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Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…

Dynamical Systems · Mathematics 2026-05-07 Nibodh Boddupalli , Timothy Matchen , Jeff Moehlis

In this paper, we review recent approaches for explaining concepts in neural networks. Concepts can act as a natural link between learning and reasoning: once the concepts are identified that a neural learning system uses, one can integrate…

Artificial Intelligence · Computer Science 2024-05-06 Jae Hee Lee , Sergio Lanza , Stefan Wermter

Background: Neuro-symbolic methods enhance the reliability of neural network classifiers through logical constraints, but they lack native support for ontologies. Objectives: We aim to develop a neuro-symbolic method that reliably outputs…

Artificial Intelligence · Computer Science 2026-01-22 Nicolas Lazzari , Valentina Presutti , Antonio Vergari

We propose neural-symbolic integration for abstract concept explanation and interactive learning. Neural-symbolic integration and explanation allow users and domain-experts to learn about the data-driven decision making process of large…

Artificial Intelligence · Computer Science 2022-01-19 Benedikt Wagner , Artur d'Avila Garcez

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…

Information Retrieval · Computer Science 2020-07-28 Yikun Xian , Zuohui Fu , Qiaoying Huang , S. Muthukrishnan , Yongfeng Zhang

The field of neuro-symbolic AI aims to benefit from the combination of neural networks and symbolic systems. A cornerstone of the field is the translation or encoding of symbolic knowledge into neural networks. Although many neuro-symbolic…

Artificial Intelligence · Computer Science 2024-11-28 Simon Odense , Artur d'Avila Garcez

Analogical Reasoning problems challenge both connectionist and symbolic AI systems as these entail a combination of background knowledge, reasoning and pattern recognition. While symbolic systems ingest explicit domain knowledge and perform…

Artificial Intelligence · Computer Science 2022-09-20 Vishwa Shah , Aditya Sharma , Gautam Shroff , Lovekesh Vig , Tirtharaj Dash , Ashwin Srinivasan

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…

Artificial Intelligence · Computer Science 2024-10-18 Zhaocheng Zhu

Artificial Intelligence (AI) is a powerful new language of science as evidenced by recent Nobel Prizes in chemistry and physics that recognized contributions to AI applied to those areas. Yet, this new language lacks semantics, which makes…

Artificial Intelligence · Computer Science 2025-11-05 Artur d'Avila Garcez , Simon Odense

Current advances in Artificial Intelligence (AI) and Machine Learning (ML) have achieved unprecedented impact across research communities and industry. Nevertheless, concerns about trust, safety, interpretability and accountability of AI…

Artificial Intelligence · Computer Science 2020-12-18 Artur d'Avila Garcez , Luis C. Lamb

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…

Artificial Intelligence · Computer Science 2026-05-12 Adam Gould , Francesca Toni

In this work, we aim to leverage prior symbolic knowledge to improve the performance of deep models. We propose a graph embedding network that projects propositional formulae (and assignments) onto a manifold via an augmented Graph…

Artificial Intelligence · Computer Science 2019-10-30 Yaqi Xie , Ziwei Xu , Mohan S. Kankanhalli , Kuldeep S. Meel , Harold Soh

Neurosymbolic artificial intelligence (AI) systems combine neural network and classical symbolic AI mechanisms to exploit the complementary strengths of large scale, generalizable learning and robust, verifiable reasoning. Numerous…

Artificial Intelligence · Computer Science 2025-07-15 Aniruddha Chattopadhyay , Raj Dandekar , Kaushik Roy

Neuro-symbolic artificial intelligence is a novel area of AI research which seeks to combine traditional rules-based AI approaches with modern deep learning techniques. Neuro-symbolic models have already demonstrated the capability to…

Artificial Intelligence · Computer Science 2021-09-14 Zachary Susskind , Bryce Arden , Lizy K. John , Patrick Stockton , Eugene B. John

Motivated by recent findings from cognitive neural science, we advocate the use of a dual-level model for concept representations: the embodied level consists of concept-oriented feature representations, and the symbolic level consists of…

Machine Learning · Computer Science 2022-03-02 Daniel T. Chang

Neurosymbolic AI combines the interpretability, parsimony, and explicit reasoning of classical symbolic approaches with the statistical learning of data-driven neural approaches. Models and policies that are simultaneously differentiable…

Artificial Intelligence · Computer Science 2024-02-09 Peter Graf , Patrick Emami

In this paper, a deep neural network approach and a neuro-symbolic one are proposed for classification and regression. The neuro-symbolic predictive models based on Logic Tensor Networks are capable of discriminating and in the same time of…

Neural and Evolutionary Computing · Computer Science 2024-06-19 Eduard Hogea , Darian Onchis

Recent advances in Wireless Physical Layer Foundation Models (WPFMs) promise a new paradigm of universal Radio Frequency (RF) representations. However, these models inherit critical limitations found in deep learning such as the lack of…

Signal Processing · Electrical Eng. & Systems 2025-11-21 Jaron Fontaine , Mohammad Cheraghinia , John Strassner , Adnan Shahid , Eli De Poorter

Automated reasoning and theorem proving have recently become major challenges for machine learning. In other domains, representations that are able to abstract over unimportant transformations, such as abstraction over translations and…

Artificial Intelligence · Computer Science 2021-12-03 Miroslav Olšák , Cezary Kaliszyk , Josef Urban

Reasoning on knowledge graphs is a challenging task because it utilizes observed information to predict the missing one. Particularly, answering complex queries based on first-order logic is one of the crucial tasks to verify learning to…

Artificial Intelligence · Computer Science 2024-10-23 Hang Yin , Zihao Wang , Yangqiu Song