相关论文: Simple Type Theory with Undefinedness, Quotation, …

In Martin-L\"of's Intensional Type Theory, identity type is a heavily used and studied concept. The reason for that is the fact that it's responsible for the recently discovered connection between Type Theory and Homotopy Theory. The main…

I present and defend a new ontology for quantum theories (or ``interpretations'' of quantum theory) called Generative Quantum Theory (GQT). GQT postulates different sets of features, and the combination of these different features can help…

The introduction of the Segment Anything Model (SAM) has paved the way for numerous semantic segmentation applications. For several tasks, quantifying the uncertainty of SAM is of particular interest. However, the ambiguous nature of the…

Cubical type theory is an extension of Martin-L\"of type theory recently proposed by Cohen, Coquand, M\"ortberg and the author which allows for direct manipulation of $n$-dimensional cubes and where Voevodsky's Univalence Axiom is provable.…

Model explanations can be valuable for interpreting and debugging predictive models. We study a specific kind called Concept Explanations, where the goal is to interpret a model using human-understandable concepts. Although popular for…

We present a method to simplify expressions in the context of an equational theory. The basic ideas and concepts of the method have been presented previously elsewhere but here we tackle the difficult task of making it efficient in…

Quantum Shannon theory is loosely defined as a collection of coding theorems, such as classical and quantum source compression, noisy channel coding theorems, entanglement distillation, etc., which characterize asymptotic properties of…

Simple type theory is suited as framework for combining classical and non-classical logics. This claim is based on the observation that various prominent logics, including (quantified) multimodal logics and intuitionistic logics, can be…

Uncertainty quantification (UQ) methods for Large Language Models (LLMs) encompass a variety of approaches, with two major types being particularly prominent: information-based, which focus on model confidence expressed as token…

This paper provides a tutorial about uncertainty quantification (UQ) for those who have no background but are interested in learning more in this area. It exploits many very simple examples, which are understandable to undergraduates, to…

Refinement types sharpen systems of simple and dependent types by offering expressive means to more precisely classify well-typed terms. We present a system of refinement types for LF in the style of recent formulations where only canonical…

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks due to large training datasets and powerful transformer architecture. However, the reliability of responses from LLMs remains a question.…

Understanding the meaning of a text is a fundamental challenge of natural language understanding (NLU) and from its early days, it has received significant attention through question answering (QA) tasks. We introduce a general…

Accurately quantifying a large language model's (LLM) predictive uncertainty is crucial for judging the reliability of its answers. While most existing research focuses on short, directly answerable questions with closed-form outputs (e.g.,…

A careful study of the classical/quantum connection with the aid of coherent states offers new insights into various technical problems. This analysis includes both canonical as well as closely related affine quantization procedures. The…

In this paper, we outline the prototype of an automated inference tool, called QUIP, which provides a uniform implementation for several nonmonotonic reasoning formalisms. The theoretical basis of QUIP is derived from well-known results…

If Uncertainty Quantification (UQ) is crucial to achieve trustworthy Machine Learning (ML), most UQ methods suffer from disparate and inconsistent evaluation protocols. We claim this inconsistency results from the unclear requirements the…

A new approach to the theory of polynomial solutions of q - difference equations is proposed. The approach is based on the representation theory of simple Lie algebras and their q - deformations and is presented here for U_q(sl(n)). First a…

This is an introductory textbook to univalent mathematics and homotopy type theory, a mathematical foundation that takes advantage of the structural nature of mathematical definitions and constructions. It is common in mathematical practice…

We introduce a modification of standard Martin-Lof type theory in which we eliminate definitional equality and replace all computation rules by propositional equalities. We show that type checking for such a system can be done in quadratic…