Related papers: A Deductive Refinement Calculus for Differential-A…

Recent advances in large language models (LLMs) have shown that reasoning ability can be significantly enhanced through Reinforcement Learning with Verifiable Rewards (RLVR). Group Relative Policy Optimization (GRPO) has emerged as the de…

The versatile Arbitrary-DERivative (ADER) scheme is cast in a multilevel framework (ML-ADER) for fast solution of system of linear hyperbolic partial differential equations. The solution is cycled through spatial operators of varying…

We introduce a novel integrability-preserving discretization for a broad class of differential equations with variable coefficients, encompassing both linear and nonlinear cases. The construction is achieved via a categorical approach that…

We present a unifying framework for designing and analysing distributional reinforcement learning (DRL) algorithms in terms of recursively estimating statistics of the return distribution. Our key insight is that DRL algorithms can be…

Logic-based approaches to AI have the advantage that their behavior can in principle be explained to a user. If, for instance, a Description Logic reasoner derives a consequence that triggers some action of the overall system, then one can…

How to improve discriminative feature learning is central in classification. Existing works address this problem by explicitly increasing inter-class separability and intra-class similarity, whether by constructing positive and negative…

Adaptive optimization methods have been widely used in deep learning. They scale the learning rates adaptively according to the past gradient, which has been shown to be effective to accelerate the convergence. However, they suffer from…

The Dynamic Logic for Propositional Assignments (DL-PA) has recently been studied as an alternative to Propositional Dynamic Logic (PDL). In DL-PA, the abstract atomic programs of PDL are replaced by assignments of propositional variables…

We introduce a new setting, the category of $\omega$PAP spaces, for reasoning denotationally about expressive differentiable and probabilistic programming languages. Our semantics is general enough to assign meanings to most practical…

We develop the representation theory for reductive linear differential algebraic groups (LDAGs). In particular, we exhibit an explicit sharp upper bound for orders of derivatives in differential representations of reductive LDAGs, extending…

Evaluating retrieval-augmented generation (RAG) presents challenges, particularly for retrieval models within these systems. Traditional end-to-end evaluation methods are computationally expensive. Furthermore, evaluation of the retrieval…

Self-play with large language models has emerged as a promising paradigm for achieving self-improving artificial intelligence. However, existing self-play frameworks often suffer from optimization instability, due to (i) non-stationary…

In the field of quality assurance of hybrid systems (that combine continuous physical dynamics and discrete digital control), Platzer's differential dynamic logic (dL) is widely recognized as a deductive verification method with solid…

Modular, distributed and multi-core architectures are currently considered a promising approach for scalability of quantum computing systems. The integration of multiple Quantum Processing Units necessitates classical and quantum-coherent…

Refinement calculus is a powerful and expressive tool for reasoning about sequential programs in a compositional manner. In this paper we present an extension of refinement calculus for reactive systems. Refinement calculus is based on…

Real world systems of interest often feature interactions between discrete and continuous dynamics. Various hybrid system formalisms have been used to model and analyze this combination of dynamics, ranging from mathematical descriptions,…

Large Language Models (LLMs) have transformed listwise document reranking by enabling global reasoning over candidate sets, yet single models often struggle to balance fine-grained relevance scoring with holistic cross-document analysis. We…

This paper presents an approach for deductive liveness verification for ordinary differential equations (ODEs) with differential dynamic logic. Numerous subtleties complicate the generalization of well-known discrete liveness verification…

Automated Program Repair (APR) is essential for ensuring software reliability and quality while enhancing efficiency and reducing developers' workload. Although rule-based and learning-based APR methods have demonstrated their…

We perform detailed computations of Lie algebras of infinitesimal CR-automorphisms associated to three specific model real analytic CR-generic submanifolds in C^9 by employing differential algebra computer tools -- mostly within the Maple…