Source-linked AI summary
A Recurrent Latent Variable Model for Sequential Data
Junyoung Chung, Kyle Kastner, Laurent Dinh, Kratarth Goel, Aaron Courville, Yoshua Bengio
TL;DR
The paper addresses whether latent random variables can improve RNN modeling of variability in highly structured sequential data. It proposes the VRNN, which combines recurrent dynamics with variational-autoencoder components, and finds benefits across speech and handwriting tasks, including the importance of temporal latent conditioning.
Problem
Deterministic RNN hidden-state transitions may inadequately model the strong, complex variability and dependencies present in highly structured sequences such as natural speech.
Method
The VRNN incorporates high-level latent random variables into an RNN and conditions their prior and inference models on the recurrent hidden state.
Results
VRNN models achieve higher log-likelihoods on speech, while VRNN-Gauss models perform well with a unimodal output function unlike standard RNN models.
Takeaways & Limitations
Latent random variables improve modeling of highly structured speech, and temporal conditioning helps model speech while VRNNs preserve handwriting diversity and style.
Takeaways & Limitations
The approach targets highly structured data with high signal-to-noise ratio and complex relationships between underlying variation factors and observations.
Abstract
from arXiv · showhide
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.
1 Introduction
The paper motivates adding high-level latent random variables to RNN hidden states because deterministic transitions may inadequately represent structured variability. It introduces the VRNN and evaluates it against related models on speech and handwriting.
- RNNs offer richly distributed states, flexible nonlinear transitions, and error-backpropagation, giving them greater expressive power than traditional DBNs.
- Standard RNN transitions are deterministic, leaving the conditional output model as the only source of randomness for structured sequences.
- Complex dependencies in highly structured data may be inefficiently modeled by standard RNN output distributions based on unimodal or mixtures of unimodal distributions.
- The VRNN extends the variational autoencoder into a recurrent framework, using high-level latent random variables to model multimodal variability in high-dimensional sequences.
- The model imposes temporal dependencies between latent random variables at neighboring timesteps, unlike approaches with independent latent variables.
- On speech modelling tasks, VRNN-based models significantly outperform standard RNN-based models and a VRNN without temporal latent dependencies.
2 Background
The background describes standard RNN sequence factorization and output-density choices, then introduces VAEs as latent-variable models with flexible nonlinear decoders and variational inference. It motivates latent states for sequences whose variability is both substantial and structured.
- An RNN recursively processes variable-length sequences while updating a hidden state through a deterministic transition function.
- RNNs factorize joint sequence probability into conditional output probabilities, with an output function mapping the previous hidden state to a distribution.
- The output function determines an RNN’s representational power by defining the family of joint distributions expressible under deterministic transitions.
- For high-dimensional real-valued sequences, a Gaussian mixture model can parameterize output mixture coefficients, means, and covariances.
- Deterministic transitions force standard RNNs to map small input variations into potentially large hidden-state variations when modeling highly variable, structured sequences.
- A VAE introduces latent variables z to capture variation in observed variables x, using a flexible conditional model p(x | z) and an approximate posterior q(z | x).
3 Variational Recurrent Neural Network
The VRNN extends the VAE to sequences by conditioning timestep-wise latent-variable operations on an RNN hidden state. This preserves nonlinear recurrent dynamics while modeling dependencies among latent variables across timesteps.
- The VRNN is a recurrent VAE that explicitly models dependencies between latent random variables across subsequent timesteps.It is designed for sequence modeling while retaining flexible nonlinear dynamics.
- Generation: Each timestep contains a VAE conditioned on the preceding RNN hidden state h_t−1, incorporating temporal structure into generation.The hidden state conditions the timestep-wise prior and generative process.
- Generation: The generating function is conditioned on both the current latent variable z_t and the preceding hidden state h_t−1.The recurrent hidden state summarizes prior sequence information for generation.
- Inference: The approximate posterior also depends on h_t−1, tying inference and generation through the same recurrent hidden state.This conditioning yields the model’s sequential factorization.
- Learning: Training maximizes a timestep-wise variational lower bound jointly over the generative and inference model parameters.The objective combines a reconstruction term with a KL-divergence term.
- Generation: The conditional prior depends on preceding inputs through h_t−1, unlike approaches with timestep-independent latent priors.This temporal prior structure is intended to improve representational power.
4 Experiment Settings
The experiments evaluate VRNNs against standard RNNs and a VRNN variant across raw-audio speech modeling and handwriting generation. Models are compared under controlled architectures, parameter matching, and common optimization procedures.
- Tasks: The evaluation covers natural speech modeling from raw audio waveforms and handwriting generation.Speech uses 200-dimensional frames of consecutive raw acoustic samples; handwriting uses coordinates and pen-state indicators.
- Datasets: Four speech datasets span single-speaker English, read speech, non-linguistic human-made sounds, and native and nonnative English accents.The datasets are Blizzard, TIMIT, Onomatopoeia2, and Accent.
- Datasets: Handwriting experiments use IAM-OnDB, containing 13,040 handwritten lines written by 500 writers.Each model learns coordinate sequences together with binary pen-up/pen-down indicators.
- Models: VRNNs are compared with standard RNNs using Gaussian and Gaussian-mixture output functions, plus VRNN-I without the conditional prior.The comparison isolates the role of the conditional prior in addition to comparing output distributions.
- Architecture: All models use a single recurrent hidden layer with dataset-specific LSTM widths, while neural feature networks generally use four rectified-linear hidden layers.The recurrent layer has 2000 LSTM units, except Blizzard with 4000 and IAM-OnDB with 1200.
- Architecture: The RNN-GMM and VRNN models match their DNN parameter counts as closely as possible to the corresponding RNN-Gauss models.GMM-based models use 20 mixture components.
5 Results and Analysis
The VRNN models achieve higher test log-likelihoods and generate cleaner, more structured speech than standard RNN variants. Latent-space transitions align with waveform transitions, while VRNN handwriting samples preserve writing style more consistently.
- Speech modelling: VRNN models achieve higher test log-likelihoods than the evaluated RNN-based models, supporting latent random variables for modelling complex sequences.VRNN scores include variational lower bounds and importance-sampling approximations; higher values are better.
- Latent space analysis: Temporal latent-space transitions coincide with waveform transitions, where KL divergence tends to increase and peaks in δt can alter RNN dynamics.Figure 2 compares latent-mean differences, temporal KL divergences, and input waveforms.
- Speech generation: VRNN-Gauss waveforms contain less noise and fewer spurious peaks than RNN-GMM samples.The models generate 2.0-second waveforms trained on Blizzard; RNN-Gauss is excluded because its samples are nearly pure noise.
- Handwriting generation: VRNN handwriting generation maintains consistent writing style within samples while supporting variation across generated examples.RNN-Gauss and RNN-GMM tend to change writing style during generation, whereas VRNN-GMM retains it from beginning to end.
6 Conclusion
The paper introduces latent random variables into RNNs to model highly structured sequences. Experiments show improved natural-speech modelling, cleaner speech generation with a simple Gaussian output, and diverse handwriting with consistent style.
- The proposed VRNN incorporates latent random variables into a recurrent neural network for sequence modelling.
- VRNNs improve modelling of highly structured natural speech and can use a simple Gaussian output function, unlike the standard RNN baseline.The standard RNN with the same Gaussian output fails to generate reasonable samples.
- Temporal conditioning of latent random variables yields higher log-likelihoods for natural speech sequences.
- In handwriting generation, VRNNs model diversity across examples while maintaining consistent writing style throughout generation.