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Enabling neural networks to learn complex logical constraints and fulfill symbolic reasoning is a critical challenge. Bridging this gap often requires guiding the neural network's output distribution to move closer to the symbolic…

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…

The recommendation system is not only a problem of inductive statistics from data but also a cognitive task that requires reasoning ability. The most advanced graph neural networks have been widely used in recommendation systems because…

Recent work on recommender systems has considered external knowledge graphs as valuable sources of information, not only to produce better recommendations but also to provide explanations of why the recommended items were chosen. Pure…

Hyperdimensional Computing affords simple, yet powerful operations to create long Hyperdimensional Vectors (hypervectors) that can efficiently encode information, be used for learning, and are dynamic enough to be modified on the fly. In…

Creating learning models that can exhibit sophisticated reasoning skills is one of the greatest challenges in deep learning research, and mathematics is rapidly becoming one of the target domains for assessing scientific progress in this…

Reason and inference require process as well as memory skills by humans. Neural networks are able to process tasks like image recognition (better than humans) but in memory aspects are still limited (by attention mechanism, size). Recurrent…

Neuro-symbolic learning was proposed to address challenges with training neural networks for complex reasoning tasks with the added benefits of interpretability, reliability, and efficiency. Neuro-symbolic learning methods traditionally…

We introduce the concept of a \textbf{neuro-symbolic pair} -- neural and symbolic approaches that are linked through a common knowledge representation. Next, we present \textbf{taxonomic networks}, a type of discrimination network in which…

Encoder-decoder architectures are prominent building blocks of state-of-the-art solutions for tasks across multiple fields where deep learning (DL) or foundation models play a key role. Although there is a growing community working on the…

Deep learning has largely improved the performance of various natural language processing (NLP) tasks. However, most deep learning models are black-box machinery, and lack explicit interpretation. In this chapter, we will introduce our…

Deep neural networks have achieved a great success in solving many machine learning and computer vision problems. The main contribution of this paper is to develop a deep network based on Tucker tensor decomposition, and analyze its…

Logic-based problems such as planning, theorem proving, or puzzles, typically involve combinatoric search and structured knowledge representation. Artificial neural networks are very successful statistical learners, however, for many years,…

Developing models that can learn to reason is a notoriously challenging problem. We focus on reasoning in relational domains, where the use of Graph Neural Networks (GNNs) seems like a natural choice. However, previous work has shown that…

Deep learning is very effective at jointly learning feature representations and classification models, especially when dealing with high dimensional input patterns. Probabilistic logic reasoning, on the other hand, is capable to take…

Reasoning, the ability to logically draw conclusions from existing knowledge, is a hallmark of human. Together with perception, they constitute the two major themes of artificial intelligence. While deep learning has pushed the limit of…

We propose a new interpretability method for neural networks, which is based on a novel mathematico-philosophical theory of reasons. Our method computes a vector for each neuron, called its reasons vector. We then can compute how strongly…

Discrete and continuous representations of content (e.g., of language or images) have interesting properties to be explored for the understanding of or reasoning with this content by machines. This position paper puts forward our opinion on…

Knowledge representation and reasoning in neural networks have been a long-standing endeavor which has attracted much attention recently. The principled integration of reasoning and learning in neural networks is a main objective of the…

Graph neural networks (GNNs) excel at predictive tasks on graph-structured data but often lack the ability to incorporate symbolic domain knowledge and perform general reasoning. Relational Bayesian Networks (RBNs), in contrast, enable…