1-Lipschitz continuous neural network with initial condition (hard)

[TingdiRen]

Thanks for the contribution! Here, I'd like to delve into a new issue. How can we achieve a 1-Lipschitz continuous neural network ( f ) while adhering to the initial condition ( f(0) = 0 )? Using a penalty method is a soft constraint, which might lead to unexpected smoothing. My idea is to append a new neural network ( g(x) ) at the end to fit the indicator function of whether ( x ) is 0, as theoretically, ( g(x) ) is also 1-Lipschitz continuous. Then the new output ( f(x) = g(x) \times f(x) ) is to ensure overall 1-Lipschitz continuity.