Principled Gradient-based Markov Chain Monte Carlo for Text Generation (2312.17710v1)

Abstract: Recent papers have demonstrated the possibility of energy-based text generation by adapting gradient-based sampling algorithms, a paradigm of MCMC algorithms that promises fast convergence. However, as we show in this paper, previous attempts on this approach to text generation all fail to sample correctly from the target LLM distributions. To address this limitation, we consider the problem of designing text samplers that are faithful, meaning that they have the target text distribution as its limiting distribution. We propose several faithful gradient-based sampling algorithms to sample from the target energy-based text distribution correctly, and study their theoretical properties. Through experiments on various forms of text generation, we demonstrate that faithful samplers are able to generate more fluent text while adhering to the control objectives better.

• The paper proposes two new faithful gradient-based samplers—one using Langevin dynamics and one inspired by Gibbs sampling—that ensure correct convergence.
• It analyzes theoretical convergence and mixing properties, providing proofs that the samplers accurately target language model distributions.
• Empirical evaluations demonstrate improved text fluency and control adherence, outperforming previous unfaithful sampling approaches.

Introduction to Gradient-based MCMC for Text Generation

The efficiency of text generation has been revolutionized by the use of energy-based models (EBMs) and gradient-based Markov Chain Monte Carlo (MCMC) methods. Existing research has adapted these methods, which promise fast convergence, for the generation of controlled text from pre-trained LLMs. Despite their promises, current gradient-based text samplers do not provably converge to their target distributions. This limitation has motivated a deeper inquiry into the design of sampling algorithms that correctly converge or are "faithful" to their target distributions.

Energy-based Models and Text Generation Challenges

Pre-trained LLMs have proven to be effective in generating fluent text. However, faithfully sampling from energy-based models of text, especially those with intractable normalization constants, has remained challenging. The discrete nature of text-based EBMs presents an additional layer of complexity in creating efficient sampling algorithms. To address the sampling difficulty, previous attempts have leveraged differentiable LLMs and auxiliary energy functions to utilize gradient information, which could theoretically accelerate convergence.

Designing Faithful Samplers

To overcome the challenges of existing unfaithful samplers that do not sample correctly from target LLM distributions, this paper introduces faithful gradient-based samplers. Two novel sampling algorithms are proposed: one based on Langevin dynamics and another inspired by the Gibbs sampler. Theoretical properties of these samplers are studied, their convergence and mixing properties are analyzed, and when applicable, proven. The research also explores the concept of hybrid samplers that combine the strengths of both approaches to improve efficiency further.

Empirical Evaluation and Practical Implementation

Experimental evaluations demonstrate that faithful gradient-based samplers produce text that is not only more fluent but also adheres more closely to control objectives. These samplers outperform existing unfaithful methods, especially in controlled text generation tasks. Additionally, the discussion on optimizing the samplers' performance, includes fine-tuning step sizes and considering automatic tuning methods or proposal merging algorithms for practical implementations. The summary concludes with an acknowledgment of the potential for extensions and future research in the field of principled probabilistic text generation approaches.