Efficient NTK using Dimensionality Reduction
This work addresses efficiency issues for researchers and practitioners using NTK in large-width neural networks, though it is incremental as it builds on existing factorization techniques.
The paper tackles the high computational cost of neural tangent kernel (NTK) analyses by using matrix factorization to reduce resource requirements in training and inference, achieving similar guarantees as prior methods.
Recently, neural tangent kernel (NTK) has been used to explain the dynamics of learning parameters of neural networks, at the large width limit. Quantitative analyses of NTK give rise to network widths that are often impractical and incur high costs in time and energy in both training and deployment. Using a matrix factorization technique, we show how to obtain similar guarantees to those obtained by a prior analysis while reducing training and inference resource costs. The importance of our result further increases when the input points' data dimension is in the same order as the number of input points. More generally, our work suggests how to analyze large width networks in which dense linear layers are replaced with a low complexity factorization, thus reducing the heavy dependence on the large width.