Related papers: Representation Theorems Obtained by Miningacross W…

The study of representations is of fundamental importance to any form of communication, and our ability to exploit them effectively is paramount. This article presents a novel theory -- Representational Systems Theory -- that is designed to…

There is growing evidence that independently trained AI systems come to represent the world in the same way. In other words, independently trained embeddings from text, vision, audio, and neural signals share an underlying geometry. We call…

The results here presented are a continuation of the algebraic research line which attempts to find properties of multiple-valued systems based on a poset of two agents. The aim of this paper is to exhibit two relationships between some…

Encoding facts as representations of entities and binary relationships between them, as learned by knowledge graph representation models, is useful for various tasks, including predicting new facts, question answering, fact checking and…

In a recent paper, new theorems linking apparently unrelated mathematical objects (event structures from concurrency theory and full graphs arising in computational biology) were discovered by cross-site data mining on huge databases, and…

Knowledge graphs represent real-world entities and their relations in a semantically-rich structure supported by ontologies. Exploring this data with machine learning methods often relies on knowledge graph embeddings, which produce latent…

In recent years, algebraic topology and its modern development, the theory of persistent homology, has shown great potential in graph representation learning. In this paper, based on the mathematics of algebraic topology, we propose a novel…

A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…

Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…

Deep neural networks come in many sizes and architectures. The choice of architecture, in conjunction with the dataset and learning algorithm, is commonly understood to affect the learned neural representations. Yet, recent results have…

With the widespread use of information technologies, information networks are becoming increasingly popular to capture complex relationships across various disciplines, such as social networks, citation networks, telecommunication networks,…

Narratives are fundamental to our perception of the world and are pervasive in all activities that involve the representation of events in time. Yet, modern online information systems do not incorporate narratives in their representation of…

Information algebras arise from the idea that information comes in pieces which can be aggregated or combined into new pieces, that information refers to questions and that from any piece of information, the part relevant to a given…

We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…

In this work, we show that neural networks can be represented via the mathematical theory of quiver representations. More specifically, we prove that a neural network is a quiver representation with activation functions, a mathematical…

Many real world systems need to operate on heterogeneous information networks that consist of numerous interacting components of different types. Examples include systems that perform data analysis on biological information networks; social…

There is a large ongoing scientific effort in mechanistic interpretability to map embeddings and internal representations of AI systems into human-understandable concepts. A key element of this effort is the linear representation…

Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…

Informally, the 'linear representation hypothesis' is the idea that high-level concepts are represented linearly as directions in some representation space. In this paper, we address two closely related questions: What does "linear…

The information technology explosion has dramatically increased the application of new mathematical ideas and has led to an increasing use of mathematics across a wide range of fields that have been traditionally labeled "pure" or…