Curvature Tuning: Provable Model Steering From a Single Parameter
- Randall Balestriero (Brown University)
Abstract
The scaling of model and data sizes has reshaped the AI landscape, establishing finetuning, e.g., with LoRA, as the standard paradigm for solving downstream tasks with a pretrained model. However, current finetuning solutions rely on weight adapters which often lack interpretability, and are overly sensitive to their hyper-parameters. In this talk, we take a different perspective and shift the focus from weights to activation functions, viewing them through the lens of smoothing spline operators. We propose Curvature Tuning (CT), an interpretable and principled steering method that modulates a model’s decision boundary by injecting a single hyperparameter into its activation functions. We show that CT provably adjusts model decision boundary curvature and, more fundamentally, projects a model onto a space of smooth functions—thereby complementing current fine-tuning methods, whose effect lies primarily in feature adaptation.
