Pruning Neural Networks via Coresets and Convex Geometry: Towards No Assumptions

Pruning is one of the predominant approaches for compressing deep neural networks (DNNs). Lately, coresets (provable data summarizations) were leveraged for pruning DNNs, adding the advantage of theoretical guarantees on the trade-off between the compression rate and the approximation error. However, coresets in this domain were either data-dependent or generated under restrictive assumptions on both the model's weights and inputs. In real-world scenarios, such assumptions are rarely satisfied, limiting the applicability of coresets. To this end, we suggest a novel and robust framework for computing such coresets under mild assumptions on the model's weights and without any assumption on the training data. The idea is to compute the importance of each neuron in each layer with respect to the output of the following layer. This is achieved by a combination of L\"{o}wner ellipsoid and Caratheodory theorem. Our method is simultaneously data-independent, applicable to various networks and datasets (due to the simplified assumptions), and theoretically supported. Experimental results show that our method outperforms existing coreset based neural pruning approaches across a wide range of networks and datasets. For example, our method achieved a $62\%$ compression rate on ResNet50 on ImageNet with $1.09\%$ drop in accuracy

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

Coresets for the Nearest-Neighbor Rule

Given a training set $P$ of labeled points, the nearest-neighbor rule predicts the class of an unlabeled query point as the label of its closest point in the set. To improve the time and space complexity of classification, a natural question is how to reduce the training set without significantly affecting the accuracy of the nearest-neighbor rule. Nearest-neighbor condensation deals with finding a subset $R \subseteq P$ such that for every point $p \in P$, $p$'s nearest-neighbor in $R$ has the same label as $p$. This relates to the concept of coresets, which can be broadly defined as subsets of the set, such that an exact result on the coreset corresponds to an approximate result on the original set. However, the guarantees of a coreset hold for any query point, and not only for the points of the training set. This paper introduces the concept of coresets for nearest-neighbor classification. We extend existing criteria used for condensation, and prove sufficient conditions to correctly classify any query point when using these subsets. Additionally, we prove that finding such subsets of minimum cardinality is NP-hard, and propose quadratic-time approximation algorithms with provable upper-bounds on the size of their selected subsets. Moreover, we show how to improve one of these algorithms to have subquadratic runtime, being the first of this kind for condensation

A Survey of Dataset Refinement for Problems in Computer Vision Datasets

Large-scale datasets have played a crucial role in the advancement of computer vision. However, they often suffer from problems such as class imbalance, noisy labels, dataset bias, or high resource costs, which can inhibit model performance and reduce trustworthiness. With the advocacy of data-centric research, various data-centric solutions have been proposed to solve the dataset problems mentioned above. They improve the quality of datasets by re-organizing them, which we call dataset refinement. In this survey, we provide a comprehensive and structured overview of recent advances in dataset refinement for problematic computer vision datasets. Firstly, we summarize and analyze the various problems encountered in large-scale computer vision datasets. Then, we classify the dataset refinement algorithms into three categories based on the refinement process: data sampling, data subset selection, and active learning. In addition, we organize these dataset refinement methods according to the addressed data problems and provide a systematic comparative description. We point out that these three types of dataset refinement have distinct advantages and disadvantages for dataset problems, which informs the choice of the data-centric method appropriate to a particular research objective. Finally, we summarize the current literature and propose potential future research topics.Comment: 33 pages, 10 figures, to be published in ACM Computing Survey