Related papers: dxo: A System for Relational Algebra and Different…

We propose semiringKanren, a relational programming language where each relation expression denotes a semiring array. We formalize a type system that restricts the arrays to finite size. We then define a semantics that is parameterized by…

Deep Symbolic Optimization (DSO) is a novel computational framework that enables symbolic optimization for scientific discovery, particularly in applications involving the search for intricate symbolic structures. One notable example is…

We present {Kanren} (read: set-Kanren), an extension to miniKanren with constraints for reasoning about sets and association lists. {Kanren} includes first-class set objects, a functionally complete family of set-theoretic constraints…

This paper presents differential-algebraic refinement logic (dARL) with which one can deductively verify both properties and relations of differential-algebraic programs (DAPs) that extend hybrid dynamical systems with…

Existing research studies on cross-sentence relation extraction in long-form multi-party conversations aim to improve relation extraction without considering the explainability of such methods. This work addresses that gap by focusing on…

Parameter estimation for ordinary differential equations (ODEs) plays a fundamental role in the analysis of dynamical systems. Generally lacking closed-form solutions, ODEs are traditionally approximated using deterministic solvers.…

We introduce MIO, a transformer-based model for inferring symbolic ordinary differential equations (ODEs) from multiple observed trajectories of a dynamical system. By combining multiple instance learning with transformer-based symbolic…

The emergence of large-language models (LLMs) has enabled a new class of semantic data processing systems (SDPSs) to support declarative queries against unstructured documents. Existing SDPSs are, however, lacking a unified algebraic…

Different relaxation approximations to partial differential equations, including conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems, have been recently proposed. The present paper focuses onto…

We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted…

We are concerned with the arithmetic of solutions to ordinary or partial nonlinear differential equations which are algebraic in the indeterminates and their derivatives. We call these solutions D-algebraic functions, and their equations…

An algorithm for the symbolic computation of recursion operators for systems of nonlinear differential-difference equations (DDEs) is presented. Recursion operators allow one to generate an infinite sequence of generalized symmetries. The…

Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…

In this paper we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with radical dependencies in the unknown function and its derivatives into a system with polynomial…

Direct Preference Optimization (DPO) have emerged as a popular method for aligning Large Language Models (LLMs) with human preferences. While DPO effectively preserves the relative ordering between chosen and rejected responses through…

Direct preference optimization (DPO) methods have shown strong potential in aligning text-to-image diffusion models with human preferences by training on paired comparisons. These methods improve training stability by avoiding the REINFORCE…

The alignment of language models with human preferences is vital for their application in real-world tasks. The problem is formulated as optimizing the model's policy to maximize the expected reward that reflects human preferences with…

We introduce \textbf{Evo}, a duality latent trajectory model that bridges autoregressive (AR) and diffusion-based language generation within a continuous evolutionary generative framework. Rather than treating AR decoding and diffusion…

We address the problem of predicting the next state of a dynamical system governed by unknown temporal partial differential equations (PDEs) using only a short trajectory. While standard transformers provide a natural black-box solution to…

For optimization of a sum of functions in a distributed computing environment, we present a novel communication efficient Newton-type algorithm that enjoys a variety of advantages over similar existing methods. Similar to Newton-MR, our…