TITLE: Dataset Meta-Learning from Kernel Ridge-Regression 

ABSTRACT: One of the most fundamental aspects of any machine learning algorithm is the
training data used by the algorithm. We introduce the novel concept of
$\epsilon$-approximation of datasets, obtaining datasets which are much smaller
than or are significant corruptions of the original training data while
maintaining similar model performance. We introduce a meta-learning algorithm
called Kernel Inducing Points (KIP) for obtaining such remarkable datasets,
inspired by the recent developments in the correspondence between
infinitely-wide neural networks and kernel ridge-regression (KRR). For KRR
tasks, we demonstrate that KIP can compress datasets by one or two orders of
magnitude, significantly improving previous dataset distillation and subset
selection methods while obtaining state of the art results for MNIST and
CIFAR-10 classification. Furthermore, our KIP-learned datasets are transferable
to the training of finite-width neural networks even beyond the lazy-training
regime, which leads to state of the art results for neural network dataset
distillation with potential applications to privacy-preservation.
One of the most fundamental aspects of any machine learning algorithm is the
training data used by the algorithm. We introduce the novel concept of
$\epsilon$-approximation of datasets, obtaining datasets which are much smaller
than or are significant corruptions of the original training data while
maintaining similar model performance. We introduce a meta-learning algorithm
called Kernel Inducing Points (KIP) for obtaining such remarkable datasets,
inspired by the recent developments in the correspondence between
infinitely-wide neural networks and kernel ridge-regression (KRR). For KRR
tasks, we demonstrate that KIP can compress datasets by one or two orders of
magnitude, significantly improving previous dataset distillation and subset
selection methods while obtaining state of the art results for MNIST and
CIFAR-10 classification. Furthermore, our KIP-learned datasets are transferable
to the training of finite-width neural networks even beyond the lazy-training
regime, which leads to state of the art results for neural network dataset
distillation with potential applications to privacy-preservation.
Dataset Meta-Learning from Kernel Ridge-Regression
http://arxiv.org/abs/2011.00050v3