"Today's expert systems deal with domains of narrow specialization. For expert systems to perform competently over a broad range of tasks, they will have to be given very much more knowledge. ... The next generation of expert systems ... will require large knowledge bases. How will we get them?"
– Edward Feigenbaum, Pamela McCorduck, H. Penny Nii, from The Rise of the Expert Company. New York: Times Books, 1988.
We introduce deep neural networks for end-to-end differentiable theorem proving that operate on dense vector representations of symbols. These neural networks are recursively constructed by following 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. The resulting neural network can be trained to infer facts from a given incomplete knowledge base using gradient descent. By doing so, it learns to (i) place representations of similar symbols in close proximity in a vector space, (ii) make use of such similarities to prove facts, (iii) induce logical rules, and (iv) it can use provided and induced logical rules for complex multi-hop reasoning.
We present the Multi-value Rule Set (MRS) for interpretable classification with feature efficient presentations. Compared to rule sets built from single-value rules, MRS adopts a more generalized form of association rules that allows multiple values in a condition. Rules of this form are more concise than classical single-value rules in capturing and describing patterns in data. Our formulation also pursues a higher efficiency of feature utilization, which reduces possible cost in data collection and storage. We propose a Bayesian framework for formulating an MRS model and develop an efficient inference method for learning a maximum a posteriori, incorporating theoretically grounded bounds to iteratively reduce the search space and improve the search efficiency.
A common problem in knowledge representation and related fields is reasoning over a large joint knowledge graph, represented as triples of a relation between two entities. The goal of this paper is to develop a more powerful neural network model suitable for inference over these relationships. Previous models suffer from weak interaction between entities or simple linear projection of the vector space. We address these problems by introducing a neural tensor network (NTN) model which allow the entities and relations to interact multiplicatively. Additionally, we observe that such knowledge base models can be further improved by representing each entity as the average of vectors for the words in the entity name, giving an additional dimension of similarity by which entities can share statistical strength.
Statistical Relational Learning (SRL) methods are the most widely used techniques to generate distributional representations of the symbolic Knowledge Bases (KBs). These methods embed any given KB into a vector space by exploiting statistical similarities among its entities and predicates but without any guarantee of preserving the underlying logical structure of the KB. This, in turn, results in poor performance of logical reasoning tasks that are solved using such distributional representations. We present a novel approach called Embed2Reason (E2R) that embeds a symbolic KB into a vector space in a logical structure preserving manner. This approach is inspired by the theory of Quantum Logic.
This paper considers the learning of Boolean rules in either disjunctive normal form (DNF, OR-of-ANDs, equivalent to decision rule sets) or conjunctive normal form (CNF, AND-of-ORs) as an interpretable model for classification. An integer program is formulated to optimally trade classification accuracy for rule simplicity. Column generation (CG) is used to efficiently search over an exponential number of candidate clauses (conjunctions or disjunctions) without the need for heuristic rule mining. This approach also bounds the gap between the selected rule set and the best possible rule set on the training data. To handle large datasets, we propose an approximate CG algorithm using randomization.
In this work, we aim to leverage prior symbolic knowledge to improve the performance of deep models. We propose a graph embedding network that projects propositional formulae (and assignments) onto a manifold via an augmented Graph Convolutional Network (GCN). To generate semantically-faithful embeddings, we develop techniques to recognize node heterogeneity, and semantic regularization that incorporate structural constraints into the embedding. Experiments show that our approach improves the performance of models trained to perform entailment checking and visual relation prediction. Interestingly, we observe a connection between the tractability of the propositional theory representation and the ease of embedding.
We present an approach to map utterances in conversation to logical forms, which will be executed on a large-scale knowledge base. To handle enormous ellipsis phenomena in conversation, we introduce dialog memory management to manipulate historical entities, predicates, and logical forms when inferring the logical form of current utterances. Dialog memory management is embodied in a generative model, in which a logical form is interpreted in a top-down manner following a small and flexible grammar. We learn the model from denotations without explicit annotation of logical forms, and evaluate it on a large-scale dataset consisting of 200K dialogs over 12.8M entities. Results verify the benefits of modeling dialog memory, and show that our semantic parsing-based approach outperforms a memory network based encoder-decoder model by a huge margin.
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.
Report Scope: The scope of the report includes, a general outlook of the analytics industry, with the scope limited to reports published during the year 2016, 2017 and 2018. This report covers only advanced analytics, artificial intelligence, and cognitive computing technologies. GNW The advanced analytics market covers the following solutions: software tools, integrated hardware appliances, and services. The advanced analytics market comprises applications for the following industries: banking and financial services, telecommunications and IT, healthcare, government and defense, transportation and logistics, and consumer goods and retail. The AI market covers machine learning, deep learning, and expert systems as these are direct derivatives of analytics.Cognitive computing market in this report covers machine learning and expert systems.