Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model (1904.09770v4)

Abstract: This paper studies a curious phenomenon in learning energy-based model (EBM) using MCMC. In each learning iteration, we generate synthesized examples by running a non-convergent, non-mixing, and non-persistent short-run MCMC toward the current model, always starting from the same initial distribution such as uniform noise distribution, and always running a fixed number of MCMC steps. After generating synthesized examples, we then update the model parameters according to the maximum likelihood learning gradient, as if the synthesized examples are fair samples from the current model. We treat this non-convergent short-run MCMC as a learned generator model or a flow model. We provide arguments for treating the learned non-convergent short-run MCMC as a valid model. We show that the learned short-run MCMC is capable of generating realistic images. More interestingly, unlike traditional EBM or MCMC, the learned short-run MCMC is capable of reconstructing observed images and interpolating between images, like generator or flow models. The code can be found in the Appendix.

• The paper proposes a non-convergent short-run MCMC approach that serves as a generator model for energy-based models, enabling effective image synthesis.
• It demonstrates that bypassing convergence requirements significantly reduces computational cost while maintaining competitive performance on image generation tasks.
• A theoretical framework based on moment matching underpins the empirical success of the method on datasets such as CIFAR-10, CelebA, and LSUN Bedrooms.

Insights into Non-Convergent Short-Run MCMC for Learning Energy-Based Models

The paper presented by Nijkamp et al. introduces an unconventional approach to learning energy-based models (EBMs) through non-convergent, non-persistent short-run MCMC. Conventionally, the primary challenge in training these models originates from the need to obtain well-mixed samples from complex EBMs using Markov chain Monte Carlo (MCMC) methods. However, the authors propose a counterintuitive yet conceptually appealing solution that circumvents this requirement by treating short-run MCMC as a generative model.

The paper focuses on a learning scheme whereby synthesized examples generated through limited iterations of MCMC starting from a uniform noise distribution are used to update the model parameters. This approach breaks away from the traditional reliance on obtaining fair samples that accurately represent the underlying model distribution. This paper provides both theoretical and empirical justifications for its approach and demonstrates strong numerical performances, particularly in realistic image generation and interpolation tasks.

Core Findings

1. Short-Run MCMC as a Generator Model: The paper positions short-run MCMC as a generator model akin to flow models. Despite not acting as a valid sampler by failing to converge to the EBM's stationary distribution, the short-run MCMC effectively generates realistic images. Moreover, it can reconstruct and interpolate between observed images, borrowing functionality from deep generative models such as variational autoencoders (VAEs) and normalizing flows.
2. Efficiency of Learning: The prescribed methodology avoids extensive computational costs owing to the non-persistent nature of short-run MCMC. The abandonment of convergence requirements frees the training mechanism from the pitfalls of mixing, thus making the learning process more feasible in terms of time and resources.
3. Theoretical Implications: The authors developed a theoretical framework grounded in moment matching estimators, drawing parallels between the resulting distribution from short-run MCMC and the data distribution in terms of sufficient statistics. This framework aligns conceptually with maximum likelihood estimation albeit in a non-traditional form where the learned model does not aim to approximate the actual EBM.
4. Experimental Results: The practical applicability of the approach was validated through experiments on datasets such as CIFAR-10, CelebA, and LSUN Bedrooms. The short-run MCMC model notably achieved Inception Scores (IS) and Fréchet Inception Distances (FID) that are competitive with more established models, including VAEs and DCGANs.

Implications and Future Directions

This work's primary impact lies in its potential to redefine how energy-based models might be taught, moving from conventional paradigms focused on model correctness to practical adaptability via dynamics. The use of energy-based dynamics instead of grassroots learning of EBM represents a fundamental shift in approach, with practical implications extending to fields such as image inpainting, style transfer, and beyond.

However, while promising, this method prompts further questions, notably concerning its applicability across a broader range of applications, optimal hyperparameter settings, and the general scalability with larger datasets or higher resolution images. Continuing efforts might further hone the balance between computational efficiency and model accuracy, integrating more sophisticated noise-injection techniques or interactive stopping criteria during MCMC transitions.

In summary, this research offers a significant addition to the EBM landscape, promoting a methodology that embraces non-convergent, dynamic processes as a viable learning strategy. As the field progresses, the insights from this approach could spark new developments in generative modeling, potentially achieving a synergy between theoretical robustness and practical efficiency.