DIVA: Dataset Derivative of a Learning Task

Abstract

We present a method to compute the derivative of a learning task with respect to a dataset. A learning task is a function from a training set to the validation error, which can be represented by a trained deep neural network (DNN). The "dataset derivative" is a linear operator, computed around the trained model, that informs how perturbations of the weight of each training sample affect the validation error, usually computed on a separate validation dataset. Our method, DIVA (Differentiable Validation) hinges on a closed-form differentiable expression of the leaveone-out cross-validation error around a pre-trained DNN. Such expression constitutes the dataset derivative. DIVA could be used for dataset auto-curation, for example removing samples with faulty annotations, augmenting a dataset with additional relevant samples, or rebalancing. More generally, DIVA can be used to optimize the dataset, along with the parameters of the model, as part of the training process without the need for a separate validation dataset, unlike bi-level optimization methods customary in AutoML. To illustrate the flexibility of DIVA, we report experiments on sample auto-curation tasks such as outlier rejection, dataset extension, and automatic aggregation of multi-modal data.

Gradient-based Bi-level Optimization for Deep Learning: A Survey

“…These algorithms can be achieved by NTK tool [Novak et al 2019] easily. The approach [Dukler et al 2021] treats the instance weights as the outer variable and assumes the pretrained model with linear representation to yield a closed-form solution for the inner level task. Besides assuming the inner level as ridge regression and least squares, some works [Ghadimi and M. Wang 2018;…”