Adversarial imitation learning has become a popular framework for imitation in continuous control.

Specifically, NTK-based analysis requires that the network weights stay very close to their initialization in the "node-wise"

Here, we examine RNNs trained using gradient descent on different tasks inspired by the neuroscience literature.

We thank the reviewers for their positive and constructive feedback on the paper. We also addressed all the other comments, and they will appear in the revised version. We trained an LSTM network on the NLP task of sentiment analysis (Fig. R2). As in our paper, we found that the resulting changes to the network weights are of low rank. Note that one may not observe this behavior for any task and network off the shelf.

Our code is available at https://github.com/microsoft/klite .

We provide theoretical results which prove that average pooling corresponds to projection within the space of square-integrable functions and show that U-Nets with average pooling implicitly learn a Haar wavelet basis representation of the data.

These give us further confidence in the validity of our theoretical analysis.