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Trajectory optimization is the core of modern model-based robotic control and motion planning. Existing trajectory optimizers, based on sequential quadratic programming (SQP) or differential dynamic programming (DDP), are often limited by…
A method is proposed for solving equality constrained nonlinear optimization problems involving twice continuously differentiable functions. The method employs a trust funnel approach consisting of two phases: a first phase to locate an…
Tau leaping is a popular method for performing fast approximate simulation of certain continuous time Markov chain models typically found in chemistry and biochemistry. This method is known to perform well when the transition rates satisfy…
We introduce a new approach to the the asymptotic iteration method (AIM) by means of which we establish the standard AIM connection with the continued fractions technique and we develop a novel termination condition in terms of the…
We present StepFun-Prover Preview, a large language model designed for formal theorem proving through tool-integrated reasoning. Using a reinforcement learning pipeline that incorporates tool-based interactions, StepFun-Prover can achieve…
Formal verification of neural networks (NNs) is a challenging and important problem. Existing efficient complete solvers typically require the branch-and-bound (BaB) process, which splits the problem domain into sub-domains and solves each…
Mathematical proofs are both paradigms of certainty and some of the most explicitly-justified arguments that we have in the cultural record. Their very explicitness, however, leads to a paradox, because the probability of error grows…
Methods to efficiently determine the relative stability of polymorphs of organic crystals are highly desired in crystal structure predictions (CSPs). Current methodologies include use of static lattice phonons, quasi-harmonic approximation…
The demand for synthetic data in mathematical reasoning has increased due to its potential to enhance the mathematical capabilities of large language models (LLMs). However, ensuring the validity of intermediate reasoning steps remains a…
Automated Theorem Proving (ATP) in formal languages remains a formidable challenge in AI, demanding rigorous logical deduction and navigating vast search spaces. While large language models (LLMs) have shown promising performance, existing…
We propose a Projected Proximal Point Algorithm (ProPPA) for solving a class of optimization problems. The algorithm iteratively computes the proximal point of the last estimated solution projected into an affine space which itself is…
In theorem proving, the task of selecting useful premises from a large library to unlock the proof of a given conjecture is crucially important. This presents a challenge for all theorem provers, especially the ones based on language…
In the field of numerical approximation, specialists considering highly complex problems have recently proposed various ways to simplify their underlying problems. In this field, depending on the problem they were tackling and the community…
The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical…
Loop under-approximation is a technique that enriches C programs with additional branches that represent the effect of a (limited) range of loop iterations. While this technique can speed up the detection of bugs significantly, it…
LLM developers are increasingly reliant on synthetic data, but generating high-quality data for complex long-context reasoning tasks remains challenging. We introduce CLIPPER, a compression-based approach for generating synthetic data…
The provably asymptotically fastest algorithm within a factor of 5 for formally described problems will be constructed. The main idea is to enumerate all programs provably equivalent to the original problem by enumerating all proofs. The…
We present a low-scaling algorithm for the random phase approximation (RPA) with \textbf{k}-point sampling in the framework of tensor hypercontraction (THC) for electron repulsion integrals (ERIs). The THC factorization is obtained via a…
We study the problem of Trajectory Optimization (TO) for a general class of stiff and constrained dynamic systems. We establish a set of mild assumptions, under which we show that TO converges numerically stably to a locally optimal and…
Existing self-evolution methods overlook the influence of fine-grained reasoning steps, which leads to the reasoner-verifier gap. The computational inefficiency of Monte Carlo (MC) process supervision further exacerbates the difficulty in…