Related papers: Product Interaction: An Algebraic Formalism for De…

If a graded Lie algebra is the direct sum of two graded sub Lie algebras, its bracket can be written in a form that mimics a "double sided semidirect product". It is called the {\it knit product} of the two subalgebras then. The integrated…

Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate. Moreover, to model concurrent and…

Recent work has shown that collaborative filter-based recommender systems can be improved by incorporating side information, such as natural language reviews, as a way of regularizing the derived product representations. Motivated by the…

We assume that, within the dense clusters of neurons that can be found in nuclei, cells may interconnect via soma-to-soma interactions, in addition to conventional synaptic connections. We illustrate this idea with a multi-layer…

Transformer models typically calculate attention matrices using dot products, which have limitations when capturing nonlinear relationships between embedding vectors. We propose Neural Attention, a technique that replaces dot products with…

The visual explanation of learned representation of models helps to understand the fundamentals of learning. The attentional models of previous works used to visualize the attended regions over an image or text using their learned weights…

Our ability to interact with the world around us relies on being able to infer what actions objects afford -- often referred to as affordances. The neural mechanisms of object-action associations are realized in the visuomotor pathway where…

Reasoning about objects, relations, and physics is central to human intelligence, and a key goal of artificial intelligence. Here we introduce the interaction network, a model which can reason about how objects in complex systems interact,…

Systems of cooperation and interaction are usually studied in the context of real or complex vector spaces. Additional insight, however, is gained when such systems are represented in vector spaces with multiplicative structures, i.e., in…

If Economics is understood as the study of the interactions among intentional agents, being rationality the main source of intentional behavior, the mathematical tools that it requires must be extended to capture systemic effects. Here we…

Interaction nets are a graphical formalism inspired by Linear Logic proof-nets often used for studying higher order rewriting e.g. \Beta-reduction. Traditional presentations of interaction nets are based on graph theory and rely on…

Since first introduced, computer simulation has been an increasingly important tool in evolutionary linguistics. Recently, with the development of deep learning techniques, research in grounded language learning has also started to focus on…

Deep learning has become the dominant approach for creating high capacity, scalable models across diverse data modalities. However, because these models rely on a large number of learned parameters, tightly couple feature extraction with…

Inference in expressive probabilistic models is generally intractable, which makes them difficult to learn and limits their applicability. Sum-product networks are a class of deep models where, surprisingly, inference remains tractable even…

This paper revisits building machine learning algorithms that involve interactions between entities, such as those between financial assets in an actively managed portfolio, or interactions between users in a social network. Our goal is to…

Based on tensor neural network, we propose an interpolation method for high dimensional non-tensor-product-type functions. This interpolation scheme is designed by using the tensor neural network based machine learning method. This means…

Reinforcement Learning formalises an embodied agent's interaction with the environment through observations, rewards and actions. But where do the actions come from? Actions are often considered to represent something external, such as the…

This paper proposes a new architecture - Attentive Tensor Product Learning (ATPL) - to represent grammatical structures in deep learning models. ATPL is a new architecture to bridge this gap by exploiting Tensor Product Representations…

Natural language processing (NLP) can be done using either top-down (theory driven) and bottom-up (data driven) approaches, which we call mechanistic and phenomenological respectively. The approaches are frequently considered to stand in…

Representation is a core issue in artificial intelligence. Humans use discrete language to communicate and learn from each other, while machines use continuous features (like vector, matrix, or tensor in deep neural networks) to represent…