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Reinforcement learning (RL) promises a framework for near-universal problem-solving. In practice however, RL algorithms are often tailored to specific benchmarks, relying on carefully tuned hyperparameters and algorithmic choices. Recently,…

We explore contemporary, data-driven techniques for solving math word problems over recent large-scale datasets. We show that well-tuned neural equation classifiers can outperform more sophisticated models such as sequence to sequence and…

Large Language Models (LLMs) have achieved remarkable performance across a wide range of mathematical benchmarks. However, concerns remain as to whether these successes reflect genuine reasoning or superficial pattern recognition. Existing…

Quantum speed-ups for dynamical simulation usually demand unitary time-evolution, whereas the large ODE/PDE systems encountered in realistic physical models are generically non-unitary. We present a universal moment-fulfilling dilation that…

The distributed subgradient method (DSG) is a widely discussed algorithm to cope with large-scale distributed optimization problems in the arising machine learning applications. Most exisiting works on DSG focus on ideal communication…

This work develops a multiscale solution decomposition (MSD) method for nonlocal-in-time problems to separate a series of known terms with multiscale singularity from the original singular solution such that the remaining unknown part…

For typical first-order logical theories, satisfying assignments have a straightforward finite representation that can directly serve as a certificate that a given assignment satisfies the given formula. For non-linear real arithmetic…

We offer a consistent dynamical formulation of stationary scattering in two and three dimensions that is based on a suitable multidimensional generalization of the transfer matrix. This is a linear operator acting in an infinite-dimensional…

In this paper, we consider the dual fractional parabolic problem in the right half space. We prove that the positive solutions are strictly increasing in $x_1$ direction without assuming the solutions be bounded. So far as we know, this is…

Many safety-critical systems must achieve high-level task specifications with guaranteed safety and correctness. Much recent progress towards this goal has been made through controller synthesis from signal temporal logic (STL)…

We propose and study a novel stochastic inertial primal-dual approach to solve composite optimization problems. These latter problems arise naturally when learning with penalized regularization schemes. Our analysis provide convergence…

We design a new algorithm for solving parametric systems having finitely many complex solutions for generic values of the parameters. More precisely, let $f = (f_1, \ldots, f_m)\subset \mathbb{Q}[y][x]$ with $y = (y_1, \ldots, y_t)$ and $x…

In this study, a new $\Delta$-evaluation method is introduced for solving a column permutation problem defined on a sparse binary matrix with the consecutive ones property. This problem models various $\mathcal{NP}$-hard problems in graph…

While prior work established a verifier-based polynomial-time framework for NP, explicit deterministic machines for concrete NP-complete problems have remained elusive. In this paper, we construct fully specified deterministic Turing…

In this two-part work, we propose an algorithmic framework for solving non-convex problems whose objective function is the sum of a number of smooth component functions plus a convex (possibly non-smooth) or/and smooth (possibly non-convex)…

Models pre-trained on large-scale datasets are often fine-tuned to support newer tasks and datasets that arrive over time. This process necessitates storing copies of the model over time for each task that the pre-trained model is…

We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…

We consider the problem of deciding the satisfiability of quantifier-free formulas in the theory of finite sets with cardinality constraints. Sets are a common high-level data structure used in programming; thus, such a theory is useful for…

This paper introduces the notion of upper-linearizable/quadratizable functions, a class that extends concavity and DR-submodularity in various settings, including monotone and non-monotone cases over different convex sets. A general…

Data assisted reconstruction algorithms, incorporating trained neural networks, are a novel paradigm for solving inverse problems. One approach is to first apply a classical reconstruction method and then apply a neural network to improve…