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As machine learning is increasingly used in essential systems, it is important to reduce or eliminate the incidence of serious bugs. A growing body of research has developed machine learning algorithms with formal guarantees about…

Answering questions within business and finance requires reasoning, precision, and a wide-breadth of technical knowledge. Together, these requirements make this domain difficult for large language models (LLMs). We introduce BizBench, a…

Reinforcement learning (RL) is a classical tool to solve network control or policy optimization problems in unknown environments. The original Q-learning suffers from performance and complexity challenges across very large networks. Herein,…

As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent…

We use valid inequalities (cuts) of the binary integer program for winner determination in a combinatorial auction (CA) as "artificial items" that can be interpreted intuitively and priced to generate Artificial Walrasian Equilibria. We…

Mathematical reasoning is a hallmark of human intelligence, and whether large language models (LLMs) can meaningfully perform it remains a central question in artificial intelligence and cognitive science. As LLMs are increasingly…

Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…

Quantum computing offers a promising avenue for advancing computational methods in science and engineering. In this work, we introduce the quantum asymptotic numerical method (qANM), a framework for solving nonlinear problems using quantum…

Large language models are now integrated into many scientific workflows, accelerating data analysis, hypothesis generation, and design space exploration. In parallel with this growth, there is a growing need to carefully evaluate whether…

In this paper, we propose a framework based on the Retrospective Approximation (RA) paradigm to solve optimization problems with a stochastic objective function and general nonlinear deterministic constraints. This framework sequentially…

Issue resolution, a complex Software Engineering (SWE) task integral to real-world development, has emerged as a compelling challenge for artificial intelligence. The establishment of benchmarks like SWE-bench revealed this task as…

In this paper we propose a set of guidelines to select a solver for the solution of nonlinear programming problems. With this in mind, we present a comparison of the convergence performances of commonly used solvers for both unconstrained…

We consider the Quantifier Elimination (QE) problem for propositional CNF formulas with existential quantifiers. QE plays a key role in formal verification. Earlier, we presented an approach based on the following observation. To perform…

In this paper, a class of general nonlinear programming problems with inequality and equality constraints is discussed. Firstly, the original problem is transformed into an associated simpler equivalent problem with only inequality…

We introduce a large-scale dataset of math word problems and an interpretable neural math problem solver that learns to map problems to operation programs. Due to annotation challenges, current datasets in this domain have been either…

Quantum Kernels are projected to provide early-stage usefulness for quantum machine learning. However, highly sophisticated classical models are hard to surpass without losing interpretability, particularly when vast datasets can be…

The well-known Turing machine is an example of a theoretical digital computer, and it was the logical basis of constructing real electronic computers. In the present paper we propose an alternative, namely, by formalising arithmetic…

Benchmarking and establishing proper statistical validation metrics for reinforcement learning (RL) remain ongoing challenges, where no consensus has been established yet. The emergence of quantum computing and its potential applications in…

We consider a specific type of nonlinear partial differential equations (PDE) that appear in mathematical finance as the result of solving some optimization problems. We review some existing in the literature examples of such problems, and…

We consider state of the art applications of artificial intelligence (AI) in modelling human financial expectations and explore the potential of quantum logic to drive future advancements in this field. This analysis highlights the…