Related papers: Integrating multiple sources to answer questions i…

With recent dramatic increases in AI system capabilities, there has been growing interest in utilizing machine learning for reasoning-heavy, quantitative tasks, particularly mathematics. While there are many resources capturing mathematics…

The decoupling of multivariate functions is a powerful modeling paradigm for learning multivariate input-output relations from data. For the single-layer case, established CPD-based methods are available, but the multi-layer case remained…

Consider a receiver in a multi-user network that wishes to decode several messages. Simultaneous joint typicality decoding is one of the most powerful techniques for determining the fundamental limits at which reliable decoding is possible.…

TensorFlow is an interface for expressing machine learning algorithms, and an implementation for executing such algorithms. A computation expressed using TensorFlow can be executed with little or no change on a wide variety of heterogeneous…

Over-the-air computation (AirComp) has emerged as a promising technology that enables simultaneous transmission and computation through wireless channels. In this paper, we investigate the networked AirComp in multiple clusters allowing…

Transformers are effective and efficient at modeling complex relationships and learning patterns from structured data in many applications. The main aim of this paper is to propose and design NLAFormer, which is a transformer-based…

We introduce the notion of an ACP process algebra. The models of the axiom system ACP are the origin of this notion. ACP process algebras have to do with processes in which no data are involved. We also introduce the notion of a meadow…

For natural and artificial systems with some symmetry structure, computational understanding and manipulation can be achieved without learning by exploiting the algebraic structure. Here we describe this algebraic coordinatization method…

In enterprise datasets, documents are rarely pure. They are not just text, nor just numbers; they are a complex amalgam of narrative and structure. Current Retrieval-Augmented Generation (RAG) systems have attempted to address this…

Generative AI tools often answer questions using source documents, e.g., through retrieval augmented generation. Current groundedness and hallucination evaluations largely frame the relationship between an answer and its sources as binary…

We consider relationships between cubic algebras and implication algebras. We first exhibit a functorial construction of a cubic algebra from an implication algebra. Then we consider an collapse of a cubic algebra to an implication algebra…

This is a slightly edited version of the transparencies for a seminar at UCL, May 7, 2003. It is intended to give a quick view of background, ideas, and some calculations, in the applicatioon of some non commutative methods to algebraic…

It is our intention here only to discuss the nature, complexity and tools concerning the design of Smart Help, an expert help facility for aiding users of Computer Algebra Systems. Although the expert help system presented here has been…

We, as a society, need artists to help us interpret and explain science, but what does an artist's studio look like when today's science is built upon the language of large, increasingly complex data? This paper presents a data…

We present Coevo, an online platform that allows both humans and artificial agents to design shapes that solve different tasks. Our goal is to explore common shared design tools that can be used by humans and artificial agents in a context…

The massive growth in the utilization of edge AI has made the applications of machine learning models ubiquitous in different domains. Despite the computation and communication efficiency of these systems, due to limited computation…

Challenges at the quantum-classical interface are examined with the goal of architecting a scaled-up quantum computer comprising many thousands of qubits in the solid-state. Separating the distinct sub-systems of the interface that perform…

In the last few years there has been a growing interest towards methods for statistical inference and learning based on computational geometry and, notably, tropical geometry, that is, the study of algebraic varieties over the min-plus…

We discuss a homological method for transferring algebra structures on complexes along suitably nice homotopy equivalences, including those obtained after an application of the Perturbation Lemma. We study the implications for the Homotopy…

We provide a foundation for working with homological and homotopical methods in categorical algebra. This involves two mutually complementary components, namely (a) the strategic selection of suitable axiomatic frameworks, some well known…