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Scaling Neural Tangent Kernels via Sketching and Random Features
Amir Zandieh · Insu Han · Haim Avron · Neta Shoham · Chaewon Kim · Jinwoo Shin

Wed Dec 08 04:30 PM -- 06:00 PM (PST) @ Virtual

The Neural Tangent Kernel (NTK) characterizes the behavior of infinitely-wide neural networks trained under least squares loss by gradient descent. Recent works also report that NTK regression can outperform finitely-wide neural networks trained on small-scale datasets. However, the computational complexity of kernel methods has limited its use in large-scale learning tasks. To accelerate learning with NTK, we design a near input-sparsity time approximation algorithm for NTK, by sketching the polynomial expansions of arc-cosine kernels: our sketch for the convolutional counterpart of NTK (CNTK) can transform any image using a linear runtime in the number of pixels. Furthermore, we prove a spectral approximation guarantee for the NTK matrix, by combining random features (based on leverage score sampling) of the arc-cosine kernels with a sketching algorithm. We benchmark our methods on various large-scale regression and classification tasks and show that a linear regressor trained on our CNTK features matches the accuracy of exact CNTK on CIFAR-10 dataset while achieving 150x speedup.

Author Information

Amir Zandieh (Max-Planck-Institut für Informatik)
Insu Han (Yale University)
Haim Avron (Tel Aviv University)
Neta Shoham (Edgify)
Chaewon Kim (KAIST)
Jinwoo Shin (KAIST)

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