We study the problem of learning probabilistic first-order logical rules for knowledge base reasoning. This learning problem is difficult because it requires learning the parameters in a continuous space as well as the structure in a discrete space. We propose a framework, Neural Logic Programming, that combines the parameter and structure learning of first-order logical rules in an end-to-end differentiable model. This approach is inspired by a recently-developed differentiable logic called TensorLog, where inference tasks can be compiled into sequences of differentiable operations. We design a neural controller system that learns to compose these operations. Empirically, our method outperforms prior work on multiple knowledge base benchmark datasets, including Freebase and WikiMovies.
Combining machine learning with logic-based expert systems in order to get the best of both worlds are becoming increasingly popular. However, to what extent machine learning can already learn to reason over rule-based knowledge is still an open problem. In this paper, we explore how symbolic logic, defined as logic programs at a character level, is learned to be represented in a high-dimensional vector space using RNN-based iterative neural networks to perform reasoning. We create a new dataset that defines 12 classes of logic programs exemplifying increased level of complexity of logical rea…
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）
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 …
MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；IBM Research（IBM研究院）；University College London（伦敦大学学院）
A hallmark of human cognition is the ability to continually acquire and distill observations of the world into meaningful, predictive theories. In this paper we present a new mechanism for logical theory acquisition which takes a set of observed facts and learns to extract from them a set of logical rules and a small set of core facts which together entail the observations. Our approach is neuro-symbolic in the sense that the rule pred- icates and core facts are given dense vector representations. The rules are applied to the core facts using a soft unification procedure to infer additional fa…
Generating Graph-Like Logical Rules for Knowledge Graph Reasoning via Diffusion Models
Laboratory for Big Data and Decision（大数据与决策实验室）；National University of Defense Technology（国防科技大学）；National Key Laboratory of Information Systems Engineering（信息系统工程国家重点实验室）；Microsoft Corporation（微软公司）；College of Computer Science and Technology（计算机科学与技术学院）
We propose a novel paradigm for solving Inductive Logic Programming (ILP) problems via deep recurrent neural networks. This proposed ILP solver is designed based on differentiable implementation of the deduction via forward chaining. In contrast to the majority of past methods, instead of searching through the space of possible first-order logic rules by using some restrictive rule templates, we directly learn the symbolic logical predicate rules by introducing a novel differentiable Neural Logic (dNL) network. The proposed dNL network is able to learn and represent Boolean functions efficient…
Interpretable and Explainable Logical Policies via Neurally Guided Symbolic Abstraction
Technical University of Darmstadt（达姆施塔特工业大学）；National Research Center for Applied Cybersecurity（国家应用网络安全研究中心）；Eindhoven University of Technology（埃因霍温理工大学）；Hessian Center for AI (hessian.AI)（黑森人工智能中心）；German Research Center for AI (DFKI)（德国人工智能研究中心）
We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a highly intepretable disentangled representation. Inference is omnidirectional rather than focused on predefined target variables, and corresponds to logical reasoning, including classical first-order logic theorem proving as a special case. The model is end-to-end differentiable, and learning minimizes a novel loss function capturing logical contradiction, …
Recent work on neuro-symbolic inductive logic programming has led to promising approaches that can learn explanatory rules from noisy, real-world data. While some proposals approximate logical operators with differentiable operators from fuzzy or real-valued logic that are parameter-free thus diminishing their capacity to fit the data, other approaches are only loosely based on logic making it difficult to interpret the learned "rules". In this paper, we propose learning rules with the recently proposed logical neural networks (LNN). Compared to others, LNNs offer strong connection to classica…
Exploring the Paradigm Shift from Grounding to Skolemization for Complex Query Answering on Knowledge Graphs
School of Computer Science and Engineering, Sun Yat-sen University（中山大学计算机科学与工程学院）；School of Data Science, Lingnan University（岭南大学数据科学学院）；School of Science and Technology, Hong Kong Metropolitan University（香港理工大学科技学院）；Department of Computing, The Hong Kong Polytechnic University（香港理工大学计算机系）
Neurosymbolic Framework for Concept-Driven Logical Reasoning in Skeleton-Based Human Action Recognition
Department of ECSE, Faculty of Engineering, Monash University, Australia（莫纳什大学工程学院电子与计算机工程系，澳大利亚）；AIM for Health Lab, Faculty of Information Technology, Monash University, Australia（莫纳什大学信息科技学院健康人工智能实验室，澳大利亚）；Department of DSAI, Faculty of Information Technology, Monash University, Australia（莫纳什大学信息科技学院数据科学与人工智能系，澳大利亚）
TU Darmstadt（达姆施塔特工业大学）；Centre for Cognitive Science, TU Darmstadt（达姆施塔特工业大学认知科学中心）；Hessian Center for AI (hessian.AI)（黑森人工智能中心）
Reasoning is an essential part of human intelligence and thus has been a long-standing goal in artificial intelligence research. With the recent success of deep learning, incorporating reasoning with deep learning systems, i.e., neuro-symbolic AI has become a major field of interest. We propose the Neuro-Symbolic Forward Reasoner (NSFR), a new approach for reasoning tasks taking advantage of differentiable forward-chaining using first-order logic. The key idea is to combine differentiable forward-chaining reasoning with object-centric (deep) learning. Differentiable forward-chaining reasoning …
Improved Logical Reasoning of Language Models via Differentiable Symbolic Programming
Carnegie Mellon University（卡内基梅隆大学）；University of Pennsylvania（宾夕法尼亚大学）；Mohamed Bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Petuum Inc.（Petuum公司）
UCL Centre for Artificial Intelligence, University College London（伦敦大学学院人工智能中心）；Facebook AI Research（Facebook 人工智能研究院）
Attempts to render deep learning models interpretable, data-efficient, and robust have seen some success through hybridisation with rule-based systems, for example, in Neural Theorem Provers (NTPs). These neuro-symbolic models can induce interpretable rules and learn representations from data via back-propagation, while providing logical explanations for their predictions. However, they are restricted by their computational complexity, as they need to consider all possible proof paths for explaining a goal, thus rendering them unfit for large-scale applications. We present Conditional Theorem …
Carnegie Mellon University（卡内基梅隆大学）；University of Southern California（南加州大学）；Bosch Center for Artificial Intelligence（博世人工智能中心）
Integrating logical reasoning within deep learning architectures has been a major goal of modern AI systems. In this paper, we propose a new direction toward this goal by introducing a differentiable (smoothed) maximum satisfiability (MAXSAT) solver that can be integrated into the loop of larger deep learning systems. Our (approximate) solver is based upon a fast coordinate descent approach to solving the semidefinite program (SDP) associated with the MAXSAT problem. We show how to analytically differentiate through the solution to this SDP and efficiently solve the associated backward pass. W…
We introduce a theorem proving approach to the specification and generation of temporal logical constraints for training neural networks. We formalise a deep embedding of linear temporal logic over finite traces (LTL$_f$) and an associated evaluation function characterising its semantics within the higher-order logic of the Isabelle theorem prover. We then proceed to formalise a loss function $\mathcal{L}$ that we formally prove to be sound, and differentiable to a function $d\mathcal{L}$. We subsequently use Isabelle's automatic code generation mechanism to produce OCaml versions of LTL$_f$, …
University of Manchester（曼彻斯特大学）；Idiap Research Institute（Idiap研究所）
Integer Linear Programming (ILP) provides a viable mechanism to encode explicit and controllable assumptions about explainable multi-hop inference with natural language. However, an ILP formulation is non-differentiable and cannot be integrated into broader deep learning architectures. Recently, Thayaparan et al. (2021a) proposed a novel methodology to integrate ILP with Transformers to achieve end-to-end differentiability for complex multi-hop inference. While this hybrid framework has been demonstrated to deliver better answer and explanation selection than transformer-based and existing ILP…
Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）；Civic AI Lab, Amsterdam（阿姆斯特丹公民人工智能实验室）
The AI community is increasingly putting its attention towards combining symbolic and neural approaches, as it is often argued that the strengths and weaknesses of these approaches are complementary. One recent trend in the literature are weakly supervised learning techniques that employ operators from fuzzy logics. In particular, these use prior background knowledge described in such logics to help the training of a neural network from unlabeled and noisy data. By interpreting logical symbols using neural networks, this background knowledge can be added to regular loss functions, hence making…
A neurosymbolic Approach with Epistemic Deep Learning for Hierarchical Image Classification
Institute for AI, Data Analysis and Systems (AIDAS) School of Engineering, Computing and Mathematics, Oxford Brookes University, UK（人工智能、数据分析和系统研究所（AIDAS）工程、计算与数学学院，英国奥克斯福德布鲁克斯大学）
Large knowledge bases (KBs) are useful in many tasks, but it is unclear how to integrate this sort of knowledge into "deep" gradient-based learning systems. To address this problem, we describe a probabilistic deductive database, called TensorLog, in which reasoning uses a differentiable process. In TensorLog, each clause in a logical theory is first converted into certain type of factor graph. Then, for each type of query to the factor graph, the message-passing steps required to perform belief propagation (BP) are "unrolled" into a function, which is differentiable. We show that these functi…
Conventional deep reinforcement learning methods are sample-inefficient and usually require a large number of training trials before convergence. Since such methods operate on an unconstrained action set, they can lead to useless actions. A recent neuro-symbolic framework called the Logical Neural Networks (LNNs) can simultaneously provide key-properties of both neural networks and symbolic logic. The LNNs functions as an end-to-end differentiable network that minimizes a novel contradiction loss to learn interpretable rules. In this paper, we utilize LNNs to define an inference graph using ba…
We propose Differentiable Satisfiability and Differentiable Answer Set Programming (Differentiable SAT/ASP) for multi-model optimization. Models (answer sets or satisfying truth assignments) are sampled using a novel SAT/ASP solving approach which uses a gradient descent-based branching mechanism. Sampling proceeds until the value of a user-defined multi-model cost function reaches a given threshold. As major use cases for our approach we propose distribution-aware model sampling and expressive yet scalable probabilistic logic programming. As our main algorithmic approach to Differentiable SAT…
University of Oxford（牛津大学）；University College London（伦敦大学学院）；Bloomsbury AI（布卢姆斯伯里人工智能公司）
We introduce neural networks for end-to-end differentiable proving of queries to knowledge bases by operating on dense vector representations of symbols. These neural networks are constructed recursively by taking inspiration from the backward chaining algorithm as used in Prolog. Specifically, we replace symbolic unification with a differentiable computation on vector representations of symbols using a radial basis function kernel, thereby combining symbolic reasoning with learning subsymbolic vector representations. By using gradient descent, the resulting neural network can be trained to in…
We introduce Differentiable Reasoning (DR), a novel semi-supervised learning technique which uses relational background knowledge to benefit from unlabeled data. We apply it to the Semantic Image Interpretation (SII) task and show that background knowledge provides significant improvement. We find that there is a strong but interesting imbalance between the contributions of updates from Modus Ponens (MP) and its logical equivalent Modus Tollens (MT) to the learning process, suggesting that our approach is very sensitive to a phenomenon called the Raven Paradox. We propose a solution to overcom…
Symbolic knowledge can provide crucial inductive bias for training neural models, especially in low data regimes. A successful strategy for incorporating such knowledge involves relaxing logical statements into sub-differentiable losses for optimization. In this paper, we study the question of how best to relax logical expressions that represent labeled examples and knowledge about a problem; we focus on sub-differentiable t-norm relaxations of logic. We present theoretical and empirical criteria for characterizing which relaxation would perform best in various scenarios. In our theoretical st…
Letter-string analogy is an important analogy learning task which seems to be easy for humans but very challenging for machines. The main idea behind current approaches to solving letter-string analogies is to design heuristic rules for extracting analogy structures and constructing analogy mappings. However, one key problem is that it is difficult to build a comprehensive and exhaustive set of analogy structures which can fully describe the subtlety of analogies. This problem makes current approaches unable to handle complicated letter-string analogy problems. In this paper, we propose Neural…
University of Alberta（阿尔伯塔大学）；Carnegie Mellon University（卡内基梅隆大学）
Natural language inference (NLI) aims to determine the logical relationship between two sentences, such as Entailment, Contradiction, and Neutral. In recent years, deep learning models have become a prevailing approach to NLI, but they lack interpretability and explainability. In this work, we address the explainability of NLI by weakly supervised logical reasoning, and propose an Explainable Phrasal Reasoning (EPR) approach. Our model first detects phrases as the semantic unit and aligns corresponding phrases in the two sentences. Then, the model predicts the NLI label for the aligned phrases…
Deep reinforcement learning (RL) methods often require many trials before convergence, and no direct interpretability of trained policies is provided. In order to achieve fast convergence and interpretability for the policy in RL, we propose a novel RL method for text-based games with a recent neuro-symbolic framework called Logical Neural Network, which can learn symbolic and interpretable rules in their differentiable network. The method is first to extract first-order logical facts from text observation and external word meaning network (ConceptNet), then train a policy in the network with …
KAIST（韩国科学技术院）；Institute for Basic Science (IBS)（基础科学研究院）
SATNet is a differentiable constraint solver with a custom backpropagation algorithm, which can be used as a layer in a deep-learning system. It is a promising proposal for bridging deep learning and logical reasoning. In fact, SATNet has been successfully applied to learn, among others, the rules of a complex logical puzzle, such as Sudoku, just from input and output pairs where inputs are given as images. In this paper, we show how to improve the learning of SATNet by exploiting symmetries in the target rules of a given but unknown logical puzzle or more generally a logical formula. We prese…
Laboratoire Psychologie de la Perception（感知心理学实验室）；Université Paris Descartes（巴黎笛卡尔大学）
In this work we propose a system for visual question answering. Our architecture is composed of two parts, the first part creates the logical knowledge base given the image. The second part evaluates questions against the knowledge base. Differently from previous work, the knowledge base is represented using hyper-dimensional computing. This choice has the advantage that all the operations in the system, namely creating the knowledge base and evaluating the questions against it, are differentiable, thereby making the system easily trainable in an end-to-end fashion.
Graphs can represent relational information among entities and graph structures are widely used in many intelligent tasks such as search, recommendation, and question answering. However, most of the graph-structured data in practice suffers from incompleteness, and thus link prediction becomes an important research problem. Though many models are proposed for link prediction, the following two problems are still less explored: (1) Most methods model each link independently without making use of the rich information from relevant links, and (2) existing models are mostly designed based on assoc…
Fondazione Bruno Kessler（布鲁诺·凯斯勒基金会）；Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）
Recent work has shown logical background knowledge can be used in learning systems to compensate for a lack of labeled training data. Many methods work by creating a loss function that encodes this knowledge. However, often the logic is discarded after training, even if it is still useful at test time. Instead, we ensure neural network predictions satisfy the knowledge by refining the predictions with an extra computation step. We introduce differentiable refinement functions that find a corrected prediction close to the original prediction. We study how to effectively and efficiently compute …
Existing Collaborative Filtering (CF) methods are mostly designed based on the idea of matching, i.e., by learning user and item embeddings from data using shallow or deep models, they try to capture the associative relevance patterns in data, so that a user embedding can be matched with relevant item embeddings using designed or learned similarity functions. However, as a cognition rather than a perception intelligent task, recommendation requires not only the ability of pattern recognition and matching from data, but also the ability of cognitive reasoning in data. In this paper, we propose …
