We consider $L^2$-regularized linear (ridge) regression over a finite data sample $X$ with bounded covariance and linear prediction targets $y$ with additive isotropic noise of finite variance. We present an iterative procedure to compute the optimal regularization strength numerically from the generative parameters in the fixed-$X$ setting and prove its convergence at limited noise levels. Our experimental evaluation over synthetic data shows that the proposed procedure combined with sample-based parameter estimates attains near-optimal random-$X$ generalization across a wide range of sample sizes, aspect ratios, and noise levels, at an added computational cost equivalent to one preliminary ridge regression in the underparameterized regime and two in the overparameterized case.

Broader Impacts NaViT enables training of vision transformers on variable size inputs, which has a profound impact on advancing adaptive computation research. By training models to handle various input size, we can explore adaptive computation techniques that dynamically adjust the computational resources based on the specific requirements of a given input. This flexibility opens up new avenues for implementing ideas that aim at adjusting allocation of compute and improving efficiency in vision tasks per input. Furthermore, NaViT computational efficiency unlocks the potential for scaling up pre-training of vision models. With the ability to handle different resolutions, models can effectively tackle more complex and diverse visual data, allowing for the development of larger and more powerful vision models.

The ubiquitous and demonstrably suboptimal choice of resizing images to a fixed resolution before processing them with computer vision models has not yet been successfully challenged.

Diffusion models (DMs) have recently gained attention with state-of-the-art performance in text-to-image synthesis.

Neural Information Processing Systems http://nips.cc/

The term resolution refers to the width and height of images input into neural networks.

The ubiquitous and demonstrably suboptimal choice of resizing images to a fixed resolution before processing them with computer vision models has not yet been successfully challenged.