The paper provides a plausible first-cut theoretical explanation of mode connectivity in deep nets trained using gradient based optimization. The results are developed based on suitable assumptions on resilience to perturbations, in particular based on dropout training and noise stability. The paper also provides approaches to construct piece-wise linear paths to connect solutions under these assumptions. The reviewers liked the paper overall. There is agreement that the paper makes a good contribution, and also does not oversell the results. Some reviewers felt that the paper can be strengthened by improving clarity on certain definitions and ideas behind path constructions.