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The emergence of large language models (LLMs) has sparked significant interest in extending their remarkable language capabilities to speech. However, modality alignment between speech and text still remains an open problem. Current…
The paper uses the formalism of indexed categories to recover the proof of a standard final coalgebra theorem, thus showing existence of final coalgebras for a special class of functors on categories with finite limits and colimits. As an…
Causal inference, a cornerstone in disciplines such as economics, genomics, and medicine, is increasingly being recognized as fundamental to advancing the field of robotics. In particular, the ability to reason about cause and effect from…
Centers of categories capture the natural operations on their objects. Homotopy coherent centers are introduced here as an extension of this notion to categories with an associated homotopy theory. These centers can also be interpreted as…
In this paper a new similarity-based learning algorithm, inspired by string edit-distance (Wagner and Fischer, 1974), is applied to the problem of bootstrapping structure from scratch. The algorithm takes a corpus of unannotated sentences…
Context. TypeState-Oriented Programming (TSOP) is a paradigm intended to help developers in the implementation and use of mutable objects whose public interface depends on their private state. Under this paradigm, well-typed programs are…
In the context of dependent type theory, we show that coinductive predicates have an equivalent topological counterpart in terms of coinductively generated positivity relations, introduced by G. Sambin to represent closed subsets in…
In this paper we present a new static data type inference algorithm for logic programming. Without the need of declaring types for predicates, our algorithm is able to automatically assign types to predicates which, in most cases,…
We present guarded dependent type theory, gDTT, an extensional dependent type theory with a `later' modality and clock quantifiers for programming and proving with guarded recursive and coinductive types. The later modality is used to…
Our goal, in the context of open-domain textual question-answering (QA), is to explain answers by showing the line of reasoning from what is known to the answer, rather than simply showing a fragment of textual evidence (a "rationale'"). If…
A datatset $X$ on $R^2$ is a finite topological space. Current research of a dataset focuses on statistical methods and the algebraic topological method \cite{carlsson}. In \cite{hu}, the concept of typed topological space was introduced…
The mixed moments for the Askey-Wilson polynomials are found using a bootstrapping method and connection coefficients. A similar bootstrapping idea on generating functions gives a new Askey-Wilson generating function. An important special…
We introduce DeepPSL a variant of probabilistic soft logic (PSL) to produce an end-to-end trainable system that integrates reasoning and perception. PSL represents first-order logic in terms of a convex graphical model -- hinge-loss Markov…
These notes are based on a series of three lectures given (online) by the first named author at the workshop "Higher Structures and Operadic Calculus" at CRM Barcelona in June 2021. The aim is to give a concise introduction to rational…
We initiate the study of model structures on (categories induced by) lattice posets, a subject we dub homotopical combinatorics. In the case of a finite total order $[n]$, we enumerate all model structures, exhibiting a rich combinatorial…
AI/ML methods are increasingly used in economics to generate binary variables (or labels) via classification algorithms. When these generated variables are included as covariates in regressions, even small misclassification errors can…
We present new induction principles for the syntax of dependent type theories, which we call relative induction principles. The result of the induction principle relative to a functor F into the syntax is stable over the codomain of F. We…
We show how (well-established) type systems based on non-idempotent intersection types can be extended to characterize termination properties of functional programming languages with pattern matching features. To model such programming…
The fact that Applicative type class allows one to express simple parsers in a variable-less combinatorial style is well appreciated among Haskell programmers for its conceptual simplicity, ease of use, and usefulness for semi-automated…
Conditional selective inference requires an exact characterization of the selection event, which is often unavailable except for a few examples like the lasso. This work addresses this challenge by introducing a generic approach to estimate…