A proper understanding of the striking generalization abilities of deep neural networks presents an enduring puzzle.

We would first like to thank all three reviewers for their thorough, constructive and considered reviews. Appendix A, our model is a nonequilibrium variant of Derrida's Random Energy Model. We will update the final manuscript to describe this analogy more explicitly. As such, this is still a matter of active research. Conditions claimed in L181-184: We will amend the manuscript to indicate that the equation directly preceding eqn.

A proper understanding of the striking generalization abilities of deep neural networks presents an enduring puzzle.

We would first like to thank all three reviewers for their thorough, constructive and considered reviews. Appendix A, our model is a nonequilibrium variant of Derrida's Random Energy Model. We will update the final manuscript to describe this analogy more explicitly. As such, this is still a matter of active research. Conditions claimed in L181-184: We will amend the manuscript to indicate that the equation directly preceding eqn.

The experiments on multitask learning are informative. I wish the experiments and theory were a bit more integrated. See my comments below for more details. The authors moved a lot of details to the appendix while keeping the main conclusions in the main submission to ease understanding. Here are some examples: (a) L181-184 what equation shows (s_A - \tilde{s_A}) depends on the said 4 things; (b) L185-186 when labelled data is scarce why is (\bar{s_A*g(s_A)}-\tilde{s_A*g(s_A)} 0; (c) L189-190 why does (\bar{s_A*g(s_A)}-\tilde{s_A*g(s_A)} tend to 0 when training data is abundant.

This paper is a nice combination of theoretical understanding and simple experiments to verify it in the case of multitask learning in neural nets. Given that there is not much known in this space, this work can be impactful. I suggest authors to add a few multi-task experiments with real datasets to verify their understanding.

A proper understanding of the striking generalization abilities of deep neural networks presents an enduring puzzle. Recently, there has been a growing body of numerically-grounded theoretical work that has contributed important insights to the theory of learning in deep neural nets. There has also been a recent interest in extending these analyses to understanding how multitask learning can further improve the generalization capacity of deep neural nets. These studies deal almost exclusively with regression tasks which are amenable to existing analytical techniques. We develop an analytic theory of the nonlinear dynamics of generalization of deep neural networks trained to solve classification tasks using softmax outputs and cross-entropy loss, addressing both single task and multitask settings.

A proper understanding of the striking generalization abilities of deep neural networks presents an enduring puzzle. Recently, there has been a growing body of numerically-grounded theoretical work that has contributed important insights to the theory of learning in deep neural nets. There has also been a recent interest in extending these analyses to understanding how multitask learning can further improve the generalization capacity of deep neural nets. These studies deal almost exclusively with regression tasks which are amenable to existing analytical techniques. We develop an analytic theory of the nonlinear dynamics of generalization of deep neural networks trained to solve classification tasks using softmax outputs and cross-entropy loss, addressing both single task and multitask settings.