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This study aims to prove the emergence of symbolic concepts (or more precisely, sparse primitive inference patterns) in well-trained deep neural networks (DNNs). Specifically, we prove the following three conditions for the emergence. (i)…

Machine Learning · Computer Science 2024-09-16 Qihan Ren , Jiayang Gao , Wen Shen , Quanshi Zhang

The current Neuro-Symbolic (NeSy) Learning paradigm suffers from an over-reliance on labeled data, so if we completely disregard labels, it leads to less symbol information, a larger solution space, and more shortcuts-issues that current…

Artificial Intelligence · Computer Science 2025-06-18 Lin-Han Jia , Wen-Chao Hu , Jie-Jing Shao , Lan-Zhe Guo , Yu-Feng Li

Neuro-symbolic reinforcement learning (NS-RL) has emerged as a promising paradigm for explainable decision-making, characterized by the interpretability of symbolic policies. NS-RL entails structured state representations for tasks with…

Artificial Intelligence · Computer Science 2024-06-14 Lirui Luo , Guoxi Zhang , Hongming Xu , Yaodong Yang , Cong Fang , Qing Li

In the ongoing quest for hybridizing discrete reasoning with neural nets, there is an increasing interest in neural architectures that can learn how to solve discrete reasoning or optimization problems from natural inputs, a task that Large…

Artificial Intelligence · Computer Science 2025-12-19 Marianne Defresne , Romain Gambardella , Sophie Barbe , Thomas Schiex

Inference-time scaling has emerged as a powerful technique for enhancing the reasoning performance of Large Language Models (LLMs). However, existing approaches often rely on heuristic strategies for parallel sampling, lacking a principled…

Machine Learning · Computer Science 2025-12-22 Youkang Wang , Jian Wang , Rubing Chen , Xiao-Yong Wei

In this paper, we propose a new deep learning approach, called neural association model (NAM), for probabilistic reasoning in artificial intelligence. We propose to use neural networks to model association between any two events in a…

Artificial Intelligence · Computer Science 2016-08-04 Quan Liu , Hui Jiang , Andrew Evdokimov , Zhen-Hua Ling , Xiaodan Zhu , Si Wei , Yu Hu

Dialog Structure Induction (DSI) is the task of inferring the latent dialog structure (i.e., a set of dialog states and their temporal transitions) of a given goal-oriented dialog. It is a critical component for modern dialog system design…

Computation and Language · Computer Science 2024-03-27 Connor Pryor , Quan Yuan , Jeremiah Liu , Mehran Kazemi , Deepak Ramachandran , Tania Bedrax-Weiss , Lise Getoor

Spatial-temporal reasoning is a challenging task in Artificial Intelligence (AI) due to its demanding but unique nature: a theoretic requirement on representing and reasoning based on spatial-temporal knowledge in mind, and an applied…

Artificial Intelligence · Computer Science 2021-05-17 Chi Zhang , Baoxiong Jia , Song-Chun Zhu , Yixin Zhu

Evaluating the health effects of complex environmental mixtures remains a central challenge in environmental health research. Existing approaches vary in their flexibility, interpretability, scalability, and support for diverse outcome…

Applications · Statistics 2025-12-15 Hyungrok Do , Yuyan Wang , Mengling Liu , Myeonggyun Lee

Recent years have witnessed a growing call for renewed emphasis on neuroscience-inspired approaches in artificial intelligence research, under the banner of NeuroAI. A prime example of this is predictive coding networks (PCNs), based on the…

Machine Learning · Computer Science 2026-03-09 Björn van Zwol , Ro Jefferson , Egon L. van den Broek

LLMs have demonstrated highly effective learning, human-like response generation,and decision-making capabilities in high-risk sectors. However, these models remain black boxes because they struggle to ensure transparency in responses. The…

Artificial Intelligence · Computer Science 2025-10-27 Maneeha Rani , Bhupesh Kumar Mishra , Dhavalkumar Thakker

A recent approach to neurosymbolic reasoning is to explicitly combine the strengths of large language models (LLMs) and symbolic solvers to tackle complex reasoning tasks. However, current approaches face significant limitations, including…

Artificial Intelligence · Computer Science 2026-01-08 Benjamin Callewaert , Simon Vandevelde , Joost Vennekens

Recent advances in statistical inference have significantly expanded the toolbox of probabilistic modeling. Historically, probabilistic modeling has been constrained to (i) very restricted model classes where exact or approximate…

Machine Learning · Computer Science 2019-10-03 Andrés R. Masegosa , Rafael Cabañas , Helge Langseth , Thomas D. Nielsen , Antonio Salmerón

Deep neural networks have emerged as the workhorse for a large section of robotics and control applications, especially as models for dynamical systems. Such data-driven models are in turn used for designing and verifying autonomous…

Machine Learning · Computer Science 2023-11-08 Kaustubh Sridhar , Souradeep Dutta , James Weimer , Insup Lee

Symbolic rule learners generate interpretable solutions, however they require the input to be encoded symbolically. Neuro-symbolic approaches overcome this issue by mapping raw data to latent symbolic concepts using a neural network.…

Machine Learning · Computer Science 2023-10-10 Theo Charalambous , Yaniv Aspis , Alessandra Russo

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

Neurosymbolic AI is an increasingly active area of research that combines symbolic reasoning methods with deep learning to leverage their complementary benefits. As knowledge graphs are becoming a popular way to represent heterogeneous and…

Artificial Intelligence · Computer Science 2025-01-13 Lauren Nicole DeLong , Ramon Fernández Mir , Jacques D. Fleuriot

In recent years, researchers in decision analysis and artificial intelligence (AI) have used Bayesian belief networks to build models of expert opinion. Using standard methods drawn from the theory of computational complexity, workers in…

Artificial Intelligence · Computer Science 2013-04-05 R. Martin Chavez , Gregory F. Cooper

Neurosymbolic (NeSy) artificial intelligence describes the combination of logic or rule-based techniques with neural networks. Compared to neural approaches, NeSy methods often possess enhanced interpretability, which is particularly…

Artificial Intelligence · Computer Science 2025-01-13 Lauren Nicole DeLong , Yojana Gadiya , Paola Galdi , Jacques D. Fleuriot , Daniel Domingo-Fernández

The goal of combining the robustness of neural networks and the expressivity of symbolic methods has rekindled the interest in neuro-symbolic AI. Recent advancements in neuro-symbolic AI often consider specifically-tailored architectures…

Artificial Intelligence · Computer Science 2021-11-24 Arseny Skryagin , Wolfgang Stammer , Daniel Ochs , Devendra Singh Dhami , Kristian Kersting