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We develop the "generalized consistent weighted sampling" (GCWS) for hashingthe "powered-GMM" (pGMM) kernel (with a tuning parameter $p$). It turns outthat GCWS provides a numerically stable scheme for applying powertransformation on the original data, regardless of the magnitude of $p$ and thedata. The power transformation is often effective for boosting the performance,in many cases considerably so. We feed the hashed data to neural networks on avariety of public classification datasets and name our method ``GCWSNet''. Ourextensive experiments show that GCWSNet often improves the classificationaccuracy. Furthermore, it is evident from the experiments that GCWSNetconverges substantially faster. In fact, GCWS often reaches a reasonableaccuracy with merely (less than) one epoch of the training process. Thisproperty is much desired because many applications, such as advertisementclick-through rate (CTR) prediction models, or data streams (i.e., data seenonly once), often train just one epoch. Another beneficial side effect is thatthe computations of the first layer of the neural networks become additionsinstead of multiplications because the input data become binary (and highlysparse).  Empirical comparisons with (normalized) random Fourier features (NRFF) areprovided. We also propose to reduce the model size of GCWSNet by count-sketchand develop the theory for analyzing the impact of using count-sketch on theaccuracy of GCWS. Our analysis shows that an ``8-bit'' strategy should workwell in that we can always apply an 8-bit count-sketch hashing on the output ofGCWS hashing without hurting the accuracy much. There are many other ways totake advantage of GCWS when training deep neural networks. For example, one canapply GCWS on the outputs of the last layer to boost the accuracy of traineddeep neural networks.

GCWSNet: Generalized Consistent Weighted Sampling for Scalable and Accurate Training of Neural Networks