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Growing dimensionality of data calls for beyond-pairwise interactions quantification. Measures of multidimensional interactions quantification are hindered, among others, by two issues: 1. Interpretation difficulties, 2. the curse of…

Weighted logic programming, a generalization of bottom-up logic programming, is a well-suited framework for specifying dynamic programming algorithms. In this setting, proofs correspond to the algorithm's output space, such as a path…

The generative capabilities of deep learning neural networks (DNNs) have been attracting increasing attention for both the remarkable artifacts they produce, but also because of the vast conceptual difference between how they are programmed…

Network data has become widespread, larger, and more complex over the years. Traditional network data is dyadic, capturing the relations among pairs of entities. With the need to model interactions among more than two entities, significant…

We present a new distributed representation in deep neural nets wherein the information is represented in native form as a matrix. This differs from current neural architectures that rely on vector representations. We consider matrices as…

Deep neural networks are composed of layers of parametrised linear operations intertwined with non linear activations. In basic models, such as the multi-layer perceptron, a linear layer operates on a simple input vector embedding of the…

Interaction nets are a graphical model of computation, which has been used to define efficient evaluators for functional calculi, and specifically lambda calculi with patterns. However, the flat structure of interaction nets forces pattern…

This paper aims to explain how a deep neural network (DNN) gradually extracts new knowledge and forgets noisy features through layers in forward propagation. Up to now, although the definition of knowledge encoded by the DNN has not reached…

Recent advances in the integration of deep learning with automated theorem proving have centered around the representation of logical formulae as inputs to deep learning systems. In particular, there has been a growing interest in adapting…

Symbolic computation, powered by modern computer algebra systems, has important applications in mathematical reasoning through exact deep computations. The efficiency of symbolic computation is largely constrained by such deep computations…

Vector-valued neural learning has emerged as a promising direction in deep learning recently. Traditionally, training data for neural networks (NNs) are formulated as a vector of scalars; however, its performance may not be optimal since…

An increasing number of computer vision tasks can be tackled with deep features, which are the intermediate outputs of a pre-trained Convolutional Neural Network. Despite the astonishing performance, deep features extracted from low-level…

With the rapid development of deep learning, most of current state-of-the-art techniques in natural langauge processing are based on deep learning models trained with argescaled static textual corpora. However, we human beings learn and…

Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…

High-level classification algorithms focus on the interactions between instances. These produce a new form to evaluate and classify data. In this process, the core is the complex network building methodology because it determines the…

Predictive coding-inspired deep networks for visual computing integrate classification and reconstruction processes in shared intermediate layers. Although synergy between these processes is commonly assumed, it has yet to be convincingly…

Convolutional Neural Networks (CNNs) have been widely applied. But as the CNNs grow, the number of arithmetic operations and memory footprint also increase. Furthermore, typical non-linear activation functions do not allow associativity of…

A social interaction is a social exchange between two or more individuals,where individuals modify and adjust their behaviors in response to their interaction partners. Our social interactions are one of most fundamental aspects of our…

A social interaction (so-called higher-order event/interaction) can be regarded as the activation of the hyperlink among the corresponding individuals. Social interactions can be, thus, represented as higher-order temporal networks, that…

In this paper, we present a formalism for representing infinite systems in quantum mechanics by employing a strategy that embraces divergences rather than avoiding them. We do this by representing physical quantities such as inner products,…