We find that they are positive-definite as expected. Supervised Differentiable Programming" by Chizat and Bach is an important contribution and we will absolutely Sec 2.2 in V1, V2) are restricted to single-hidden-layer networks. It is still an open research question to determine what are the main factors that determine these performance gaps. We will expand discussion around this.

The paper was proofread, well-structured, and very clear. The experiments were clearly described in detail, and provided relevant results. Below we outline some detailed comments of the results. In particular, Chizat and Bach prove that the training of an NTK parameterized network is closely modeled by "lazy training" (their terminology for a linearized model). This paper is not referenced in the related work section.

This work introduces the first toolkit around path-norms that is fully able to encompass general DAG ReLU networks with biases, skip connections and any operation based on the extraction of order statistics: max pooling, GroupSort etc. This toolkit notably allows us to establish generalization bounds for modern neural networks that are not only the most widely applicable path-norm based ones, but also recover or beat the sharpest known bounds of this type. These extended path-norms further enjoy the usual benefits of path-norms: ease of computation, invariance under the symmetries of the network, and improved sharpness on feedforward networks compared to the product of operators' norms, another complexity measure most commonly used. The versatility of the toolkit and its ease of implementation allow us to challenge the concrete promises of path-norm-based generalization bounds, by numerically evaluating the sharpest known bounds for ResNets on ImageNet.

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