Neuro-symbolic artificial intelligence (AI) systems typically couple a neural perception module to a discrete symbolic solver through a non-differentiable boundary, preventing constraint-satisfaction feedback from reaching the perception encoder during training. We introduce AS2 (Attention-Based Soft Answer Sets), a fully differentiable neuro-symbolic architecture that replaces the discrete solver with a soft, continuous approximation of the Answer Set Programming (ASP) immediate consequence operator $T_P$. AS2 maintains per-position probability distributions over a finite symbol domain throughout the forward pass and trains end-to-end by minimizing the fixed-point residual of a probabilistic lift of $T_P$, thereby differentiating through the constraint check without invoking an external solver at either training or inference time. The architecture is entirely free of conventional positional embeddings. Instead, it encodes problem structure through constraint-group membership embeddings that directly reflect the declarative ASP specification, making the model agnostic to arbitrary position indexing. On Visual Sudoku, AS2 achieves 99.89% cell accuracy and 100% constraint satisfaction (verified by Clingo) across 1,000 test boards, using a greedy constrained decoding procedure that requires no external solver. On MNIST Addition with $N \in \{2, 4, 8\}$ addends, AS2 achieves digit accuracy above 99.7% across all scales. These results demonstrate that a soft differentiable fixpoint operator, combined with constraint-aware attention and declarative constraint specification, can match or exceed pipeline and solver-based neuro-symbolic systems while maintaining full end-to-end differentiability.
KU Leuven, Department of Computer Science（比利时鲁汶大学）
Neuro-symbolic and statistical relational artificial intelligence both integrate frameworks for learning with logical reasoning. This survey identifies several parallels across seven different dimensions between these two fields. These cannot only be used to characterize and position neuro-symbolic artificial intelligence approaches but also to identify a number of directions for further research.
National Key Laboratory for Novel Software Technology, Nanjing University（计算机软件新技术全国重点实验室，南京大学）
Neural-symbolic computing aims at integrating robust neural learning and sound symbolic reasoning into a single framework, so as to leverage the complementary strengths of both of these, seemingly unrelated (maybe even contradictory) AI paradigms. The central challenge in neural-symbolic computing is to unify the formulation of neural learning and symbolic reasoning into a single framework with common semantics, that is, to seek a joint representation between a neural model and a logical theory that can support the basic grounding learned by the neural model and also stick to the semantics of …
BiNSGPS: Geometry Problem Solving via Bidirectional Neuro-Symbolic Interaction
MAIS, Institute of Automation of Chinese Academy of Sciences（自动化研究所）；School of Artificial Intelligence, University of Chinese Academy of Sciences（中国科学院大学人工智能学院）
Taxonomic Networks: A Representation for Neuro-Symbolic Pairing
School of Interactive Computing（交互计算学院）；Georgia Institute of Technology（佐治亚理工学院）；College of Computing and Informatics（计算与信息学院）；Drexel University（德雷塞尔大学）
Social norms underlie all human social interactions, yet formalizing and reasoning with them remains a major challenge for AI systems. We present a novel system for taking social rules of thumb (ROTs) in natural language from the Social Chemistry 101 dataset and converting them to first-order logic where reasoning is performed using a neuro-symbolic theorem prover. We accomplish this in several steps. First, ROTs are converted into Abstract Meaning Representation (AMR), which is a graphical representation of the concepts in a sentence, and align the AMR with RoBERTa embeddings. We then generat…
LTLZinc: a Benchmarking Framework for Continual Learning and Neuro-Symbolic Temporal Reasoning
University of Pisa（比萨大学）；University of Modena and Reggio Emilia（摩德纳和雷焦艾米利亚大学）；KU Leuven（鲁汶大学）；University of Florence（佛罗伦萨大学）；University of Siena（锡耶纳大学）
Howard University（霍华德大学）；College of Engineering and Architecture（工程与建筑学院）；DoD Center of Excellence in Artificial Intelligence and Machine Learning（美国国防部人工智能与机器学习卓越中心）；U.S. Army Research Laboratory（美国陆军研究实验室）
Vehicle: Bridging the Embedding Gap in the Verification of Neuro-Symbolic Programs
University of Western Australia（西澳大利亚大学）；Well-Typed（Well-Typed公司）；University of Strathclyde（思克莱德大学）；Heriot-Watt University（赫瑞-瓦特大学）；University of Birmingham（伯明翰大学）
Peking University（北京大学）；National Institute of Informatics（国立信息学研究所）；Guangzhou University（广州大学）
Learning first-order logic programs (LPs) from relational facts which yields intuitive insights into the data is a challenging topic in neuro-symbolic research. We introduce a novel differentiable inductive logic programming (ILP) model, called differentiable first-order rule learner (DFOL), which finds the correct LPs from relational facts by searching for the interpretable matrix representations of LPs. These interpretable matrices are deemed as trainable tensors in neural networks (NNs). The NNs are devised according to the differentiable semantics of LPs. Specifically, we first adopt a nov…
Neuro-Symbolic Artificial Intelligence -- the combination of symbolic methods with methods that are based on artificial neural networks -- has a long-standing history. In this article, we provide a structured overview of current trends, by means of categorizing recent publications from key conferences. The article is meant to serve as a convenient starting point for research on the general topic.
We study the problem of learning worst-case-safe parameters for programs that use neural networks as well as symbolic, human-written code. Such neurosymbolic programs arise in many safety-critical domains. However, because they can use nondifferentiable operations, it is hard to learn their parameters using existing gradient-based approaches to safe learning. Our approach to this problem, Differentiable Symbolic Execution (DSE), samples control flow paths in a program, symbolically constructs worst-case "safety losses" along these paths, and backpropagates the gradients of these losses through…
Humans have the ability to seamlessly combine low-level visual input with high-level symbolic reasoning often in the form of recognising objects, learning relations between them and applying rules. Neuro-symbolic systems aim to bring a unifying approach to connectionist and logic-based principles for visual processing and abstract reasoning respectively. This paper presents a complete neuro-symbolic method for processing images into objects, learning relations and logical rules in an end-to-end fashion. The main contribution is a differentiable layer in a deep learning architecture from which …
ANDRE: An Attention-based Neuro-symbolic Differentiable Rule Extractor for Inductive Logic Programming
Dept. of Mechanical and Aerospace Engineering, George Washington University, USA（机械与航空航天工程系，乔治华盛顿大学）；Dept. of Mechanical Engineering Sciences, University of Surrey, UK（机械工程科学系，萨里大学）
Adobe（奥多比公司）；Georgia Tech（佐治亚理工学院）；Facebook AI Research（Facebook人工智能研究院）
There are two classes of generative art approaches: neural, where a deep model is trained to generate samples from a data distribution, and symbolic or algorithmic, where an artist designs the primary parameters and an autonomous system generates samples within these constraints. In this work, we propose a new hybrid genre: neuro-symbolic generative art. As a preliminary study, we train a generative deep neural network on samples from the symbolic approach. We demonstrate through human studies that subjects find the final artifacts and the creation process using our neuro-symbolic approach to …
IBM Research – Zurich（IBM苏黎世研究院）；ETH Zürich（苏黎世联邦理工学院）
Neither deep neural networks nor symbolic AI alone has approached the kind of intelligence expressed in humans. This is mainly because neural networks are not able to decompose joint representations to obtain distinct objects (the so-called binding problem), while symbolic AI suffers from exhaustive rule searches, among other problems. These two problems are still pronounced in neuro-symbolic AI which aims to combine the best of the two paradigms. Here, we show that the two problems can be addressed with our proposed neuro-vector-symbolic architecture (NVSA) by exploiting its powerful operator…
We present a new AI task and baseline solution for Inter-Subjective Reasoning. We define inter-subjective information, to be a mixture of objective and subjective information possibly shared by different parties. Examples may include commodities and their objective properties as reported by IR (Information Retrieval) systems, that need to be cross-referenced with subjective user reviews from an online forum. For an AI system to successfully reason about both, it needs to be able to combine symbolic reasoning of objective facts with the shared consensus found on subjective user reviews. To this…
University of Trento（特伦托大学）；University of Pisa（比萨大学）
Neuro-symbolic predictors learn a mapping from sub-symbolic inputs to higher-level concepts and then carry out (probabilistic) logical inference on this intermediate representation. This setup offers clear advantages in terms of consistency to symbolic prior knowledge, and is often believed to provide interpretability benefits in that - by virtue of complying with the knowledge - the learned concepts can be better understood by human stakeholders. However, it was recently shown that this setup is affected by reasoning shortcuts whereby predictions attain high accuracy by leveraging concepts wi…
Bosch Research（博世研究院）；Carnegie Mellon University（卡内基梅隆大学）；Information Sciences Institute, Viterbi School of Engineering, University of Southern California（南加州大学维特比工程学院信息科学研究所）；Michigan State University（密歇根州立大学）
This chapter illustrates how suitable neuro-symbolic models for language understanding can enable domain generalizability and robustness in downstream tasks. Different methods for integrating neural language models and knowledge graphs are discussed. The situations in which this combination is most appropriate are characterized, including quantitative evaluation and qualitative error analysis on a variety of commonsense question answering benchmark datasets.
