Additionally,though traditional PINNs (vanilla-PINNs) are typically stored andtrained in32-bit floating-point (fp32) ontheGPU, weshow that for DT-PINNs, using fp64 on the GPU leads to significantly faster training times than fp32 vanilla-PINNs with comparable accuracy. PINNscanbeusedboth to discover/infer PDEs that govern a given data set, and as direct PDE solvers.

First, the gating mechanism is ubiquitous in RNNs, and usually thought of as a heuristic forsmoothingoptimization[28].

We thank all 3 reviewers for their thoughtful comments. " nearest neighbor theory papers have largely not worried too much about constants......This analysis is " In the evolution of the study of nearest neighbor, early work focused on consistency, and later Y ou are absolutely correct that very few work studies the constant. We argue that this is "a feature, not " The scope of the analysis is very limited to distributed nearest neighbor classification (along with some distributional The latter is a fairly interesting direction, due to its connection with deep learning. " Currently the paper has lots of small typos. Please proofread carefully and revise.. " Thanks for pointing out, and we " Also, I find T able 1 ... How is the risk percentage defined in comparison to the oracle KNN/OWNN? " I'd suggest adding error bars to T able 1 (for example, to denote standard deviations across experimental repeats).