Predictive State Recurrent Neural Networks

Abstract

We present a new model, Predictive State Recurrent Neural Networks (PSRNNs), for filtering and prediction in dynamical systems. PSRNNs draw on insights from both Recurrent Neural Networks (RNNs) and Predictive State Representations (PSRs), and inherit advantages from both types of models. Like many successful RNN architectures, PSRNNs use (potentially deeply composed) bilinear transfer functions to combine information from multiple sources. We show that such bilinear functions arise naturally from state updates in Bayes filters like PSRs, in which observations can be viewed as gating belief states. We also show that PSRNNs can be learned effectively by combining Backpropogation Through Time (BPTT) with an initialization derived from a statistically consistent learning algorithm for PSRs called two-stage regression (2SR). Finally, we show that PSRNNs can be factorized using tensor decomposition, reducing model size and suggesting interesting connections to existing multiplicative architectures such as LSTMs. We applied PSRNNs to 4 datasets, and showed that we outperform several popular alternative approaches to modeling dynamical systems in all cases.

Neural Network Based Nonlinear Weighted Finite Automata

“…A nonlinear extension of PSR has been proposed for deterministic controlled dynamical systems in [Rudary and Singh, 2004]. More recently, building upon reproducing kernel Hilbert space embedding of PSR [Boots et al, 2013], non-linearity is introduced into PSR using recurrent neural networks [Downey et al, 2017, Venkatraman et al, 2017. One of the main differences with these approaches is that our learning algorithm does not rely on back-propagation through time and we instead investigate how the spectral learning method for WFA can be beneficially extended to the nonlinear setting.…”