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Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This…

The Refinement Calculus of Reactive Systems (RCRS) is a compositional formal framework for modeling and reasoning about reactive systems. RCRS provides a language which allows to describe atomic components as symbolic transition systems or…

The automation of scientific research through large language models (LLMs) presents significant opportunities but faces critical challenges in knowledge synthesis and quality assurance. We introduce Feedback-Refined Agent Methodology…

The Augmented Lagrangian Method (ALM) is an iterative method for the solution of equality-constrained non-linear programming problems. In contrast to the quadratic penalty method, the ALM can satisfy equality constraints in an exact way.…

We present $\textbf{Research Math Agents (RMA)}$, an agentic framework for automated reasoning on research-level mathematical problems. Unlike prior studies centered on competition mathematics or formal theorem proving, RMA targets…

In the research on computational effects, defined algebraically, effect symbols are often expected to obey certain equations. If we orient these equations, we get a rewrite system, which may be an effective way of transforming or optimizing…

The affine rank minimization (ARM) problem arises in many real-world applications. The goal is to recover a low-rank matrix from a small amount of noisy affine measurements. The original problem is NP-hard, and so directly solving the…

We apply program verification technology to the problem of specifying and verifying automatic differentiation (AD) algorithms. We focus on define-by-run, a style of AD where the program that must be differentiated is executed and monitored…

The escalating scale of Large Language Models (LLMs) necessitates efficient adaptation techniques. Model merging has gained prominence for its efficiency and controllability. However, existing merging techniques typically serve as post-hoc…

Recently, improving the relevance and diversity of dialogue system has attracted wide attention. For a post x, the corresponding response y is usually diverse in the real-world corpus, while the conventional encoder-decoder model tends to…

This paper introduces and studies a new model of computation called an Alternating Automatic Register Machine (AARM). An AARM possesses the basic features of a conventional register machine and an alternating Turing machine, but can carry…

We introduce a new programming language and its categorical semantics in order to design and implement neural networks within the framework of algebraic effects and handlers for arrows. Our language enables us to construct neural networks…

Code generation has attracted increasing attention with the rise of Large Language Models (LLMs). Many studies have developed powerful code LLMs by synthesizing code-related instruction data and applying supervised fine-tuning. However,…

We explore asynchronous programming with algebraic effects. We complement their conventional synchronous treatment by showing how to naturally also accommodate asynchrony within them, namely, by decoupling the execution of operation calls…

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…

Sequential recommendation aims to recommend the next item of users' interest based on their historical interactions. Recently, the self-attention mechanism has been adapted for sequential recommendation, and demonstrated state-of-the-art…

We present an effect system for core Eff, a simplified variant of Eff, which is an ML-style programming language with first-class algebraic effects and handlers. We define an expressive effect system and prove safety of operational…

Model-checking is one of the most powerful techniques for verifying systems and programs, which since the pioneering results by Knapik et al., Ong, and Kobayashi, is known to be applicable to functional programs with higher-order types…

DEEPTHINK methods improve reasoning by generating, refining, and aggregating populations of candidate solutions, which enables strong performance on complex mathematical and scientific tasks. However, existing frameworks often lack reliable…

This paper aims to improve the performance of large language models by addressing the variable computational demands in inference steps, where some tokens require more computational resources than others. We present HARP, a simple…