A Novel Predictive-Coding-Inspired Variational RNN Model for Online Prediction and Recognition

This study introduces PV-RNN, a novel variational RNN inspired by predictive-coding ideas. The model learns to extract the probabilistic structures hidden in fluctuating temporal patterns by dynamically changing the stochasticity of its latent states. Its architecture attempts to address two major concerns of variational Bayes RNNs: how latent variables can learn meaningful representations and how the inference model can transfer future observations to the latent variables. PV-RNN does both by introducing adaptive vectors mirroring the training data, whose values can then be adapted differently during evaluation. Moreover, prediction errors during backpropagation-rather than external inputs during the forward computation-are used to convey information to the network about the external data. For testing, we introduce error regression for predicting unseen sequences as inspired by predictive coding that leverages those mechanisms. As in other variational Bayes RNNs, our model learns by maximizing a lower bound on the marginal likelihood of the sequential data, which is composed of two terms: the negative of the expectation of prediction errors and the negative of the Kullback-Leibler divergence between the prior and the approximate posterior distributions. The model introduces a weighting parameter, the meta-prior, to balance the optimization pressure placed on those two terms. We test the model on two data sets with probabilistic structures and show that with high values of the meta-prior, the network develops deterministic chaos through which the randomness of the data is imitated. For low values, the model behaves as a random process. The network performs best on intermediate values and is able to capture the latent probabilistic structure with good generalization. Analyzing the meta-prior's impact on the network allows us to precisely study the theoretical value and practical benefits of incorporating stochastic dynamics in our model. We demonstrate better prediction performance on a robot imitation task with our model using error regression compared to a standard variational Bayes model lacking such a procedure.