Closed-form $\ell_r$ norm scaling with data for overparameterized linear regression and diagonal linear networks under $\ell_p$ bias
NeutralArtificial Intelligence
- A recent study has provided a unified characterization of the scaling of parameter norms in overparameterized linear regression and diagonal linear networks under $l_p$ bias. This work addresses the unresolved question of how the family of $l_r$ norms behaves with varying sample sizes, revealing a competition between signal spikes and null coordinates in the data.
- The findings are significant as they offer closed-form predictions for critical thresholds in norm behavior, which can enhance understanding and performance in machine learning models that utilize these statistical methods.
- This development contributes to ongoing discussions in the field of machine learning regarding the behavior of algorithms under different conditions, particularly in relation to generalization error and the optimization of learning processes, highlighting the importance of scaling laws in complex models.
— via World Pulse Now AI Editorial System
