Transferring Implicit Regularization Theories Across Model Classes: From Diffusion to Transformers

TL;DR: The implicit regularization mechanism found in diffusion models might exist in transformers or LLMs—let’s seek out similar “double timescale” effects and see how transferable these principles are.

Research Question: Does the implicit dynamical regularization manifesting as a separation between $\tau_\mathrm{gen}$ and $\tau_\mathrm{mem}$ in diffusion models also appear in other overparameterized architectures (e.g., transformers, LLMs), and can insights from one domain inform regularization strategies in another?

Hypothesis: Architectures such as transformers will exhibit analogous timescale separations, and adapting diffusion-inspired training diagnostics or regularization schedules will improve generalization and reduce memorization in these models as well.

Experiment Plan: - Track training dynamics (e.g., accuracy, overfitting signals) in transformer models on reasoning and generative tasks, using metrics from Kang et al. (2024).

• Define analogues of $\tau_\mathrm{gen}$ and $\tau_\mathrm{mem}$, and compare their scaling with data size and model size.
• Implement “diffusion-inspired” dynamic regularization or early stopping, then evaluate impact on generalization and memorization.
• Cross-validate findings across multiple architectures.

References:

• Bonnaire, T., Urfin, R., Biroli, G., & M'ezard, M. (2025). Why Diffusion Models Don't Memorize: The Role of Implicit Dynamical Regularization in Training. arXiv.org.
• Kang, K., Setlur, A. R., Ghosh, D., Steinhardt, J., Tomlin, C. J., Levine, S., & Kumar, A. (2024). What Do Learning Dynamics Reveal About Generalization in LLM Reasoning? arXiv.org.