相关论文: Value, Representation, Information and Communicati…

This paper outlines a conceptual framework for understanding recent developments in information retrieval and natural language processing that attempts to integrate dense and sparse retrieval methods. I propose a representational approach…

In this extended abstract we provide a unifying framework that can be used to characterize and compare the expressive power of query languages for different data base models. The framework is based upon the new idea of valid partition, that…

Learning the right graph representation from noisy, multisource data has garnered significant interest in recent years. A central tenet of this problem is relational learning. Here the objective is to incorporate the partial information…

We argue that representations in AI models, particularly deep networks, are converging. First, we survey many examples of convergence in the literature: over time and across multiple domains, the ways by which different neural networks…

Quantum mechanics has transformed our understanding of reality, yet deep philosophical puzzles remain unresolved. Is there a consistent way to describe quantum measurement, the emergence of space and time, and the role of observers within…

We study the fundamental problem of learning an unknown object from data using a prescribed model class. We introduce a unified framework that accommodates objects in arbitrary Hilbert spaces, general (possibly vector-valued) random linear…

To deal with uncertainty in reasoning, interval-valued logic has been developed. But uniform intervals cannot capture the difference in degrees of belief for different values in the interval. To salvage the problem triangular and…

Within the biological, physical, and social sciences, there are two broad quantitative traditions: statistical and mathematical modeling. Both traditions have the common pursuit of advancing our scientific knowledge, but these traditions…

Word similarity has many applications to social science and cultural analytics tasks like measuring meaning change over time and making sense of contested terms. Yet traditional similarity methods based on cosine similarity between word…

We investigate the Platonic Representation Hypothesis (PRH) through a tripartite statistical framework of representations: signal, bias, and noise. {1) Signal:} We propose that Platonic alignment arises from the universal relationship…

Phrase representations play an important role in data science and natural language processing, benefiting various tasks like Entity Alignment, Record Linkage, Fuzzy Joins, and Paraphrase Classification. The current state-of-the-art method…

This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored, and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact…

We set up a parametrised monadic translation for a class of call-by-value functional languages, and prove a corresponding soundness theorem. We then present a series of concrete instantiations of our translation, demonstrating that a number…

The vast corpus of physics equations forms an implicit network of mathematical relationships that traditional analysis cannot fully explore. This work introduces a graph-based framework combining neural networks with symbolic analysis to…

Much mathematical writing exists that is, explicitly or implicitly, based on set theory, often Zermelo-Fraenkel set theory (ZF) or one of its variants. In ZF, the domain of discourse contains only sets, and hence every mathematical object…

The topic of this paper is the subtle interplay between countability and representations. In particular, we establish that the definition of countability of a certain set $X$ crucially hinges on the associated equivalence relation $=_{X}$.…

We introduce "representative generation," extending the theoretical framework for generation proposed by Kleinberg et al. (2024) and formalized by Li et al. (2024), to additionally address diversity and bias concerns in generative models.…

The combination of argumentation and probability paves the way to new accounts of qualitative and quantitative uncertainty, thereby offering new theoretical and applicative opportunities. Due to a variety of interests, probabilistic…

Information theory is introduced in this lecture note with a particular emphasis on its relevance to algebraic coding theory. The document develops the mathematical foundations for quantifying uncertainty and information transmission by…

Scientific discovery is a cumulative process and requires new ideas to be situated within an ever-expanding landscape of existing knowledge. An emerging and critical challenge is how to identify conceptually relevant prior work from rapidly…