Expressive power of outer product manifolds on feed-forward neural networks
This addresses the problem of high parameter counts and training time for deep learning practitioners, offering a method to reduce computational costs while maintaining or improving performance.
The paper tackled the inefficiency of hierarchical neural networks by mathematically describing their structure using Riemannian metrics to enable switching to shallow networks early in training, achieving performance that sometimes surpasses the original network after just a few epochs.
Hierarchical neural networks are exponentially more efficient than their corresponding "shallow" counterpart with the same expressive power, but involve huge number of parameters and require tedious amounts of training. Our main idea is to mathematically understand and describe the hierarchical structure of feedforward neural networks by reparametrization invariant Riemannian metrics. By computing or approximating the tangent subspace, we better utilize the original network via sparse representations that enables switching to shallow networks after a very early training stage. Our experiments show that the proposed approximation of the metric improves and sometimes even surpasses the achievable performance of the original network significantly even after a few epochs of training the original feedforward network.