Abstract: LSTMs are powerful tools for modeling contextual information, as evidenced by their success at the task of language modeling. However, modeling contexts in very high dimensional space can lead to poor generalizability. We introduce the Pyramidal Recurrent Unit (PRU), which enables learning representations in high dimensional space with more generalization power and fewer parameters. PRUs replace the linear transformation in LSTMs with more sophisticated interactions including pyramidal and grouped linear transformations. This architecture gives strong results on word-level language modeling while reducing the number of parameters significantly. In particular, PRU improves the perplexity of a recent state-of-the-art language model Merity et al. (2018) by up to 1.3 points while learning 15-20% fewer parameters. For similar number of model parameters, PRU outperforms all previous RNN models that exploit different gating mechanisms and transformations. We provide a detailed examination of the PRU and its behavior on the language modeling tasks. Our code is open-source and available at https://sacmehta.github.io/PRU/

Introduction: Long short term memory (LSTM) units BIBREF1 are popular for many sequence modeling tasks and are used extensively in language modeling. A key to their success is their articulated gating structure, which allows for more control over the information passed along the recurrence. However, despite the sophistication of the gating mechanisms employed in LSTMs and similar recurrent units, the input and context vectors are treated with simple linear transformations prior to gating. Non-linear transformations such as convolutions BIBREF2 have been used, but these have not achieved the performance of well regularized LSTMs for language modeling BIBREF3 . A natural way to improve the expressiveness of linear transformations is to increase the number of dimensions of the input and context vectors, but this comes with a significant increase in the number of parameters which may limit generalizability. An example is shown in Figure FIGREF1 , where LSTMs performance decreases with the increase in dimensions of the input and context vectors. Moreover, the semantics of the input and context vectors are different, suggesting that each may benefit from specialized treatment. Guided by these insights, we introduce a new recurrent unit, the Pyramidal Recurrent Unit (PRU), which is based on the LSTM gating structure. Figure FIGREF2 provides an overview of the PRU. At the heart of the PRU is the pyramidal transformation (PT), which uses subsampling to effect multiple views of the input vector. The subsampled representations are combined in a pyramidal fusion structure, resulting in richer interactions between the individual dimensions of the input vector than is possible with a linear transformation. Context vectors, which have already undergone this transformation in the previous cell, are modified with a grouped linear transformation (GLT) which allows the network to learn latent representations in high dimensional space with fewer parameters and better generalizability (see Figure FIGREF1 ). We show that PRUs can better model contextual information and demonstrate performance gains on the task of language modeling. The PRU improves the perplexity of the current state-of-the-art language model BIBREF0 by up to 1.3 points, reaching perplexities of 56.56 and 64.53 on the Penn Treebank and WikiText2 datasets while learning 15-20% fewer parameters. Replacing an LSTM with a PRU results in improvements in perplexity across a variety of experimental settings. We provide detailed ablations which motivate the design of the PRU architecture, as well as detailed analysis of the effect of the PRU on other components of the language model.

Question: what previous RNN models do they compare with?
Answer: Variational LSTM, CharCNN, Pointer Sentinel-LSTM, RHN, NAS Cell, SRU, QRNN, RAN, 4-layer skip-connection LSTM, AWD-LSTM, Quantized LSTM