Related papers: A Deductive Refinement Calculus for Differential-A…
This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and…
Agentic Reinforcement Learning (ARL) trains large language models to interleave reasoning with external tool execution to solve complex tasks. Most existing ARL methods train a single set of parameters to support both reasoning and tool-use…
Particle Flow Filters estimate the ``a posteriori" probability density function (PDF) by moving an ensemble of particles according to the likelihood. Particles are propagated under the system dynamics until a measurement becomes available…
The purpose of this article is to develop an algebraic approach to the problem of integrable classification of differential-difference equations with one continuous and two discrete variables. As a classification criterion, we put forward…
Reinforcement Learning with Verifiable Rewards (RLVR) has demonstrated promising gains in enhancing the reasoning capabilities of large language models. However, its dependence on domain-specific verifiers significantly restricts its…
Differential-algebraic equations (DAEs) are widely used for modeling of dynamical systems. In numerical analysis of DAEs, consistent initialization and index reduction are important preprocessing prior to numerical integration. Existing DAE…
The Dirac quantization `procedure' for constrained systems is well known to have many subtleties and ambiguities. Within this ill-defined framework, we explore the generality of a particular interpretation of the Dirac procedure known as…
Programs written in dynamic languages make heavy use of features --- run-time type tests, value-indexed dictionaries, polymorphism, and higher-order functions --- that are beyond the reach of type systems that employ either purely syntactic…
Large Language Models (LLMs) have shown remarkable reasoning capabilities, while their practical applications are limited by severe factual hallucinations due to limitations in the timeliness, accuracy, and comprehensiveness of their…
Relational verification encompasses information flow security, regression verification, translation validation for compilers, and more. Effective alignment of the programs and computations to be related facilitates use of simpler relational…
Recent work has shown logical background knowledge can be used in learning systems to compensate for a lack of labeled training data. Many methods work by creating a loss function that encodes this knowledge. However, often the logic is…
Deep reinforcement learning (DRL) has recently emerged as a promising approach to solve combinatorial optimization problems such as job shop scheduling. However, the policies learned by DRL are typically represented by deep neural networks…
Recent advancements in Large Language Models (LLMs) have significantly improved their performance across various Natural Language Processing (NLP) tasks. However, LLMs still struggle with generating non-factual responses due to limitations…
Crafting effective reward signals remains a central challenge in Reinforcement Learning (RL), especially for complex reasoning tasks. Existing automated reward optimization methods typically rely on derivative-free search heuristics that…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…
Discovering causal structure among a set of variables is a fundamental problem in many empirical sciences. Traditional score-based casual discovery methods rely on various local heuristics to search for a Directed Acyclic Graph (DAG)…
Solving mathematical problems requires advanced reasoning abilities and presents notable challenges for large language models. Previous works usually synthesize data from proprietary models to augment existing datasets, followed by…
Assessing the reasoning ability of Large Language Models (LLMs) over data remains an open and pressing research question. Compared with LLMs, human reasoning can derive corresponding modifications to the output based on certain kinds of…
Programmatic reinforcement learning (PRL) offers an interpretable alternative to deep reinforcement learning by representing policies as human-readable and -editable programs. While gradient-based methods have been developed to optimize…
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…