Parameter-Efficient Fine-Tuning (PEFT) methods provide a streamlined and efficient tool for adapting large models to domain-specific multimodal downstream tasks. Although these methods proved their tangible effects in practice, their principal aspects remain under-explored. Therefore we remain curious about the underlying generalization mechanisms in various PEFT methods and how they can be further enhanced. In this paper, we reveal the flatness preference widely present in various PEFTs, where a small fraction of sharp dimensions dominates the generalization of PEFT. This finding suggests an appealing possibility: we may be satisfied with a better generalization by merely attending to this small fraction of sharp dimensions instead of all of them. Furthermore, we propose Flatness Preference Optimization (FlatPO) to flatten these key sharpness dimensions, leading various PEFTs toward better generalization. Extensive experiments demonstrate the effectiveness of our findings and the proposed method. Code is available at https://github.com/Can-Lin/FlatPO.
A common heuristic used to explain the generalization of first-order gradient methods on non-convex neural networks is that "flat interpolators generalize well" (Hochreiter and Schmidhuber, 1994; Keskar et al., 2017), where flatness can be measured by the trace of the Hessian of the empirical loss. However, Dinh et al. 2017) showed that, using symmetry of the network that can change flatness while keeping the population and empirical losses unchanged, any interpolator can be made sharper or flatter. This result makes the earlier heuristic statement vacuous. In this paper, we show that for learning an unknown multi-index model with $2$-layer non-convex homogeneous neural networks, there is a connection between flatness and generalization, despite the existence of symmetries. This connection pertains to the "flattest" interpolators, i.e., the interpolators that have orderwise minimum flatness among all interpolators. First, we show that there exists a natural class of non-generalizing interpolators whose flatness cannot be made closer to the flattest possible, even using symmetries. Second, we show that for data generated by a sum of single-index models, if the approximation error and label noise are low, any flattest interpolator achieves small population loss, i.e., the flattest interpolators always generalize. This establishes a direct link between flatness and generalization which applies to a large class of activations and realistic data distributions.