Implicit Regularization Paths of Weighted Neural Representations

In recent years, neural networks have become state-of-the-art models for tasks in computer vision and natural language processing by learning rich representations from large datasets. Pretrained neural networks, such as ResNet, which are trained on massive datasets like ImageNet, serve as valuable resources for new, smaller datasets [32]. These pretrained models reduce computational burden and generalize well in tasks such as image classification and object detection due to their rich feature space [32, 69]. Furthermore, pretrained features or neural embeddings, such as the neural tangent kernel, extracted from these models, serve as valuable representations of diverse data [33, 66]. However, despite their usefulness, fitting models based on pretrained features on large datasets can be challenging due to computational and memory constraints. When dealing with highdimensional pretrained features and large sample sizes, direct application of even simple linear regression may be computationally infeasible or memory-prohibitive [23, 44]. To address this issue, subsampling has emerged as a practical solution that reduces the dataset size, thereby alleviating the computational and memory burden. Subsampling involves creating smaller datasets by randomly selecting a subset of the original data points.