[Paper Review] A Recurrent Latent Variable Model for Sequential Data

Jun‐Young Chung, Kyle Kastner+4 more|arXiv (Cornell University)|Jun 7, 2015

Generative Adversarial Networks and Image Synthesis18 references696 citations

TL;DR

This paper proposes the Variational Recurrent Neural Network (VRNN), a generative model that integrates latent random variables into the hidden state of an RNN to better capture complex, multimodal dependencies in sequential data. By modeling temporal dependencies in the latent space and using variational inference, the VRNN achieves significantly higher log-likelihood and generates higher-quality speech and handwriting samples than standard RNNs or models without temporal latent dependencies.

ABSTRACT

In this paper, we explore the inclusion of latent random variables into the dynamic hidden state of a recurrent neural network (RNN) by combining elements of the variational autoencoder. We argue that through the use of high-level latent random variables, the variational RNN (VRNN)1 can model the kind of variability observed in highly structured sequential data such as natural speech. We empirically evaluate the proposed model against related sequential models on four speech datasets and one handwriting dataset. Our results show the important roles that latent random variables can play in the RNN dynamic hidden state.

Motivation & Objective

• To address the limitation of standard RNNs in modeling complex, multimodal sequential variability due to their deterministic hidden states.
• To explore whether high-level latent random variables can improve generative modeling of structured sequential data such as speech and handwriting.
• To investigate the impact of modeling temporal dependencies between latent variables in an RNN framework.
• To demonstrate that latent variables enable better generation with simpler output distributions (e.g., Gaussian) compared to standard RNNs.

Proposed method

• Integrates latent random variables into the RNN hidden state, forming a variational RNN (VRNN) that combines RNN dynamics with variational inference.
• Uses a recognition model to infer posterior distributions over latent variables at each timestep, conditioned on past observations and hidden states.
• Models the prior over latent variables using a time-dependent distribution that depends on the previous hidden state and latent variable.
• Applies the reparameterization trick to enable end-to-end backpropagation through the stochastic computation graph for training.
• Employs a conditional decoder to generate observations from the latent state, using either Gaussian or Gaussian Mixture Model (GMM) output distributions.
• Trains the model via variational inference by maximizing a lower bound on the log-likelihood of the observed sequence.

Experimental results

Research questions

• RQ1 Can the inclusion of latent random variables in the RNN hidden state improve modeling of complex sequential data such as natural speech?
• RQ2 Does modeling temporal dependencies between latent variables enhance the performance of RNN-based generative models?
• RQ3 Can a simple Gaussian output distribution in the VRNN generate high-quality samples when standard RNNs with the same output fail?
• RQ4 How does the VRNN compare to standard RNNs and other RNN variants in terms of log-likelihood and sample quality on speech and handwriting datasets?
• RQ5 What role do latent variable transitions play in guiding the generation of diverse yet consistent sequences?

Key findings

• The VRNN achieves significantly higher log-likelihood on all four speech datasets compared to standard RNNs and RNNs with GMM outputs, demonstrating improved modeling capacity.
• The VRNN with a Gaussian output distribution (VRNN-Gauss) generates less noisy, higher-quality speech waveforms than the RNN with a GMM (RNN-GMM), which produces high-frequency noise.
• The VRNN model without temporal dependencies in the latent space performs worse than the full VRNN, confirming the importance of temporal latent dynamics.
• Latent space analysis shows that latent variable transitions align with signal transitions in the waveform, with increased KL divergence and latent state changes during phonetic transitions.
• In handwriting generation, the VRNN maintains consistent writing style throughout samples, while RNN-based models tend to shift styles mid-sequence.
• Visual inspection confirms that VRNN-generated samples are more diverse and realistic, especially in maintaining stylistic coherence over long sequences.