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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 14: Focus Session: Physics of AI I (joint session SOE/DY)

SOE 14.4: Vortrag

Donnerstag, 12. März 2026, 10:30–10:45, GÖR/0226

Mirror, Mirror of the Flow: How Does Regularization Shape Implicit Bias? — •Tom Jacobs, Chao Zhou, and Rebekka Burkholz — CISPA Helmholtz Center, Saarbrucken, Germany

Implicit bias plays an important role in explaining how overparameterized models generalize well. Explicit regularization like weight decay is often employed in addition to prevent overfitting. While both concepts have been studied separately, in practice, they often act in tandem. Understanding their interplay is key to controlling the shape and strength of implicit bias, as it can be modified by explicit regularization. To this end, we incorporate explicit regularization into the mirror flow framework and analyze its lasting effects on the geometry of the training dynamics, covering three distinct effects: positional bias, type of bias, and range shrinking. The mirror flow framework relies on Noether style parameter symmetry preservation, the regularization controls them. Our analytical approach encompasses a broad class of problems, including sparse coding, matrix sensing, single-layer attention, and LoRA, for which we demonstrate the utility of our insights. To exploit the lasting effect of regularization and highlight the potential benefit of dynamic weight decay schedules, we propose to switch off weight decay during training, which can improve generalization, as we demonstrate in experiments.

Keywords: Parameter symmetry; Optimization geometry; Implicit bias; Weight decay; Overparameterization