Related papers: Pushing the envelope of Optimization Modulo Theori…

Real continuous submodular functions, as a generalization of the corresponding discrete notion to the continuous domain, gained considerable attention recently. The analog notion for entropy functions requires additional properties: a real…

Large Language Models (LLMs) excel at various tasks, including problem-solving and question-answering. However, LLMs often find Math Word Problems (MWPs) challenging because solving them requires a range of reasoning and mathematical…

Solving optimization problems with parallel algorithms has a long tradition in OR. Its future relevance for solving hard optimization problems in many fields, including finance, logistics, production and design, is leveraged through the…

Large Language Models (LLMs) are demonstrating rapid improvements on complex reasoning benchmarks, particularly when allowed to utilize intermediate reasoning steps before converging on a final solution. However, current literature often…

We introduce a new approximate solution technique for first-order Markov decision processes (FOMDPs). Representing the value function linearly w.r.t. a set of first-order basis functions, we compute suitable weights by casting the…

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…

While policy-based reinforcement learning (RL) achieves tremendous successes in practice, it is significantly less understood in theory, especially compared with value-based RL. In particular, it remains elusive how to design a provably…

Multi-task learning (MTL) is a widely explored paradigm that enables the simultaneous learning of multiple tasks using a single model. Despite numerous solutions, the key issues of optimization conflict and task imbalance remain…

We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…

We propose a model-based procedure for automatically preventing security threats using formal models. We encode system models and potential threats as satisfiability modulo theory (SMT) formulas. This model allows us to ask security…

Optimization of LLM training and inference configurations, such as hyperparameters, data mixtures, and prompts, is critical to performance, but it is often approached heuristically in practice, leading to potentially suboptimal outcomes. By…

Large language models (LLMs) employ safety mechanisms to prevent harmful outputs, yet these defenses primarily rely on semantic pattern matching. We show that encoding harmful prompts as coherent mathematical problems -- using formalisms…

Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…

Compilers for statically typed functional programming languages are notorious for generating confusing type error messages. When the compiler detects a type error, it typically reports the program location where the type checking failed as…

We consider {\em profit-maximization} problems for {\em combinatorial auctions} with {\em non-single minded valuation functions} and {\em limited supply}. We obtain fairly general results that relate the approximability of the…

Ontology embeddings map classes, relations, and individuals in ontologies into $\mathbb{R}^n$, and within $\mathbb{R}^n$ similarity between entities can be computed or new axioms inferred. For ontologies in the Description Logic…

This work presents a novel algorithm for impulsive optimal control of linear time-varying systems with the inclusion of input magnitude constraints. Impulsive optimal control problems, where the optimal input solution is a sum of delta…

Recent research in areas such as SAT solving and Integer Linear Programming has shown that the performances of a single arbitrarily efficient solver can be significantly outperformed by a portfolio of possibly slower on-average solvers. We…

Prompt optimization (PO) provides a practical way to improve response quality when users lack the time or expertise to manually craft effective prompts. Existing methods typically rely on LLMs' self-generation ability to optimize prompts.…

Reliability and fault tolerance are critical attributes of embedded cyber-physical systems that require a high safety-integrity level. For such systems, the use of formal functional safety specifications has been strongly advocated in most…