Related papers: The Liouville Generator for Producing Integrable E…

A positive integer is expressed as a sum of squares of positive integers in a unique way applying a special technique. The expression, thus obtained is resolved into two factors using the concept of the Clifford algebra. This technique is…

Generative design is an increasingly important tool in the industrial world. It allows the designers and engineers to easily explore vast ranges of design options, providing a cheaper and faster alternative to the trial and failure…

Evaluating Retrieval-Augmented Generation (RAG) systems remains a challenging task: existing metrics often collapse heterogeneous behaviors into single scores and provide little insight into whether errors arise from retrieval,reasoning, or…

The generators and commutation relations are calculated explicitly for higher symmetry algebras of a class of hyperbolic Euler-Lagrange systems of Liouville type (in particular, for 2D Toda chains associated with semi-simple complex Lie…

Large Language Models (LLMs) have been successful in mathematical reasoning tasks such as formal theorem proving when integrated with interactive proof assistants like Lean. Existing approaches involve training or fine-tuning an LLM on a…

Add to each level of binary tree edges to make the induced graph on the level a uniform expander. It is shown that such a graph admits no non-constant bounded harmonic functions.

Querying tables with unstructured data is challenging due to the presence of text (or image), either embedded in the table or in external paragraphs, which traditional SQL struggles to process, especially for tasks requiring semantic…

We develop a geometric framework for the numerical integration of mechanical systems evolving on manifolds. After briefly reviewing classical numerical methods and highlighting their limitations and shortcomings in non-flat (non-Euclidean)…

Identifiability, or recovery of the true latent representations from which the observed data originates, is de facto a fundamental goal of representation learning. Yet, most deep generative models do not address the question of…

Image compression methods are usually optimized isolatedly for human perception or machine analysis tasks. We reveal fundamental commonalities between these objectives: preserving accurate semantic information is paramount, as it directly…

We study the design and implementation of numerical methods to solve the generalized Langevin equation (GLE) focusing on canonical sampling properties of numerical integrators. For this purpose, we cast the GLE in an extended phase space…

Learning to sample from complex unnormalized distributions is a fundamental challenge in computational physics and machine learning. While score-based and variational methods have achieved success in continuous domains, extending them to…

Generative approaches have been recently shown to be effective for both Entity Disambiguation and Entity Linking (i.e., joint mention detection and disambiguation). However, the previously proposed autoregressive formulation for EL suffers…

It is expected that progress toward true artificial intelligence will be achieved through the emergence of a system that integrates representation learning and complex reasoning (LeCun et al. 2015). In response to this prediction, research…

A line of work in planning uses LLM not to generate a plan, but to generate a formal representation in some planning language, which can be input into a symbolic solver to deterministically find a plan. While showing improved trust and…

In the past few years, there has been an explosive surge in the use of machine learning (ML) techniques to address combinatorial optimization (CO) problems, especially mixed-integer linear programs (MILPs). Despite the achievements, the…

Variational integrators are derived for structure-preserving simulation of stochastic forced Hamiltonian systems. The derivation is based on a stochastic discrete Hamiltonian which approximates a type-II stochastic generating function for…

This paper presents the mechanization of a process algebra for Mobile Ad hoc Networks and Wireless Mesh Networks, and the development of a compositional framework for proving invariant properties. Mechanizing the core process algebra in…

It is known, due to Mordukhai-Boltovski, Ritt, Prelle, Singer, Christopher and others, that if a given rational ODE has a Liouvillian first integral then the corresponding integrating factor of the ODE must be of a very special form of a…

Prevalent retrieval-based tool-use pipelines struggle with a dual semantic challenge: their retrievers often employ encoders that fail to capture complex semantics, while the Large Language Model (LLM) itself lacks intrinsic tool knowledge…