Parallelizing Autoregressive Generation with Variational State Space Models (2407.08415v1)

Abstract: Attention-based models such as Transformers and recurrent models like state space models (SSMs) have emerged as successful methods for autoregressive sequence modeling. Although both enable parallel training, none enable parallel generation due to their autoregressiveness. We propose the variational SSM (VSSM), a variational autoencoder (VAE) where both the encoder and decoder are SSMs. Since sampling the latent variables and decoding them with the SSM can be parallelized, both training and generation can be conducted in parallel. Moreover, the decoder recurrence allows generation to be resumed without reprocessing the whole sequence. Finally, we propose the autoregressive VSSM that can be conditioned on a partial realization of the sequence, as is common in language generation tasks. Interestingly, the autoregressive VSSM still enables parallel generation. We highlight on toy problems (MNIST, CIFAR) the empirical gains in speed-up and show that it competes with traditional models in terms of generation quality (Transformer, Mamba SSM).

• The paper presents VSSM, a novel VAE-SSM hybrid that parallelizes both training and generation to significantly reduce computation time.
• It utilizes a fully parallelizable architecture with SSMs and the prefix-sum algorithm to enable simultaneous processing of entire sequences.
• Experiments on MNIST and CIFAR demonstrate competitive log-likelihood and generation speed, highlighting its practical efficiency in sequence modeling.

Parallelizing Autoregressive Generation with Variational State Space Models

The paper "Parallelizing Autoregressive Generation with Variational State Space Models" by Lambrechts et al., addresses a critical limitation in existing autoregressive sequence models: the inability to parallelize both training and generation phases simultaneously. This work introduces the Variational State Space Model (VSSM), which leverages the architecture of Variational Autoencoders (VAEs) combined with State Space Models (SSMs) to achieve parallelization in both phases.

Overview

The authors propose VSSM as a hybrid model where both the encoder and decoder are SSMs. This architecture enables parallelization during training and generation due to the linear time-invariance nature of SSMs, which can be computed in parallel using the prefix-sum algorithm. Unlike traditional autoregressive models that process sequences token by token, the VSSM processes entire sequences in a parallel manner, significantly reducing computational time. Moreover, VSSM introduces an autoregressive variant capable of conditioning on partially observed sequences while maintaining parallel generation capabilities.

Technical Contributions

1. Architecture Design: The VSSM is a VAE where both encoder and decoder are modeled as stacked SSMs. The paper details the implementation of VSSM using discretized latent spaces and uniform priors, which facilitate parallelizability by allowing simultaneous sampling of latent variables during both training and inference.
2. Training Objective: The VSSM training aligns with maximizing the Evidence Lower Bound (ELBO), accounting for the log-likelihood of observed sequences given the latent variables and the KL divergence between the approximate posterior and the prior distributions.
3. Autoregressive Conditioning: For applications like LLMing that require conditioning on partial sequences, the authors propose an autoregressive VSSM. This model uses a partially padded input sequence to generate the rest of the sequence in parallel.
4. Parallel and Recurrent Sampling: The parallel and recurrent nature of the VSSM sampling algorithm allows efficient and resumable sequence generation. This algorithm leverages the independence property of the latent variables and the conditional independence structure in the model to parallelize the sampling process.

Experimental Results

The empirical evaluation on two toy datasets, MNIST and CIFAR, demonstrates the competitiveness of the VSSM. The results indicate that VSSM achieves generation times comparable to existing architectures like Transformers and other SSMs while producing similar, if not better, sequence quality.

Quantitative Metrics:

• The VSSM showed a significant reduction in generation time, operating in linear time with respect to the sequence length.
• Likelihood evaluations using importance sampling exhibited that the VSSM performs competitively, showing similar log-likelihood values to the traditional models.

Implications and Future Work

The introduction of VSSM opens new avenues for efficient sequence modeling, particularly in applications requiring fast and large-scale sequence generation, such as text generation, audio synthesis, and time-series forecasting. The ability to parallelize both training and generation phases can lead to significant computational savings and faster deployment of models in practical scenarios.

On a theoretical level, this work bridges the methodologies of VAEs and SSMs, providing a robust framework for future research in combining these paradigms. Further challenges include scaling the VSSM for more complex and longer sequences, improving the partial posterior approximation, and exploring its application in more varied domains.

In summary, this paper effectively demonstrates the feasibility of parallelizing autoregressive generation with variational state space models, setting a foundation for future advancements in efficient sequence modeling. The innovative approach and promising results highlight the potential of VSSM in addressing computational inefficiencies in autoregressive sequence modeling.