Human conceptual knowledge supports the ability to generate novel yet highly structured concepts, and the form of this conceptual knowledge is of great interest to cognitive scientists. One tradition has emphasized structured knowledge, viewing concepts as embedded in intuitive theories or organized in complex symbolic knowledge structures. A second tradition has emphasized statistical knowledge, viewing conceptual knowledge as an emerging from the rich correlational structure captured by training neural networks and other statistical models. In this paper, we explore a synthesis of these two traditions through a novel neuro-symbolic model for generating new concepts. Using simple visual concepts as a testbed, we bring together neural networks and symbolic probabilistic programs to learn a generative model of novel handwritten characters. Two alternative models are explored with more generic neural network architectures. We compare each of these three models for their likelihoods on held-out character classes and for the quality of their productions, finding that our hybrid model learns the most convincing representation and generalizes further from the training observations.
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.
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 …
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…
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.
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…
In structured prediction, the goal is to jointly predict many output variables that together encode a structured object -- a path in a graph, an entity-relation triple, or an ordering of objects. Such a large output space makes learning hard and requires vast amounts of labeled data. Different approaches leverage alternate sources of supervision. One approach -- entropy regularization -- posits that decision boundaries should lie in low-probability regions. It extracts supervision from unlabeled examples, but remains agnostic to the structure of the output space. Conversely, neuro-symbolic app…
UCLA（加州大学洛杉矶分校）；University of Trento（特伦托大学）；University of Edinburgh（爱丁堡大学）
We design a predictive layer for structured-output prediction (SOP) that can be plugged into any neural network guaranteeing its predictions are consistent with a set of predefined symbolic constraints. Our Semantic Probabilistic Layer (SPL) can model intricate correlations, and hard constraints, over a structured output space all while being amenable to end-to-end learning via maximum likelihood. SPLs combine exact probabilistic inference with logical reasoning in a clean and modular way, learning complex distributions and restricting their support to solutions of the constraint. As such, the…
Numerous neuro-symbolic approaches have recently been proposed typically with the goal of adding symbolic knowledge to the output layer of a neural network. Ideally, such losses maximize the probability that the neural network's predictions satisfy the underlying domain. Unfortunately, this type of probabilistic inference is often computationally infeasible. Neuro-symbolic approaches therefore commonly resort to fuzzy approximations of this probabilistic objective, sacrificing sound probabilistic semantics, or to sampling which is very seldom feasible. We approach the problem by first assuming…
Neuro-Symbolic Imitation Learning: Discovering Symbolic Abstractions for Skill Learning
Intelligent Autonomous Systems, TU Darmstadt, Germany（图腾达姆施塔特大学智能自主系统研究所）；German Research Center for AI, Germany（德国人工智能研究中心）；Hessian Centre for Artificial Intelligence, Germany（黑森州人工智能中心）；Honda Research Institute EU, Germany（本田欧洲研究院）
MIT Computer Science and Artificial Intelligence Laboratory（麻省理工学院计算机科学与人工智能实验室）
Decision-making is challenging in robotics environments with continuous object-centric states, continuous actions, long horizons, and sparse feedback. Hierarchical approaches, such as task and motion planning (TAMP), address these challenges by decomposing decision-making into two or more levels of abstraction. In a setting where demonstrations and symbolic predicates are given, prior work has shown how to learn symbolic operators and neural samplers for TAMP with manually designed parameterized policies. Our main contribution is a method for learning parameterized polices in combination with …
We propose an efficient interpretable neuro-symbolic model to solve Inductive Logic Programming (ILP) problems. In this model, which is built from a set of meta-rules organised in a hierarchical structure, first-order rules are invented by learning embeddings to match facts and body predicates of a meta-rule. To instantiate it, we specifically design an expressive set of generic meta-rules, and demonstrate they generate a consequent fragment of Horn clauses. During training, we inject a controlled \pw{Gumbel} noise to avoid local optima and employ interpretability-regularization term to furthe…
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）
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…
Rensselaer Polytechnic Institute（伦斯勒理工学院）；IBM T.J. Watson Research Center（IBM托马斯·J·沃森研究中心）；IBM Research（IBM研究院）
Most existing Time series classification (TSC) models lack interpretability and are difficult to inspect. Interpretable machine learning models can aid in discovering patterns in data as well as give easy-to-understand insights to domain specialists. In this study, we present Neuro-Symbolic Time Series Classification (NSTSC), a neuro-symbolic model that leverages signal temporal logic (STL) and neural network (NN) to accomplish TSC tasks using multi-view data representation and expresses the model as a human-readable, interpretable formula. In NSTSC, each neuron is linked to a symbolic express…
A Learnability Analysis on Neuro-Symbolic Learning
National Key Laboratory for Novel Software Technology, Nanjing University（南京大学计算机软件新技术国家重点实验室）；School of Artificial Intelligence, Nanjing University（南京大学人工智能学院）
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）
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；The University of Texas at San Antonio（德克萨斯大学圣安东尼奥分校）
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 outperform state-of-the-art deep learning models in domains such as image and video reasoning. They have also been shown to obtain high accuracy with significantly less training data than traditional models. Due to the recency of the field's emergence and relative sparsity of published results, the performance characteristics of these models are not well understo…
State Key Lab of Novel Software Technology, Nanjing University（南京大学计算机软件新技术国家重点实验室）；University of Toronto（多伦多大学）；Birkbeck, University of London（伦敦大学伯贝克学院）
MIT Computer Science and Artificial Intelligence Laboratory（麻省理工学院计算机科学与人工智能实验室）
In robotic domains, learning and planning are complicated by continuous state spaces, continuous action spaces, and long task horizons. In this work, we address these challenges with Neuro-Symbolic Relational Transition Models (NSRTs), a novel class of models that are data-efficient to learn, compatible with powerful robotic planning methods, and generalizable over objects. NSRTs have both symbolic and neural components, enabling a bilevel planning scheme where symbolic AI planning in an outer loop guides continuous planning with neural models in an inner loop. Experiments in four robotic plan…
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…
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）
Max Planck Institute for Software Systems（马克斯·普朗克软件系统研究所）；TU Darmstadt（达姆施塔特工业大学）
Formal verification has emerged as a powerful approach to ensure the safety and reliability of deep neural networks. However, current verification tools are limited to only a handful of properties that can be expressed as first-order constraints over the inputs and output of a network. While adversarial robustness and fairness fall under this category, many real-world properties (e.g., "an autonomous vehicle has to stop in front of a stop sign") remain outside the scope of existing verification technology. To mitigate this severe practical restriction, we introduce a novel framework for verify…
A Neuro-Symbolic Framework for Answering Graph Pattern Queries in Knowledge Graphs
University of Antwerp（安特卫普大学）；Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）；Elsevier（爱思唯尔）；Universidad Católica de Chile（智利天主教大学）；CENIA Chile（智利CENIA机构）；Inst. for Math. and Comp. Eng.（数学与计算工程研究所）；IMFD Chile（智利IMFD机构）
Unlocking the Potential of Generative AI through Neuro-Symbolic Architectures: Benefits and Limitations
ICB UMR 6303 CNRS（ICB UMR 6303 法国国家科学研究中心）；Université Marie et Louis Pasteur（玛丽和路易·巴斯德大学）；UTBM（贝尔福-蒙贝利亚尔技术大学）；Université Bourgogne Europe（勃艮第欧洲大学）；Institut universitaire de France (IUF)（法国大学研究院）
Humans have the ability to rapidly understand rich combinatorial concepts from limited data. Here we investigate this ability in the context of auditory signals, which have been evolved in a cultural transmission experiment to study the emergence of combinatorial structure in language. We propose a neuro-symbolic generative model which combines the strengths of previous approaches to concept learning. Our model performs fast inference drawing on neural network methods, while still retaining the interpretability and generalization from limited data seen in structured generative approaches. This…
When neural networks are used to solve differential equations, they usually produce solutions in the form of black-box functions that are not directly mathematically interpretable. We introduce a method for generating symbolic expressions to solve differential equations while leveraging deep learning training methods. Unlike existing methods, our system does not require learning a language model over symbolic mathematics, making it scalable, compact, and easily adaptable for a variety of tasks and configurations. As part of the method, we propose a novel neural architecture for learning mathem…
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）
