Recent few-shot learning algorithms have enabled models to quickly adapt to new tasks based on only a few training samples. Previous few-shot learning works have mainly focused on classification and reinforcement learning. In this paper, we propose a method that focuses on regression tasks. Our model is based on the idea that the degree of freedom of the unknown function can be significantly reduced if it is represented as a linear combination of a set of sparsifying basis functions. This enables using a few labelled samples to learn a good approximation of the entire function. We design a Basis Function Learner network to encode the basis functions for a task distribution, and a Weights Generator to generate the weight vector for a novel task. We show that our model outperforms current state of the art meta-learning methods in various regression tasks.
The paper proposes a regression approach that, given a few training (support) samples of a regression task (input and desired output pairs), should be able to output the values of the target function on additional (query) inputs. The proposed method is to learn a set of basis functions (MLPs) and a weight generator that for a given support set predicts weights using which the basis functions are linearly combined to form the predicted regression function, which is later tested (using the MSE metric) w.r.t. the ground truth. The method is trained on a large collection of randomly sampled task from the target family and is tested on a separate set of random tasks. The experiments include: 
* sinusoidal wave prediction from a few samples
* MNIST and CelebA inpainting from a set of known pixel values (in 28x28 and 32x32 resolution respectively)
* additional experiments on heat equation and 2D Gaussian distribution task in Appendix
The experiments show that the proposed approach outperforms the other methods on the sinusoidal wave toy problem, and yet performs less good then than Kim et al. 2019 on MNIST and CelebA.
I propose to reject the paper in its current form, and consider the following negative points for further improvement:
1. The posed problem is not really few-shot learning, in (now classical) few-shot learning, such as few-shot classification on benchmarks such as miniImageNet, CUB, tieredImageNet, CIFAR-FS, FC100, etc. the meta-training is done on a disjoint set of categories and testing is done on a completely new set of categories unseen during training. The gap between disjoint visual categories is very large, and it does not come close to being tested on a different from training samples sinusoidal wave or different set of hidden pixels in inpainting on the same (seen during training) set of classes (where the basis function module could learn a set of basis functions for every class). In the proposed setting, I think a better definition would be "learning a structured regression" from a set of sample points to a function, and not few-shot regression.
If the authors would like to keep the "few-shot flavour", I would suggest re-formulating the experiments, and meta-train on some set of classes (e.g. inpainting over digits 0 to 4) and meta-test on a different set of classes (e.g. inpainting over digits 5 to 9). This partially holds for faces as they are all mostly different categories (different people), but in 32x32 resolution and MSE metric, I don't think they are sufficiently different.
2. I would expect stronger results on the more realistic MNIST and CelebA experiments (although as suggested in 1. the setting there should be different), currently it does less well then existing method.
3. An emerging important class of few-shot regression problems is few-shot object detection, where the bounding box coordinates of objects location need to be regressed. There are several papers and benchmarks in this space, and it will help the current paper to test on this challenging family of problems. Please see the following papers for benchmarks and settings:
* LSTD: A Low-Shot Transfer Detector for Object Detection, Chen et al. 2018
* RepMet: Representative-based metric learning for classification and one-shot object detection, Karlinsky et al. 2019
* Few-shot Object Detection via Feature Reweighting, Kang et al. 2019