Related papers: Accelerating Certifiable Estimation with Precondit…

Uncertainty calibration is essential for the safe deployment of large language models (LLMs), particularly when users rely on verbalized confidence estimates. While prior work has focused on classifiers or short-form generation, confidence…

This paper deals with the algorithmic aspects of solving feasibility problems of semidefinite programming (SDP), aka linear matrix inequalities (LMI). Since in some SDP instances all feasible solutions have irrational entries, numerical…

We consider the problem of minimizing a polynomial $f$ over the binary hypercube. We show that, for a specific set of polynomials, their binary non-negativity can be checked in a polynomial time via minimum cut algorithms, and we construct…

We present a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few linear measurements. In contrast to state of the art…

By extending the classical analysis techniques due to Samokish, Faddeev and Faddeeva, and Longsine and McCormick among others, we prove the convergence of preconditioned steepest descent with implicit deflation (PSD-id) method for solving…

It is well known that reformulating the original problem can be crucial for the performance of mixed-integer programming (MIP) solvers. To ensure correctness, all transformations must preserve the fea sibility status and optimal value of…

Estimating the predictive uncertainty of a Bayesian learning model is critical in various decision-making problems, e.g., reinforcement learning, detecting adversarial attack, self-driving car. As the model posterior is almost always…

Atomic norm methods have recently been proposed for spectral super-resolution with flexibility in dealing with missing data and miscellaneous noises. A notorious drawback of these convex optimization methods however is their lower…

In model-based reinforcement learning for safety-critical control systems, it is important to formally certify system properties (e.g., safety, stability) under the learned controller. However, as existing methods typically apply formal…

Chance-constrained programs (CCP) represent a trade-off between conservatism and robustness in optimization. In many CCPs, one optimizes an objective under a probabilistic constraint continuously parameterized by a random vector $\xi$. In…

We present a highly efficient proximal Markov chain Monte Carlo methodology to perform Bayesian computation in imaging problems. Similarly to previous proximal Monte Carlo approaches, the proposed method is derived from an approximation of…

Answer verification is crucial not only for evaluating large language models (LLMs) by matching their unstructured outputs against standard answers, but also serves as the reward model to guide LLM optimization. Most evaluation frameworks…

In this work, we propose a preconditioned augmented Lagrangian method (ALM) for solving semidefinite programming (SDP) problems. The preconditioner is implemented via a weighted penalty function in the ALM subproblem, with the weight matrix…

With the emergence of cloud computing services, computationally weak devices (Clients) can delegate expensive tasks to more powerful entities (Servers). This raises the question of verifying a result at a lower cost than that of recomputing…

Large Language Models (LLMs) show promise for automated grading, but their outputs can be unreliable. Rather than improving grading accuracy directly, we address a complementary problem: \textit{predicting when an LLM grader is likely to be…

We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…

Real-world robotics applications demand object pose estimation methods that work reliably across a variety of scenarios. Modern learning-based approaches require large labeled datasets and tend to perform poorly outside the training domain.…

Estimating the absolute orientation of a local system relative to a global navigation satellite system (GNSS) reference often suffers from local minima and high dependency on satellite availability. Existing methods for this alignment task…

Formal verification of neural networks (NNs) is a challenging and important problem. Existing efficient complete solvers typically require the branch-and-bound (BaB) process, which splits the problem domain into sub-domains and solves each…

In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…