input to the output of this first layer this is the vector quantization partition or the spline partition that you that that that you obtain importantly we're going through a single layer so the tiling is convex right these are convex regions right makes sense okay moreover let's remember that these are splines after all so we can ask what what is the mapping from the input of the first layer to the output of the first layer well it's just a very simple affine map because it's an affine spline after all okay that once you know