arXiv subjects

Paul Smolensky

Publications and source records attributed to Paul Smolensky.

33 records · Page 2Linked to original sources

arXiv2020

Enhancing the Transformer with Explicit Relational Encoding for Math Problem Solving

We incorporate Tensor-Product Representations within the Transformer in order to better support the explicit representation of relation structure. Our Tensor-Product Transformer (TP-Transformer) sets a new state of the art on the recently-introduced Mathematics Dataset containing 56 categories of free-form math word-problems. The essential component of the model is a novel attention mechanism, called TP-Attention, which explicitly encodes the relations between each Transformer cell and the other cells from which values have been retrieved by attention. TP-Attention goes beyond linear combination of retrieved values, strengthening representation-building and resolving ambiguities introduced by multiple layers of standard attention. The TP-Transformer's attention maps give better insights into how it is capable of solving the Mathematics Dataset's challenging problems. Pretrained models and code will be made available after publication.

cs.LG↗

arXiv2020

Mapping Natural-language Problems to Formal-language Solutions Using Structured Neural Representations

Generating formal-language programs represented by relational tuples, such as Lisp programs or mathematical operations, to solve problems stated in natural language is a challenging task because it requires explicitly capturing discrete symbolic structural information implicit in the input. However, most general neural sequence models do not explicitly capture such structural information, limiting their performance on these tasks. In this paper, we propose a new encoder-decoder model based on a structured neural representation, Tensor Product Representations (TPRs), for mapping Natural-language problems to Formal-language solutions, called TP-N2F. The encoder of TP-N2F employs TPR `binding' to encode natural-language symbolic structure in vector space and the decoder uses TPR `unbinding' to generate, in symbolic space, a sequential program represented by relational tuples, each consisting of a relation (or operation) and a number of arguments. TP-N2F considerably outperforms LSTM-based seq2seq models on two benchmarks and creates new state-of-the-art results. Ablation studies show that improvements can be attributed to the use of structured TPRs explicitly in both the encoder and decoder. Analysis of the learned structures shows how TPRs enhance the interpretability of TP-N2F.

cs.CL↗

arXiv2020

Universal linguistic inductive biases via meta-learning

How do learners acquire languages from the limited data available to them? This process must involve some inductive biases - factors that affect how a learner generalizes - but it is unclear which inductive biases can explain observed patterns in language acquisition. To facilitate computational modeling aimed at addressing this question, we introduce a framework for giving particular linguistic inductive biases to a neural network model; such a model can then be used to empirically explore the effects of those inductive biases. This framework disentangles universal inductive biases, which are encoded in the initial values of a neural network's parameters, from non-universal factors, which the neural network must learn from data in a given language. The initial state that encodes the inductive biases is found with meta-learning, a technique through which a model discovers how to acquire new languages more easily via exposure to many possible languages. By controlling the properties of the languages that are used during meta-learning, we can control the inductive biases that meta-learning imparts. We demonstrate this framework with a case study based on syllable structure. First, we specify the inductive biases that we intend to give our model, and then we translate those inductive biases into a space of languages from which a model can meta-learn. Finally, using existing analysis techniques, we verify that our approach has imparted the linguistic inductive biases that it was intended to impart.

cs.CL↗

arXiv2019

A Simple Recurrent Unit with Reduced Tensor Product Representations

idely used recurrent units, including Long-short Term Memory (LSTM) and the Gated Recurrent Unit (GRU), perform well on natural language tasks, but their ability to learn structured representations is still questionable. Exploiting reduced Tensor Product Representations (TPRs) --- distributed representations of symbolic structure in which vector-embedded symbols are bound to vector-embedded structural positions --- we propose the TPRU, a simple recurrent unit that, at each time step, explicitly executes structural-role binding and unbinding operations to incorporate structural information into learning. A gradient analysis of our proposed TPRU is conducted to support our model design, and its performance on multiple datasets shows the effectiveness of our design choices. Furthermore, observations on a linguistically grounded study demonstrate the interpretability of our TPRU.

cs.NE↗

arXiv2019

Augmenting Compositional Models for Knowledge Base Completion Using Gradient Representations

Neural models of Knowledge Base data have typically employed compositional representations of graph objects: entity and relation embeddings are systematically combined to evaluate the truth of a candidate Knowedge Base entry. Using a model inspired by Harmonic Grammar, we propose to tokenize triplet embeddings by subjecting them to a process of optimization with respect to learned well-formedness conditions on Knowledge Base triplets. The resulting model, known as Gradient Graphs, leads to sizable improvements when implemented as a companion to compositional models. Also, we show that the "supracompositional" triplet token embeddings it produces have interpretable properties that prove helpful in performing inference on the resulting triplet representations.

cs.CL↗

arXiv2019

Predicting the Argumenthood of English Prepositional Phrases

Distinguishing between arguments and adjuncts of a verb is a longstanding, nontrivial problem. In natural language processing, argumenthood information is important in tasks such as semantic role labeling (SRL) and prepositional phrase (PP) attachment disambiguation. In theoretical linguistics, many diagnostic tests for argumenthood exist but they often yield conflicting and potentially gradient results. This is especially the case for syntactically oblique items such as PPs. We propose two PP argumenthood prediction tasks branching from these two motivations: (1) binary argument-adjunct classification of PPs in VerbNet, and (2) gradient argumenthood prediction using human judgments as gold standard, and report results from prediction models that use pretrained word embeddings and other linguistically informed features. Our best results on each task are (1) $acc.=0.955$, $F_1=0.954$ (ELMo+BiLSTM) and (2) Pearson's $r=0.624$ (word2vec+MLP). Furthermore, we demonstrate the utility of argumenthood prediction in improving sentence representations via performance gains on SRL when a sentence encoder is pretrained with our tasks.

cs.CL↗

arXiv2019

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.

cs.CL↗

arXiv2019

Quantum Language Processing

We present a representation for linguistic structure that we call a Fock-space representation, which allows us to embed problems in language processing into small quantum devices. We further develop a formalism for understanding both classical as well as quantum linguistic problems and phrase them both as a Harmony optimization problem that can be solved on a quantum computer which we show is related to classifying vectors using quantum Boltzmann machines. We further provide a new training method for learning quantum Harmony operators that describe a language. This also provides a new algorithm for training quantum Boltzmann machines that requires no approximations and works in the presence of hidden units. We additionally show that quantum language processing is BQP-complete, meaning that it is polynomially equivalent to the circuit model of quantum computing which implies that quantum language models are richer than classical models unless BPP=BQP. It also implies that, under certain circumstances, quantum Boltzmann machines are more expressive than classical Boltzmann machines. Finally, we examine the performance of our approach numerically for the case of classical harmonic grammars and find that the method is capable of rapidly parsing even non-trivial grammars. This suggests that the work may have value as a quantum inspired algorithm beyond its initial motivation as a new quantum algorithm.

quant-ph↗

arXiv2018

A Neural-Symbolic Approach to Design of CAPTCHA

CAPTCHAs based on reading text are susceptible to machine-learning-based attacks due to recent significant advances in deep learning (DL). To address this, this paper promotes image/visual captioning based CAPTCHAs, which is robust against machine-learning-based attacks. To develop image/visual-captioning-based CAPTCHAs, this paper proposes a new image captioning architecture by exploiting tensor product representations (TPR), a structured neural-symbolic framework developed in cognitive science over the past 20 years, with the aim of integrating DL with explicit language structures and rules. We call it the Tensor Product Generation Network (TPGN). The key ideas of TPGN are: 1) unsupervised learning of role-unbinding vectors of words via a TPR-based deep neural network, and 2) integration of TPR with typical DL architectures including Long Short-Term Memory (LSTM) models. The novelty of our approach lies in its ability to generate a sentence and extract partial grammatical structure of the sentence by using role-unbinding vectors, which are obtained in an unsupervised manner. Experimental results demonstrate the effectiveness of the proposed approach.

cs.CL↗

arXiv2018

Learning and analyzing vector encoding of symbolic representations

We present a formal language with expressions denoting general symbol structures and queries which access information in those structures. A sequence-to-sequence network processing this language learns to encode symbol structures and query them. The learned representation (approximately) shares a simple linearity property with theoretical techniques for performing this task.

cs.AI↗

arXiv2018

Discrete symbolic optimization and Boltzmann sampling by continuous neural dynamics: Gradient Symbolic Computation

Gradient Symbolic Computation is proposed as a means of solving discrete global optimization problems using a neurally plausible continuous stochastic dynamical system. Gradient symbolic dynamics involves two free parameters that must be adjusted as a function of time to obtain the global maximizer at the end of the computation. We provide a summary of what is known about the GSC dynamics for special cases of settings of the parameters, and also establish that there is a schedule for the two parameters for which convergence to the correct answer occurs with high probability. These results put the empirical results already obtained for GSC on a sound theoretical footing.

cs.CL↗

arXiv2017

Tensor Product Generation Networks for Deep NLP Modeling

We present a new approach to the design of deep networks for natural language processing (NLP), based on the general technique of Tensor Product Representations (TPRs) for encoding and processing symbol structures in distributed neural networks. A network architecture --- the Tensor Product Generation Network (TPGN) --- is proposed which is capable in principle of carrying out TPR computation, but which uses unconstrained deep learning to design its internal representations. Instantiated in a model for image-caption generation, TPGN outperforms LSTM baselines when evaluated on the COCO dataset. The TPR-capable structure enables interpretation of internal representations and operations, which prove to contain considerable grammatical content. Our caption-generation model can be interpreted as generating sequences of grammatical categories and retrieving words by their categories from a plan encoded as a distributed representation.

cs.CV↗

arXiv2017

Question-Answering with Grammatically-Interpretable Representations

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 (Toutanova et al. 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.

cs.CL↗

arXiv2016

Reasoning in Vector Space: An Exploratory Study of Question Answering

Question answering tasks have shown remarkable progress with distributed vector representation. In this paper, we investigate the recently proposed Facebook bAbI tasks which consist of twenty different categories of questions that require complex reasoning. Because the previous work on bAbI are all end-to-end models, errors could come from either an imperfect understanding of semantics or in certain steps of the reasoning. For clearer analysis, we propose two vector space models inspired by Tensor Product Representation (TPR) to perform knowledge encoding and logical reasoning based on common-sense inference. They together achieve near-perfect accuracy on all categories including positional reasoning and path finding that have proved difficult for most of the previous approaches. We hypothesize that the difficulties in these categories are due to the multi-relations in contrast to uni-relational characteristic of other categories. Our exploration sheds light on designing more sophisticated dataset and moving one step toward integrating transparent and interpretable formalism of TPR into existing learning paradigms.

cs.CL↗

arXiv2016

Basic Reasoning with Tensor Product Representations

In this paper we present the initial development of a general theory for mapping inference in predicate logic to computation over Tensor Product Representations (TPRs; Smolensky (1990), Smolensky & Legendre (2006)). After an initial brief synopsis of TPRs (Section 0), we begin with particular examples of inference with TPRs in the 'bAbI' question-answering task of Weston et al. (2015) (Section 1). We then present a simplification of the general analysis that suffices for the bAbI task (Section 2). Finally, we lay out the general treatment of inference over TPRs (Section 3). We also show the simplification in Section 2 derives the inference methods described in Lee et al. (2016); this shows how the simple methods of Lee et al. (2016) can be formally extended to more general reasoning tasks.

cs.AI↗