Many recent breakthroughs in deep learning were achieved by training increasingly larger models on massivedatasets. However,training such models can be prohibitively expensive. For instance, the cluster used to train GPT-3 costs over $250 million2. Asaresult, most researchers cannot afford totrain state oftheart models and contribute to their development.

These are upper bounds on the zero-one estimation error of any predictor in a hypothesis set, expressed in terms of its surrogate loss estimation error.

Most existing works have focused on ranking from pairwise comparisons. In contrast, we focus on ranking frommulti-wise (or m-wise) comparisons. The pairwise comparisons can be viewed as multi-wise comparisons withm = 2. One motivation is that in many scenarios, multi-wise comparisons are more common.

Blind image deblurring (BID) is an important yet challenging image recovery problem. Most existing deep learning methods require supervised training with ground truth (GT) images. This paper introduces a self-supervised method for BID that does not require GT images. The key challenge is to regularize the training to prevent over-fitting due to the absence of GT images. By leveraging an exact relationship among the blurred image, latent image, and blur kernel across consecutive scales, we propose an effective cross-scale consistency loss.

Hence, when a message passing kernel satisfies the naturality condition for local isomorphisms of the edge neighbourhood (Eq.