We introduce an architecture, the Tensor Product Recurrent Network (TPRN). In our application of TPRN, internal representations learned by end-to-end optimization in a deep neural network performing a textual question-answering (QA) task can be interpreted using basic concepts from linguistic theory. No performance penalty need be paid for this increased interpretability: the proposed model performs comparably to a state-of-the-art system on the SQuAD QA task. The internal representation which is interpreted is a Tensor Product Representation: for each input word, the model selects a symbol to encode the word, and a role in which to place the symbol, and binds the two together. The selection is via soft attention. The overall interpretation is built from interpretations of the symbols, as recruited by the trained model, and interpretations of the roles as used by the model. We find support for our initial hypothesis that symbols can be interpreted as lexical-semantic word meanings, while roles can be interpreted as approximations of grammatical roles (or categories) such as subject, wh-word, determiner, etc. Fine-grained analysis reveals specific correspondences between the learned roles and parts of speech as assigned by a standard tagger ( 2003), and finds several discrepancies in the model's favor. In this sense, the model learns significant aspects of grammar, after having been exposed solely to linguistically unannotated text, questions, and answers: no prior linguistic knowledge is given to the model. What is given is the means to build representations using symbols and roles, with an inductive bias favoring use of these in an approximately discrete manner.
The present work constitutes a different approach to reintroducing approximately symbolic representations and rule-based processing into neural network computation over continuous distributed representations. In computation with TPRs, the symbols and rules are internal to the DNN; there is no separation between a central network controller and peripheral quasi-discrete modules. Items in memories are distributed representations that are combined by addition superposition rather than by being slotted into external discrete locations. Computation over TPRs is massively parallel @cite_20 .
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In this paper we present a proof-of-concept implementation of Neural Theorem Provers (NTPs), end-to-end differentiable counterparts of discrete theorem provers that perform first-order inference on vector representations of symbols using function-free, possibly parameterized, rules. As such, NTPs follow a long tradition of neural-symbolic approaches to automated knowledge base inference, but differ in that they are differentiable with respect to representations of symbols in a knowledge base and can thus learn representations of predicates, constants, as well as rules of predefined structure. Furthermore, they still allow us to incorporate domainknowledge provided as rules. The NTP presented here is realized via a differentiable version of the backward chaining algorithm. It operates on substitution representations and is able to learn complex logical dependencies from training facts of small knowledge bases. 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. The computational power of massively parallel networks of simple processing elements resides in the communication bandwidth provided by the hardware connections between elements. These connections can allow a significant fraction of the knowledge of the system to be applied to an instance of a problem in a very short time. One kind of computation for which massively parallel networks appear to be well suited is large constraint satisfaction searches, but to use the connections efficiently two conditions must be met: First, a search technique that is suitable for parallel networks must be found. Second, there must be some way of choosing internal representations which allow the preexisting hardware connections to be used efficiently for encoding the constraints in the domain being searched. We describe a general parallel search method, based on statistical mechanics, and we show how it leads to a general learning rule for modifying the connection strengths so as to incorporate knowledge about a task domain in an efficient way. We describe some simple examples in which the learning algorithm creates internal representations that are demonstrably the most efficient way of using the preexisting connectivity structure. Classification, which involves finding rules that partition a given da.ta set into disjoint groups, is one class of data mining problems. Approaches proposed so far for mining classification rules for large databases are mainly decision tree based symbolic learning methods. The connectionist approach based on neura.l networks has been thought not well suited for data mining. One of the major reasons cited is that knowledge generated by neural networks is not explicitly represented in the form of rules suitable for verification or interpretation by humans. This paper examines this issue. With our newly developed algorithms, rules which are similar to, or more concise than those generated by the symbolic methods can be extracted from the neural networks. The data mining process using neural networks with the emphasis on rule extraction is described. ExperimenM results and comparison with previously published works are presented.