%0 Journal Article %1 du2020fewshot %A Du, Simon S. %A Hu, Wei %A Kakade, Sham M. %A Lee, Jason D. %A Lei, Qi %D 2020 %K few-shot learning %T Few-Shot Learning via Learning the Representation, Provably %U http://arxiv.org/abs/2002.09434 %X This paper studies few-shot learning via representation learning, where one uses $T$ source tasks with $n_1$ data per task to learn a representation in order to reduce the sample complexity of a target task for which there is only $n_2 (n_1)$ data. Specifically, we focus on the setting where there exists a good common representation between source and target, and our goal is to understand how much of a sample size reduction is possible. First, we study the setting where this common representation is low-dimensional and provide a fast rate of $Ołeft(\mathcalCłeft(\Phi\right)n_1T + kn_2\right)$; here, $\Phi$ is the representation function class, $Cłeft(\Phi\right)$ is its complexity measure, and $k$ is the dimension of the representation. When specialized to linear representation functions, this rate becomes $Ołeft(dkn_1T + kn_2\right)$ where $d (k)$ is the ambient input dimension, which is a substantial improvement over the rate without using representation learning, i.e. over the rate of $Ołeft(dn_2\right)$. Second, we consider the setting where the common representation may be high-dimensional but is capacity-constrained (say in norm); here, we again demonstrate the advantage of representation learning in both high-dimensional linear regression and neural network learning. Our results demonstrate representation learning can fully utilize all $n_1T$ samples from source tasks.

@article{du2020fewshot, abstract = {This paper studies few-shot learning via representation learning, where one uses $T$ source tasks with $n_1$ data per task to learn a representation in order to reduce the sample complexity of a target task for which there is only $n_2 (\ll n_1)$ data. Specifically, we focus on the setting where there exists a good \emph{common representation} between source and target, and our goal is to understand how much of a sample size reduction is possible. First, we study the setting where this common representation is low-dimensional and provide a fast rate of $O\left(\frac{\mathcal{C}\left(\Phi\right)}{n_1T} + \frac{k}{n_2}\right)$; here, $\Phi$ is the representation function class, $\mathcal{C}\left(\Phi\right)$ is its complexity measure, and $k$ is the dimension of the representation. When specialized to linear representation functions, this rate becomes $O\left(\frac{dk}{n_1T} + \frac{k}{n_2}\right)$ where $d (\gg k)$ is the ambient input dimension, which is a substantial improvement over the rate without using representation learning, i.e. over the rate of $O\left(\frac{d}{n_2}\right)$. Second, we consider the setting where the common representation may be high-dimensional but is capacity-constrained (say in norm); here, we again demonstrate the advantage of representation learning in both high-dimensional linear regression and neural network learning. Our results demonstrate representation learning can fully utilize all $n_1T$ samples from source tasks.}, added-at = {2020-03-15T04:04:04.000+0100}, author = {Du, Simon S. and Hu, Wei and Kakade, Sham M. and Lee, Jason D. and Lei, Qi}, biburl = {https://www.bibsonomy.org/bibtex/2c446ed503057797f31e5db8166a3d021/kirk86}, description = {[2002.09434] Few-Shot Learning via Learning the Representation, Provably}, interhash = {68ec21c25dcb344ca1408ca66451387e}, intrahash = {c446ed503057797f31e5db8166a3d021}, keywords = {few-shot learning}, note = {cite arxiv:2002.09434}, timestamp = {2020-03-15T04:04:04.000+0100}, title = {Few-Shot Learning via Learning the Representation, Provably}, url = {http://arxiv.org/abs/2002.09434}, year = 2020 }