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Large Language Models (LLMs) increasingly rely on reinforcement learning with verifiable rewards (RLVR) to elicit reliable chain-of-thought reasoning. However, the training process remains bottlenecked by the computationally expensive…

Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability…

Boosting is a learning scheme that combines weak prediction rules to produce a strong composite estimator, with the underlying intuition that one can obtain accurate prediction rules by combining "rough" ones. Although boosting is proved to…

We describe an algorithm that takes as input a complex sequence $(u_n)$ given by a linear recurrence relation with polynomial coefficients along with initial values, and outputs a simple explicit upper bound $(v_n)$ such that $|u_n| \leq…

We study realizable continual linear regression under random task orderings, a common setting for developing continual learning theory. In this setup, the worst-case expected loss after $k$ learning iterations admits a lower bound of…

This paper presents a novel robust trajectory optimization method for constrained nonlinear dynamical systems subject to unknown bounded disturbances. In particular, we seek optimal control policies that remain robustly feasible with…

Looping, reusing a block of layers across depth, and depth growing, training shallow-to-deep models by duplicating middle layers, have both been linked to stronger reasoning, but their relationship remains unclear. We provide a mechanistic…

A cutting-plane model for a nonsmooth function is the maximum of several first-order expansions centered at different points. Using such a model in a bundle method leads to linear convergence (of serious steps) to a minimum. In smooth…

In current Large Language Models we can trust the production of smoothly flowing prose on the basis of the principles of machine learning. However, there is no comparably principled basis to justify trust in the content of the text…

Parallel dataflow systems are a central part of most analytic pipelines for big data. The iterative nature of many analysis and machine learning algorithms, however, is still a challenge for current systems. While certain types of bulk…

Test-time scaling has emerged as an effective way to improve language models on challenging reasoning tasks. However, most existing methods treat each problem in isolation and do not systematically reuse knowledge from prior reasoning…

The calibration and training of a neural network is a complex and time-consuming procedure that requires significant computational resources to achieve satisfactory results. Key obstacles are a large number of hyperparameters to select and…

Deep neural networks provide unprecedented performance gains in many real world problems in signal and image processing. Despite these gains, future development and practical deployment of deep networks is hindered by their blackbox nature,…

The usability of Reinforcement Learning is restricted by the large computation times it requires. Curriculum Reinforcement Learning speeds up learning by defining a helpful order in which an agent encounters tasks, i.e. from simple to hard.…

Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…

We introduce an efficient combination of polyhedral analysis and predicate partitioning. Template polyhedral analysis abstracts numerical variables inside a program by one polyhedron per control location, with a priori fixed directions for…

Deep unfolded neural networks are designed by unrolling the iterations of optimization algorithms. They can be shown to achieve faster convergence and higher accuracy than their optimization counterparts. This paper proposes a new…

We consider the speed planning problem for a robotic manipulator. In particular, we present an algorithm for finding the time-optimal speed law along an assigned path that satisfies velocity and acceleration constraints and respects the…

In this paper, we study three applications of recursion to problems in coding and random permutations. First, we consider locally recoverable codes with partial locality and use recursion to estimate the minimum distance of such codes. Next…

We consider the problem of reinforcement learning when provided with (1) a baseline control policy and (2) a set of constraints that the learner must satisfy. The baseline policy can arise from demonstration data or a teacher agent and may…