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An active topic in the study of random constraint satisfaction problems (CSPs) is the geometry of the space of satisfying or almost satisfying assignments as the function of the density, for which a precise landscape of predictions has been…
Satisfiability modulo theories (SMT) is a core tool in formal verification. While the SMT-LIB specification language can be used to interact with theorem proving software, a high-level interface allows for faster and easier specifications…
Many intellectual endeavors require mathematical problem solving, but this skill remains beyond the capabilities of computers. To measure this ability in machine learning models, we introduce MATH, a new dataset of 12,500 challenging…
Satisfiability Modulo Theories (SMT) solvers check the satisfiability of quantifier-free first-order logic formulas. We consider the theory of non-linear real arithmetic where the formulae are logical combinations of polynomial constraints.…
Traditional ML models utilize controlled approximations during high loads, employing faster, but less accurate models in a process called accuracy scaling. However, this method is less effective for generative text-to-image models due to…
The evaluation of mathematical reasoning capabilities is essential for advancing Artificial General Intelligence (AGI). While Large Language Models (LLMs) have shown impressive performance in solving mathematical problems, existing…
Constraint answer set programming integrates answer set programming with constraint processing. System EZSMT+ is a constraint answer set programming tool that utilizes satisfiability modulo theory solvers for search. Its theoretical…
Inference-time scaling has recently emerged as a powerful paradigm for improving the reasoning capability of large language models. Among various approaches, Sequential Monte Carlo (SMC) has become a particularly important framework,…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by…
Existing math datasets evaluate the reasoning abilities of large language models (LLMs) by either using the final answer or the intermediate reasoning steps derived from static examples. However, the former approach fails to surface model's…
In this paper, we present long-awaited algorithmic advances toward the efficient construction of near-optimal replenishment policies for a true inventory management classic, the economic warehouse lot scheduling problem. While this paradigm…
Stochastic approximation techniques play an important role in solving many problems encountered in machine learning or adaptive signal processing. In these contexts, the statistics of the data are often unknown a priori or their direct…
In this paper, we study stochastic submodular maximization problems with general matroid constraints, that naturally arise in online learning, team formation, facility location, influence maximization, active learning and sensing objective…
Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…
We present a Bounded Model Checking technique for higher-order programs. The vehicle of our study is a higher-order calculus with general references. Our technique is a symbolic state syntactical translation based on SMT solvers, adapted to…
Quantitative model checkers for Markov Decision Processes typically use finite-precision arithmetic. If all the coefficients in the process are rational numbers, then the model checking results are rational, and so they can be computed…
Automated Theorem Proving (ATP) represents a core research direction in artificial intelligence for achieving formal reasoning and verification, playing a significant role in advancing machine intelligence. However, current large language…
This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum…
Modern software for propositional satisfiability problems gives a powerful automated reasoning toolkit, capable of outputting not only a satisfiable/unsatisfiable signal but also a justification of unsatisfiability in the form of resolution…