Deep neural networks have enabled technological wonders ranging from voice recognition to machine transition to protein engineering, but their design and application is nonetheless notoriously unprincipled.
The development of tools and methods to guide this process is one of the grand challenges of deep learning theory.
In Reverse Engineering the Neural Tangent Kernel, we propose a paradigm for bringing some principle to the art of architecture design using recent theoretical breakthroughs: first design a good kernel function – often a much easier task – and then “reverse-engineer” a net-kernel equivalence to translate the chosen kernel into a neural network.
Our main theoretical result enables the design of activation functions from first principles, and we use it to create one activation function that mimics deep \(\textrm{ReLU}\) network performance with just one hidden layer and another that soundly outperforms deep \(\textrm{ReLU}\) networks on a synthetic task.
Kernels back to networks. Foundational works derived formulae that map from wide neural networks to their corresponding kernels. We obtain an inverse mapping, permitting us to start from a desired kernel and turn it back into a network architecture.
