Constructing Extreme Learning Machines with zero Spectral Bias
This solves the challenge of resolving higher frequencies in neural networks for domains like physics simulations, though it is incremental as it adapts existing methods to ELMs.
The paper tackled the problem of Spectral Bias in Extreme Learning Machines (ELMs), showing that ELMs are not inherently free of it, but by implementing Fourier Feature Embeddings, they completely eliminated Spectral Bias, enabling practical applications like Physics Informed Neural Networks.
The phenomena of Spectral Bias, where the higher frequency components of a function being learnt in a feedforward Artificial Neural Network (ANN) are seen to converge more slowly than the lower frequencies, is observed ubiquitously across ANNs. This has created technology challenges in fields where resolution of higher frequencies is crucial, like in Physics Informed Neural Networks (PINNs). Extreme Learning Machines (ELMs) that obviate an iterative solution process which provides the theoretical basis of Spectral Bias (SB), should in principle be free of the same. This work verifies the reliability of this assumption, and shows that it is incorrect. However, the structure of ELMs makes them naturally amenable to implementation of variants of Fourier Feature Embeddings, which have been shown to mitigate SB in ANNs. This approach is implemented and verified to completely eliminate SB, thus bringing into feasibility the application of ELMs for practical problems like PINNs where resolution of higher frequencies is essential.