Related papers: A First Proof Sprint
Constrained optimization problems where both the objective and constraints may be nonsmooth and nonconvex arise across many learning and data science settings. In this paper, we show for any Lipschitz, weakly convex objectives and…
Estimating spectral gaps of quantum many-body Hamiltonians is a highly challenging computational task, even under assumptions of locality and translation-invariance. Yet, the quest for rigorous gap certificates is motivated by their broad…
We introduce ProofNet, a benchmark for autoformalization and formal proving of undergraduate-level mathematics. The ProofNet benchmarks consists of 371 examples, each consisting of a formal theorem statement in Lean 3, a natural language…
Prompt engineering is crucial for fully leveraging large language models (LLMs), yet most existing optimization methods follow a single trajectory, resulting in limited adaptability, gradient conflicts, and high computational overhead. We…
This paper considers optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network to lie in…
Network design problems have been studied from the 1950s, as they can be used in a wide range of real-world applications, e.g., design of communication and transportation networks. In classical network design problems, the objective is to…
In this work we provide algorithmic solutions to five fundamental problems concerning the verification, synthesis and correction of concurrent systems that can be modeled by bounded p/t-nets. We express concurrency via partial orders and…
Multiphase ranking functions ($\mathit{M{\Phi}RFs}$) were proposed as a means to prove the termination of a loop in which the computation progresses through a number of "phases", and the progress of each phase is described by a different…
With the increasing availability of parallel computing power, there is a growing focus on parallelizing algorithms for important automated reasoning problems such as Boolean satisfiability (SAT). Divide-and-Conquer (D&C) is a popular…
Multi-LLM revision pipelines, in which a second model reviews and improves a draft produced by a first, are widely assumed to derive their gains from genuine error correction. We question this assumption with a controlled decomposition…
We propose a methodology for verifying security properties of network protocols at design level. It can be separated in two main parts: context and requirements analysis and informal verification; and formal representation and procedural…
We formalize the problem of multi-agent path finding with deadlines (MAPF-DL). The objective is to maximize the number of agents that can reach their given goal vertices from their given start vertices within a given deadline, without…
We study auto research as a closed empirical loop driven by external measurement. Each submitted trial carries a hypothesis, an executable code edit, an evaluator-owned outcome, and feedback that shapes the next proposal. The output is not…
Linear Dynamical Systems, both discrete and continuous, are invaluable mathematical models in a plethora of applications such the verification of probabilistic systems, model checking, computational biology, cyber-physical systems, and…
We present a method for establishing invariant manifolds for saddle--center fixed points. The method is based on cone conditions, suitably formulated to allow for application in computer assisted proofs, and does not require rigorous…
Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…
This paper explores recent progress related to constraint maps. Building on the exposition in [14], our goal is to provide a clear and accessible account of some of the more intricate arguments behind the main results in this work. Along…
This report answers queries about extending the blinding index approach to a situation with measurements at multiple time points. The key question is how to test if there is progressive unblinding. A related question is how to apportion…
The software system under test can be modeled as a graph comprising of a set of vertices, (V) and a set of edges, (E). Test Cases are Test Paths over the graph meeting a particular test criterion. In this paper, we present a method to…
Agentic reinforcement learning (RL) holds great promise for the development of autonomous agents under complex GUI tasks, but its scalability remains severely hampered by the verification of task completion. Existing task verification is…