Neuro-symbolic approaches to artificial intelligence, which combine neural networks with classical symbolic techniques, are growing in prominence, necessitating formal approaches to reason about their correctness. We propose a novel modelling formalism called neuro-symbolic concurrent stochastic games (NS-CSGs), which comprise two probabilistic finite-state agents interacting in a shared continuous-state environment. Each agent observes the environment using a neural perception mechanism, which converts inputs such as images into symbolic percepts, and makes decisions symbolically. We focus on the class of NS-CSGs with Borel state spaces and prove the existence and measurability of the value function for zero-sum discounted cumulative rewards under piecewise-constant restrictions on the components of this class of models. To compute values and synthesise strategies, we present, for the first time, practical value iteration (VI) and policy iteration (PI) algorithms to solve this new subclass of continuous-state CSGs. These require a finite decomposition of the environment induced by the neural perception mechanisms of the agents and rely on finite abstract representations of value functions and strategies closed under VI or PI. First, we introduce a Borel measurable piecewise-constant (B-PWC) representation of value functions, extend minimax backups to this representation and propose a value iteration algorithm called B-PWC VI. Second, we introduce two novel representations for the value functions and strategies, constant-piecewise-linear (CON-PWL) and constant-piecewise-constant (CON-PWC) respectively, and propose Minimax-action-free PI by extending a recent PI method based on alternating player choices for finite state spaces to Borel state spaces, which does not require normal-form games to be solved.
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.
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.
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）
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…
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 …
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…
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）
We introduce Natlog, a lightweight Logic Programming language, sharing Prolog's unification-driven execution model, but with a simplified syntax and semantics. Our proof-of-concept Natlog implementation is tightly embedded in the Python-based deep-learning ecosystem with focus on content-driven indexing of ground term datasets. As an overriding of our symbolic indexing algorithm, the same function can be delegated to a neural network, serving ground facts to Natlog's resolution engine. Our open-source implementation is available as a Python package at https://pypi.org/project/natlog/ .
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…
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 …
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…
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…
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.
