End-to-End Differentiable Proving

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 infer facts from a given incomplete knowledge base. It learns to (i) place representations of similar symbols in close proximity in a vector space, (ii) make use of such similarities to prove queries, (iii) induce logical rules, and (iv) use provided and induced logical rules for multi-hop reasoning. We demonstrate that this architecture outperforms ComplEx, a state-of-the-art neural link prediction model, on three out of four benchmark knowledge bases while at the same time inducing interpretable function-free first-order logic rules.Comment: NIPS 2017 camera-ready, NIPS 201

The Mechanics of Embodiment: A Dialogue on Embodiment and Computational Modeling

Embodied theories are increasingly challenging traditional views of cognition by arguing that conceptual representations that constitute our knowledge are grounded in sensory and motor experiences, and processed at this sensorimotor level, rather than being represented and processed abstractly in an amodal conceptual system. Given the established empirical foundation, and the relatively underspecified theories to date, many researchers are extremely interested in embodied cognition but are clamouring for more mechanistic implementations. What is needed at this stage is a push toward explicit computational models that implement sensory-motor grounding as intrinsic to cognitive processes. In this article, six authors from varying backgrounds and approaches address issues concerning the construction of embodied computational models, and illustrate what they view as the critical current and next steps toward mechanistic theories of embodiment. The first part has the form of a dialogue between two fictional characters: Ernest, the �experimenter�, and Mary, the �computational modeller�. The dialogue consists of an interactive sequence of questions, requests for clarification, challenges, and (tentative) answers, and touches the most important aspects of grounded theories that should inform computational modeling and, conversely, the impact that computational modeling could have on embodied theories. The second part of the article discusses the most important open challenges for embodied computational modelling

Comparative Experiments on Disambiguating Word Senses: An Illustration of the Role of Bias in Machine Learning

This paper describes an experimental comparison of seven different learning algorithms on the problem of learning to disambiguate the meaning of a word from context. The algorithms tested include statistical, neural-network, decision-tree, rule-based, and case-based classification techniques. The specific problem tested involves disambiguating six senses of the word ``line'' using the words in the current and proceeding sentence as context. The statistical and neural-network methods perform the best on this particular problem and we discuss a potential reason for this observed difference. We also discuss the role of bias in machine learning and its importance in explaining performance differences observed on specific problems.Comment: 10 page

RNNs Implicitly Implement Tensor Product Representations

Recurrent neural networks (RNNs) can learn continuous vector representations of symbolic structures such as sequences and sentences; these representations often exhibit linear regularities (analogies). Such regularities motivate our hypothesis that RNNs that show such regularities implicitly compile symbolic structures into tensor product representations (TPRs; Smolensky, 1990), which additively combine tensor products of vectors representing roles (e.g., sequence positions) and vectors representing fillers (e.g., particular words). To test this hypothesis, we introduce Tensor Product Decomposition Networks (TPDNs), which use TPRs to approximate existing vector representations. We demonstrate using synthetic data that TPDNs can successfully approximate linear and tree-based RNN autoencoder representations, suggesting that these representations exhibit interpretable compositional structure; we explore the settings that lead RNNs to induce such structure-sensitive representations. By contrast, further TPDN experiments show that the representations of four models trained to encode naturally-occurring sentences can be largely approximated with a bag of words, with only marginal improvements from more sophisticated structures. We conclude that TPDNs provide a powerful method for interpreting vector representations, and that standard RNNs can induce compositional sequence representations that are remarkably well approximated by TPRs; at the same time, existing training tasks for sentence representation learning may not be sufficient for inducing robust structural representations.Comment: Accepted to ICLR 201