Related papers: Use and abuse of instance parameters in the Lean m…
We present PackLib^2, the first fully integrated benchmark library for multi-dimensional packing instances. PackLib^2 combines a systematic collection of all benchmark instances from previous literature with a well-organized set of new and…
The exact parameter values of mathematical models are often uncertain or even unknown. Nevertheless, we may have access to crude information about the parameters, e.g., that some of them are nonzero. Such information can be captured by…
Mathematical reasoning is essential for problem-solving in education, science, and industry, serving as a crucial benchmark for evaluating artificial intelligence systems. As Large Language Models (LLMs) improve their reasoning…
This paper introduces the Egison programming language whose feature is strong pattern-matching facility against not only algebraic data types but also non-free data types whose data have multiple ways of representation such as sets and…
Pattern-matching programming is an example of a rule-based programming style developed in functional languages. This programming style is intensively used in dialects of ML but is restricted to algebraic data-types. This restriction limits…
Learning from Label Proportions (LLP) is a weakly supervised learning method that aims to perform instance classification from training data consisting of pairs of bags containing multiple instances and the class label proportions within…
Formalized mathematics has recently garnered significant attention for its ability to assist mathematicians across various fields. Premise retrieval, as a common step in mathematical formalization, has been a challenge, particularly for…
The purpose of this paper is twofold. Firstly, to emphasise that the class of Lie algebras with chain lattices of ideals are elementary blocks in the embedding or decomposition of Lie algebras with finite lattice of ideals. Secondly, to…
We introduce a machine-learning-based tool for the Lean proof assistant that suggests relevant premises for theorems being proved by a user. The design principles for the tool are (1) tight integration with the proof assistant, (2) ease of…
Linear type systems have a long and storied history, but not a clear path forward to integrate with existing languages such as OCaml or Haskell. In this paper, we study a linear type system designed with two crucial properties in mind:…
As originally proposed, type classes provide overloading and ad-hoc definition, but can still be understood (and implemented) in terms of strictly parametric calculi. This is not true of subsequent extensions of type classes. Functional…
We observe a disconnect between the developers and the end users of linear algebra libraries. On the one hand, the numerical linear algebra and the high-performance communities invest significant effort in the development and optimization…
In-context learning (ICL) refers to the process of adding a small number of localized examples from a training set of labelled data to an LLM's prompt with an objective to effectively control the generative process seeking to improve the…
Pattern matching is a powerful tool for symbolic computations, based on the well-defined theory of term rewriting systems. Application domains include algebraic expressions, abstract syntax trees, and XML and JSON data. Unfortunately, no…
By allowing models to predict without task-specific training, in-context learning (ICL) with pretrained LLMs has enormous potential in NLP. However, a number of problems persist in ICL. In particular, its performance is sensitive to the…
We implement a user-extensible ad hoc connection between the Lean proof assistant and the computer algebra system Mathematica. By reflecting the syntax of each system in the other and providing a flexible interface for extending…
Benchmarking is an important tool for assessing the relative performance of alternative solving approaches. However, the utility of benchmarking is limited by the quantity and quality of the available problem instances. Modern constraint…
We describe in this paper new design techniques used in the \cpp exact linear algebra library \linbox, intended to make the library safer and easier to use, while keeping it generic and efficient. First, we review the new simplified…
The growing trend of legal disputes over the unauthorized use of data in machine learning (ML) systems highlights the urgent need for reliable data-use auditing mechanisms to ensure accountability and transparency in ML. We present the…
Type classes are a popular tool for implementing generic algorithms and data structures without loss of efficiency, bridging the gap between parametric and ad-hoc polymorphism. Since their initial development in Haskell, they now feature…