相关论文: Phantom Types and Subtyping

Hidden Markov Models (HMMs) can be accurately approximated using co-occurrence frequencies of pairs and triples of observations by using a fast spectral method in contrast to the usual slow methods like EM or Gibbs sampling. We provide a…

Let $K\subset \mathbb{R}$ be a self-similar set generated by some iterated function system. In this paper we prove, under some assumptions, that $K$ can be identified with a subshift of finite type. With this identification, we can…

We present an approach to support partiality in type-level computation without compromising expressiveness or type safety. Existing frameworks for type-level computation either require totality or implicitly assume it. For example, type…

We construct an iterative method for factorising small strict n-categories into a unique (up to isomorphism) collection of small 1- categories. Following this we develop the theory to include a large class of $\infty$-categories. We use…

In [4] we describe a variation of the classical permutation decoding algorithm that can be applied to any binary affine-invariant code; in particular, it can be applied to first-order Reed-Muller codes successfully. In this paper we study…

Take a multiplicative monoid of sequences in which the multiplication is given by Hadamard product. The set of linear combinations of interleaving monoid elements then yields a ring. For hypergeometric sequences, the resulting ring is a…

We present a novel approach to solving the floorplanning problem by leveraging fine-tuned Large Language Models (LLMs). Inspired by subitizing--the human ability to instantly and accurately count small numbers of items at a glance--we…

We introduce a high-level language with Python-like syntax for string-to-string, polyregular, first-order definable transductions. This language features function calls, boolean variables, and nested for-loops. We devise and implement a…

Hidden Markov Models, HMM's, are mathematical models of Markov processes with state that is hidden, but from which information can leak. They are typically represented as 3-way joint-probability distributions. We use HMM's as denotations of…

Understanding the internal representations of large language models (LLMs) can help explain models' behavior and verify their alignment with human values. Given the capabilities of LLMs in generating human-understandable text, we propose…

We describe the translation of the Suggested Upper Merged Ontology (SUMO) to Typed First-order Form (TFF) with level 0 polymorphism. Building on our prior work to create a TPTP FOF translation of SUMO for use in the E and Vampire theorem…

When scripts in untyped languages grow into large programs, maintaining them becomes difficult. A lack of explicit type annotations in typical scripting languages forces programmers to must (re)discover critical pieces of design information…

We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…

We discuss hidden symmetries of three-dimensional field configurations revealed at the one-particle level by the use of pseudoclassical particle models. We argue that at the quantum field theory level, these can be naturally explained in…

Hierarchical modeling provides a framework for modeling the complex interactions typical of problems in applied statistics. By capturing these relationships, however, hierarchical models also introduce distinctive pathologies that quickly…

In the theory of programming languages, type inference is the process of inferring the type of an expression automatically, often making use of information from the context in which the expression appears. Such mechanisms turn out to be…

Most pretrained language models rely on subword tokenization, which processes text as a sequence of subword tokens. However, different granularities of text, such as characters, subwords, and words, can contain different kinds of…

Detecting butterfly hybrids requires knowledge of the parent subspecies, and the process can be tedious when encountering a new subspecies. This study focuses on a specific scenario where a model trained to recognize hybrid species A can…

Detecting hallucinations in large language models (LLMs) remains a fundamental challenge for their trustworthy deployment. Going beyond basic uncertainty-driven hallucination detection frameworks, we propose a simple yet powerful method…

Large language models (LLMs) frequently generate hallucinations-content that deviates from factual accuracy or provided context-posing challenges for diagnosis due to the complex interplay of underlying causes. This paper introduces a…