Efficient NTK using Dimensionality Reduction

Recently, neural tangent kernel (NTK) has been used to explain the dynamics of learning parameters of neural networks, at the large width limit. Quantitative analyses of NTK give rise to network widths that are often impractical and incur high costs in time and energy in both training and deployment. Using a matrix factorization technique, we show how to obtain similar guarantees to those obtained by a prior analysis while reducing training and inference resource costs. The importance of our result further increases when the input points' data dimension is in the same order as the number of input points. More generally, our work suggests how to analyze large width networks in which dense linear layers are replaced with a low complexity factorization, thus reducing the heavy dependence on the large width

Data pruning and neural scaling laws: fundamental limitations of score-based algorithms

Data pruning algorithms are commonly used to reduce the memory and computational cost of the optimization process. Recent empirical results reveal that random data pruning remains a strong baseline and outperforms most existing data pruning methods in the high compression regime, i.e., where a fraction of $30\%$ or less of the data is kept. This regime has recently attracted a lot of interest as a result of the role of data pruning in improving the so-called neural scaling laws; in [Sorscher et al.], the authors showed the need for high-quality data pruning algorithms in order to beat the sample power law. In this work, we focus on score-based data pruning algorithms and show theoretically and empirically why such algorithms fail in the high compression regime. We demonstrate ``No Free Lunch" theorems for data pruning and present calibration protocols that enhance the performance of existing pruning algorithms in this high compression regime using randomization

One-shot Network Pruning at Initialization with Discriminative Image Patches

One-shot Network Pruning at Initialization (OPaI) is an effective method to decrease network pruning costs. Recently, there is a growing belief that data is unnecessary in OPaI. However, we obtain an opposite conclusion by ablation experiments in two representative OPaI methods, SNIP and GraSP. Specifically, we find that informative data is crucial to enhancing pruning performance. In this paper, we propose two novel methods, Discriminative One-shot Network Pruning (DOP) and Super Stitching, to prune the network by high-level visual discriminative image patches. Our contributions are as follows. (1) Extensive experiments reveal that OPaI is data-dependent. (2) Super Stitching performs significantly better than the original OPaI method on benchmark ImageNet, especially in a highly compressed model.Comment: BMVC 202