The reviews for this paper were overall positive. The authors present an algorithm that, without having any bias related to images, allows one to learn locally connected weights, and provide a study of inductive bias of convolutions. The reviewers appreciated the contributions which address an 'important ML problem' and the developments in particular the interesting results obtained with MLPs on CIFAR-10. The reviewers pointed out several venues for improvement, in particular, the positioning of the paper, the empirical evidence provided to support the claims made, and the thoroughness of the empirical evaluation. A reviewer for instance would have liked to see 'experiments about stacking the searched operation to a deeper model and proving the searched operation is transferable among different datasets (such as between CIFAR and ImageNet, or between CIFAR and SVHN' in order 'to prove that the proposed algorithm is able to search a similar operation from the fully connected networks'. A reviewer would have expected comparisons of Beta-LASSO 'with naive LASSO or other regularizers' over a range of values of the regularization. The authors submitted a response to the reviewers' comments, as well as confidential comments to the area chair. After reading the response, updating the reviews, and discussion, the reviewers maintained their overall positive assessment about the paper. They also encourage the authors to follow their suggestions while preparing the final version to make the paper more impactful. Accept.