Tuning the Implicit Regularizer of Masked Diffusion Language Models: Enhancing Generalization via Insights from $k$-Parity

TL;DR

This paper investigates how masked diffusion language models generalize, revealing that their implicit regularization can be tuned to improve performance and prevent grokking, especially on large-scale models.

Contribution

The work provides a theoretical decomposition of the MD objective into signal and noise regimes and demonstrates how tuning mask distribution enhances generalization and scalability.

Findings

MD objective enables rapid generalization without grokking.

Optimizing mask probability improves perplexity significantly.

Method scales effectively to large models, outperforming baselines.

Abstract

Masked Diffusion Language Models have recently emerged as a powerful generative paradigm, yet their generalization properties remain understudied compared to their auto-regressive counterparts. In this work, we investigate these properties within the setting of the $k$-parity problem (computing the XOR sum of $k$ relevant bits), where neural networks typically exhibit grokking -- a prolonged plateau of chance-level performance followed by sudden generalization. We theoretically decompose the Masked Diffusion (MD) objective into a Signal regime which drives feature learning, and a Noise regime which serves as an implicit regularizer. By training nanoGPT using MD objective on the $k$-parity problem, we demonstrate that MD objective fundamentally alters the learning landscape, enabling rapid and simultaneous generalization without experiencing grokking. Furthermore, we leverage our theoretical insights to optimize the distribution of the mask probability in the MD objective. Our method significantly improves perplexity for 50M-parameter models and achieves superior results across both pre-training from scratch and supervised fine-tuning. Specifically, we observe performance gains peaking at $8.8\%$ and $5.8\%$, respectively, on 8B-parameter models, confirming the scalability and effectiveness of our framework in large-scale masked diffusion language model regimes.