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

Three-order normalized PMI and other lessons in tensor analysis of verbal selectional preferences

We investigate several questions in transitive verb structure representation by decomposing tensors populated with different subject-verb-object association measures, including a novel generalization of normalized pointwise mutual information to the higher-order (>2) case. Which association measure works the best in modeling verb structures? Should we include occurrences with unfilled arguments in our statistics? We also investigate qualitatively the latent dimensions, and the difference between each noun as a subject versus an object

MorphTE: Injecting Morphology in Tensorized Embeddings

In the era of deep learning, word embeddings are essential when dealing with text tasks. However, storing and accessing these embeddings requires a large amount of space. This is not conducive to the deployment of these models on resource-limited devices. Combining the powerful compression capability of tensor products, we propose a word embedding compression method with morphological augmentation, Morphologically-enhanced Tensorized Embeddings (MorphTE). A word consists of one or more morphemes, the smallest units that bear meaning or have a grammatical function. MorphTE represents a word embedding as an entangled form of its morpheme vectors via the tensor product, which injects prior semantic and grammatical knowledge into the learning of embeddings. Furthermore, the dimensionality of the morpheme vector and the number of morphemes are much smaller than those of words, which greatly reduces the parameters of the word embeddings. We conduct experiments on tasks such as machine translation and question answering. Experimental results on four translation datasets of different languages show that MorphTE can compress word embedding parameters by about 20 times without performance loss and significantly outperforms related embedding compression methods.Comment: 20 pages, 6 figures, 18 tables. Published at NeurIPS 202