MIRE: Matched Implicit Neural Representations

Implicit Neural Representations (INRs) are continuous function learners for conventional digital signal representations. With the aid of positional embeddings and/or exhaustively fine-tuned activation functions, INRs have surpassed many limitations of traditional discrete representations. However, existing works only find a continuous representation for the digital signal by solely using a single, fixed activation function throughout the INR, and it has not yet been explored to match the INR to the given signal. As current INRs are not matched to the signal being represented by the INR, we hypothesize that this approach could restrict the representation power and generalization capabilities of INRs, limiting their broader applicability. A way to match the INR to the signal being represented is through matching the activation of each layer in the sense of minimizing the mean squared loss. In this paper, we introduce MIRE, a method to find the highly matched activation function for each layer in INR through dictionary learning. To showcase the effectiveness of the proposed method, we utilize a dictionary that includes seven activation atoms: Raised Cosines (RC), Root Raised Cosines (RRC), Prolate Spheroidal Wave Function (PSWF), Sinc, Gabor Wavelet, Gaussian, and Sinusoidal. Experimental results demonstrate that MIRE not only significantly improves INR performance across various tasks, such as image representation, image inpainting, 3D shape representation, novel view synthesis, super-resolution, and reliable edge detection, but also eliminates the need for the previously required exhaustive search for activation parameters, which had to be conducted even before INR training could begin.