally intractable: it is a nonconvex mixed-integer linear programming problem which cannot be naively brute-forced except in the simplest cases due to exponential scaling of runtime with number of spins. We prove new theoretical results which allow us to reduce the search space to one with quadratic scaling. We utilize this theory to develop general purpose algorithmic solutions to the reverse Ising problem. In particular, we demonstrate Ising formulations of 3-bit and 4-bit integer multiplication which use fewer total spins than previously known methods by a factor of more than three. Our results increase the practicality of implementing such circuits on modern Ising hardware, where spins are at a premium.

Data-driven models for nonlinear dynamical systems based on approximating the underlying Koopman operator or generator have proven to be successful tools for forecasting, feature learning, state estimation, and control. It has become well known that the Koopman generators for control-affine systems also have affine dependence on the input, leading to convenient finite-dimensional bilinear approximations of the dynamics. Yet there are still two main obstacles that limit the scope of current approaches for approximating the Koopman generators of systems with actuation. First, the performance of existing methods depends heavily on the choice of basis functions over which the Koopman generator is to be approximated; and there is currently no universal way to choose them for systems that are not measure preserving. Secondly, if we do not observe the full state, then it becomes necessary to account for the dependence of the output time series on the sequence of supplied inputs when constructing observables to approximate Koopman operators. To address these issues, we write the dynamics of observables governed by the Koopman generator as a bilinear hidden Markov model, and determine the model parameters using the expectation-maximization (EM) algorithm. The E-step involves a standard Kalman filter and smoother, while the M-step resembles control-affine dynamic mode decomposition for the generator. We demonstrate the performance of this method on three examples, including recovery of a finite-dimensional Koopman-invariant subspace for an actuated system with a slow manifold; estimation of Koopman eigenfunctions for the unforced Duffing equation; and model-predictive control of a fluidic pinball system based only on noisy observations of lift and drag.