Local neural implicit functions with modulated periodic activations

An apparatus for signal processing, comprising:

• at least one processor;
• at least one memory;
• a modulator network comprising a plurality of modulator layers, wherein each of the plurality of modulator layers of the modulator network is configured to output a different set of modulation parameters based on a same digital signal;
• an encoder configured to produce a latent vector representing the digital signal, wherein the modulator network takes the latent vector as input;
• and
• a synthesizer network comprising a plurality of synthesizer layers, wherein the synthesizer network represents a continuous function of a signal parameter of the digital signal, and wherein each of the synthesizer layers is configured to receive the set of modulation parameters from a corresponding modulator layer of the modulator network.

A method for training a neural network, comprising:

• receiving a digital signal comprising signal values corresponding to discrete sample locations;
• generating modulation parameters based on the digital signal using a modulator network, wherein each of a plurality of modulator layers of the modulator network outputs a set of the modulation parameters, encoding the digital signal to produce a latent vector, wherein the modulator network takes the latent vector as input to produce the modulation parameters;
• generating a predicted signal value of the digital signal for at least one of the original sample locations using a synthesizer network, wherein each of a plurality of synthesizer layers of the synthesizer network receives the set of the modulation parameters from a corresponding modulator layer of the modulator network;
• computing a loss function based on the predicted signal value and a value of the original signal values corresponding to the at least one of the original sample locations;
• and
• training the modulator network and the synthesizer network based on the loss function.