We introduce the Deep Symbolic Network (DSN) model, which aims at becoming the white-box version of Deep Neural Networks (DNN). The DSN model provides a simple, universal yet powerful structure, similar to DNN, to represent any knowledge of the world, which is transparent to humans. The conjecture behind the DSN model is that any type of real world objects sharing enough common features are mapped into human brains as a symbol. Those symbols are connected by links, representing the composition, correlation, causality, or other relationships between them, forming a deep, hierarchical symbolic network structure. Powered by such a structure, the DSN model is expected to learn like humans, because of its unique characteristics. First, it is universal, using the same structure to store any knowledge. Second, it can learn symbols from the world and construct the deep symbolic networks automatically, by utilizing the fact that real world objects have been naturally separated by singularities. Third, it is symbolic, with the capacity of performing causal deduction and generalization. Fourth, the symbols and the links between them are transparent to us, and thus we will know what it has learned or not - which is the key for the security of an AI system. Fifth, its transparency enables it to learn with relatively small data. Sixth, its knowledge can be accumulated. Last but not least, it is more friendly to unsupervised learning than DNN. We present the details of the model, the algorithm powering its automatic learning ability, and describe its usefulness in different use cases. The purpose of this paper is to generate broad interest to develop it within an open source project centered on the Deep Symbolic Network (DSN) model towards the development of general AI.
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 concept graphs. Embodied concept representations are modality specific and exist in the form of feature vectors in a feature space. Symbolic concept representations, on the other hand, are amodal and language specific, and exist in the form of word / knowledge-graph embeddings in a concept / knowledge space. The human conceptual system comprises both embodied…
The ability to use symbols is the pinnacle of human intelligence, but has yet to be fully replicated in machines. Here we argue that the path towards symbolically fluent artificial intelligence (AI) begins with a reinterpretation of what symbols are, how they come to exist, and how a system behaves when it uses them. We begin by offering an interpretation of symbols as entities whose meaning is established by convention. But crucially, something is a symbol only for those who demonstrably and actively participate in this convention. We then outline how this interpretation thematically unifies …
Towards Symbolic XAI -- Explanation Through Human Understandable Logical Relationships Between Features
Berlin Institute for the Foundations of Learning（柏林学习与数据基础研究所）；Machine Learning Group, Technical University of Berlin（柏林技术大学机器学习组）；Department of Artificial Intelligence, Korea University（韩国大学人工智能系）；Department of Mathematics and Computer Science, Free University of Berlin（柏林自由大学数学与计算机科学系）
University of Bologna（博洛尼亚大学）；TU Darmstadt（达姆施塔特工业大学）；University of Modena and Reggio Emilia（摩德纳-雷焦艾米利亚大学）
Deep learning is bringing remarkable contributions to the field of argumentation mining, but the existing approaches still need to fill the gap toward performing advanced reasoning tasks. In this position paper, we posit that neural-symbolic and statistical relational learning could play a crucial role in the integration of symbolic and sub-symbolic methods to achieve this goal.
Università degli Studi di Urbino “Carlo Bo”（乌尔比诺“卡洛·博”大学）
Opaque models belonging to the machine learning world are ever more exploited in the most different application areas. These models, acting as black boxes (BB) from the human perspective, cannot be entirely trusted if the application is critical unless there exists a method to extract symbolic and human-readable knowledge out of them. In this paper we analyse a recurrent design adopted by symbolic knowledge extractors for BB regressors - that is, the creation of rules associated with hypercubic input space regions. We argue that this kind of partitioning may lead to suboptimal solutions when t…
Generating complex behaviors that satisfy the preferences of non-expert users is a crucial requirement for AI agents. Interactive reward learning from trajectory comparisons (a.k.a. RLHF) is one way to allow non-expert users to convey complex objectives by expressing preferences over short clips of agent behaviors. Even though this parametric method can encode complex tacit knowledge present in the underlying tasks, it implicitly assumes that the human is unable to provide richer feedback than binary preference labels, leading to intolerably high feedback complexity and poor user experience. W…
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…
Robots that interact with humans in a physical space or application need to think about the person's posture, which typically comes from visual sensors like cameras and infra-red. Artificial intelligence and machine learning algorithms use information from these sensors either directly or after some level of symbolic abstraction, and the latter usually partitions the range of observed values to discretize the continuous signal data. Although these representations have been effective in a variety of algorithms with respect to accuracy and task completion, the underlying models are rarely interp…
Michigan State University（密歇根州立大学）；Sichuan University（四川大学）；Florida Institute for Human and Machine Cognition（佛罗里达人类与机器认知研究所）
We demonstrate a library for the integration of domain knowledge in deep learning architectures. Using this library, the structure of the data is expressed symbolically via graph declarations and the logical constraints over outputs or latent variables can be seamlessly added to the deep models. The domain knowledge can be defined explicitly, which improves the models' explainability in addition to the performance and generalizability in the low-data regime. Several approaches for such an integration of symbolic and sub-symbolic models have been introduced; however, there is no library to faci…
School of Computer Science, Sun Yat-Sen University（中山大学计算机学院）；Noah’s Ark Lab Huawei（华为诺亚方舟实验室）；UM-SJTU Joint Institute, Shanghai Jiao Tong University（上海交通大学密西根学院）
Recent progress in deep reinforcement learning (DRL) can be largely attributed to the use of neural networks. However, this black-box approach fails to explain the learned policy in a human understandable way. To address this challenge and improve the transparency, we propose a Neural Symbolic Reinforcement Learning framework by introducing symbolic logic into DRL. This framework features a fertilization of reasoning and learning modules, enabling end-to-end learning with prior symbolic knowledge. Moreover, interpretability is achieved by extracting the logical rules learned by the reasoning m…
Deep reinforcement learning (DRL) has gained great success by learning directly from high-dimensional sensory inputs, yet is notorious for the lack of interpretability. Interpretability of the subtasks is critical in hierarchical decision-making as it increases the transparency of black-box-style DRL approach and helps the RL practitioners to understand the high-level behavior of the system better. In this paper, we introduce symbolic planning into DRL and propose a framework of Symbolic Deep Reinforcement Learning (SDRL) that can handle both high-dimensional sensory inputs and symbolic planni…
Deep reinforcement learning (DRL) brings the power of deep neural networks to bear on the generic task of trial-and-error learning, and its effectiveness has been convincingly demonstrated on tasks such as Atari video games and the game of Go. However, contemporary DRL systems inherit a number of shortcomings from the current generation of deep learning techniques. For example, they require very large datasets to work effectively, entailing that they are slow to learn even when such datasets are available. Moreover, they lack the ability to reason on an abstract level, which makes it difficult…
University of California, Los Angeles（加州大学洛杉矶分校）；Peking University（北京大学）
This paper develops a novel methodology for using symbolic knowledge in deep learning. From first principles, we derive a semantic loss function that bridges between neural output vectors and logical constraints. This loss function captures how close the neural network is to satisfying the constraints on its output. An experimental evaluation shows that it effectively guides the learner to achieve (near-)state-of-the-art results on semi-supervised multi-class classification. Moreover, it significantly increases the ability of the neural network to predict structured objects, such as rankings a…
Automaton Distillation: Neuro-Symbolic Transfer Learning for Deep Reinforcement Learning
University of Texas at San Antonio（德克萨斯大学圣安东尼奥分校）；University of Central Florida（中佛罗里达大学）；Air Force Research Laboratory（空军研究实验室）；Florida International University（佛罗里达国际大学）；University of Colorado（科罗拉多大学）
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 …
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…
University of Toronto（多伦多大学）；Vector Institute（矢量研究所）；Schwartz Reisman Institute for Technology and Society（施瓦茨·赖斯曼技术与社会研究所）；Pontificia Universidad Católica de Chile（智利天主教大学）；Centro Nacional de Inteligencia Artificial（国家人工智能中心）
Natural and formal languages provide an effective mechanism for humans to specify instructions and reward functions. We investigate how to generate policies via RL when reward functions are specified in a symbolic language captured by Reward Machines, an increasingly popular automaton-inspired structure. We are interested in the case where the mapping of environment state to a symbolic (here, Reward Machine) vocabulary -- commonly known as the labelling function -- is uncertain from the perspective of the agent. We formulate the problem of policy learning in Reward Machines with noisy symbolic…
Abstract symbolic reasoning, as required in domains such as mathematics and logic, is a key component of human intelligence. Solvers for these domains have important applications, especially to computer-assisted education. But learning to solve symbolic problems is challenging for machine learning algorithms. Existing models either learn from human solutions or use hand-engineered features, making them expensive to apply in new domains. In this paper, we instead consider symbolic domains as simple environments where states and actions are given as unstructured text, and binary rewards indicate…
Deep Reinforcement Learning (deep RL) has made several breakthroughs in recent years in applications ranging from complex control tasks in unmanned vehicles to game playing. Despite their success, deep RL still lacks several important capacities of human intelligence, such as transfer learning, abstraction and interpretability. Deep Symbolic Reinforcement Learning (DSRL) seeks to incorporate such capacities to deep Q-networks (DQN) by learning a relevant symbolic representation prior to using Q-learning. In this paper, we propose a novel extension of DSRL, which we call Symbolic Reinforcement …
Symbolic Relational Deep Reinforcement Learning based on Graph Neural Networks and Autoregressive Policy Decomposition
Czech Technical University in Prague（布拉格捷克技术大学）；Artificial Intelligence Center, Department of Computer Science, Faculty of Electrical Engineering（电气工程学院计算机科学系人工智能中心）
Airbus Central Research & Technology（空客中央研究与技术部）；TU Wien（维也纳工业大学）；Fraunhofer（弗劳恩霍夫研究所）
Cognitive theories for reasoning are about understanding how humans come to conclusions from a set of premises. Starting from hypothetical thoughts, we are interested which are the implications behind basic everyday language and how do we reason with them. A widely studied topic is whether cognitive theories can account for typical reasoning tasks and be confirmed by own empirical experiments. This paper takes a different view and we do not propose a theory, but instead take findings from the literature and show how these, formalized as cognitive principles within a logical framework, can esta…
Sequences and time-series often arise in robot tasks, e.g., in activity recognition and imitation learning. In recent years, deep neural networks (DNNs) have emerged as an effective data-driven methodology for processing sequences given sufficient training data and compute resources. However, when data is limited, simpler models such as logic/rule-based methods work surprisingly well, especially when relevant prior knowledge is applied in their construction. However, unlike DNNs, these "structured" models can be difficult to extend, and do not work well with raw unstructured data. In this work…
The notion of equality (identity) is simple and ubiquitous, making it a key case study for broader questions about the representations supporting abstract relational reasoning. Previous work suggested that neural networks were not suitable models of human relational reasoning because they could not represent mathematically identity, the most basic form of equality. We revisit this question. In our experiments, we assess out-of-sample generalization of equality using both arbitrary representations and representations that have been pretrained on separate tasks to imbue them with structure. We f…
Aligning LLM+PDDL Symbolic Plans with Human Objective Specifications through Evolutionary Algorithm Guidance
College of Engineering and Computer Science, University of Central Florida（中央佛罗里达大学工程与计算机科学学院）；Robotics Institute, Carnegie Mellon University（卡内基梅隆大学机器人研究所）
Explanations for \emph{black-box} models help us understand model decisions as well as provide information on model biases and inconsistencies. Most of the current explainability techniques provide a single level of explanation, often in terms of feature importance scores or feature attention maps in input space. Our focus is on explaining deep discriminative models at \emph{multiple levels of abstraction}, from fine-grained to fully abstract explanations. We achieve this by using the natural properties of \emph{hyperbolic geometry} to more efficiently model a hierarchy of symbolic features an…
Model-based reinforcement learning algorithms are typically more sample efficient than their model-free counterparts, especially in sparse reward problems. Unfortunately, many interesting domains are too complex to specify the complete models required by traditional model-based approaches. Learning a model takes a large number of environment samples, and may not capture critical information if the environment is hard to explore. If we could specify an incomplete model and allow the agent to learn how best to use it, we could take advantage of our partial understanding of many domains. Existing…
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；Beijing Forestry University（北京林业大学）；Griffith University（格里菲斯大学）
There is a wide gap between symbolic reasoning and deep learning. In this research, we explore the possibility of using deep learning to improve symbolic reasoning. Briefly, in a reasoning system, a deep feedforward neural network is used to guide rewriting processes after learning from algebraic reasoning examples produced by humans. To enable the neural network to recognise patterns of algebraic expressions with non-deterministic sizes, reduced partial trees are used to represent the expressions. Also, to represent both top-down and bottom-up information of the expressions, a centralisation …
University of Urbino（乌尔比诺大学）；Alma Mater Studiorum —University of Bologna（博洛尼亚大学）
As opaque decision systems are being increasingly adopted in almost any application field, issues about their lack of transparency and human readability are a concrete concern for end-users. Amongst existing proposals to associate human-interpretable knowledge with accurate predictions provided by opaque models, there are rule extraction techniques, capable of extracting symbolic knowledge out of an opaque model. However, how to assess the level of readability of the extracted knowledge quantitatively is still an open issue. Finding such a metric would be the key, for instance, to enable autom…
Large Language Models as symbolic DNA of cultural dynamics
Human Energy（人类能源）；San Francisco VA Medical Center（旧金山退伍军人医疗中心）；University of California, San Francisco（加州大学旧金山分校）；University of California, Berkeley（加州大学伯克利分校）
Facebook（脸书）；EPFL（洛桑联邦理工学院）；University of Washington（华盛顿大学）；Carnegie Mellon University（卡内基梅隆大学）
One of the challenges faced by conversational agents is their inability to identify unstated presumptions of their users' commands, a task trivial for humans due to their common sense. In this paper, we propose a zero-shot commonsense reasoning system for conversational agents in an attempt to achieve this. Our reasoner uncovers unstated presumptions from user commands satisfying a general template of if-(state), then-(action), because-(goal). Our reasoner uses a state-of-the-art transformer-based generative commonsense knowledge base (KB) as its source of background knowledge for reasoning. W…
