The associative property of multidimensional discrete convolution says that:
$$Y=(x \circledast h_1) \circledast h_2=x\circledast(h_1\circledast h_2)$$
where $h_1$ and $h_2$ are the filters and $x$ is the input.
I was able to do exploit this property in Keras with Conv2D
: first, I convolve $h_1$ and $h_2$, then I convolve the result with $x$ (i.e. the rightmost part of the equation above).
Up to this point, I don't have any problem, and I also understand that convolution is linear.
The problem is when two Conv2D layers have a non-linear activation function after the convolution. For example, consider the following two operations
$$Y_1=\text{ReLU}(x \circledast h_1)$$ $$Y_2=\text{ReLU}(Y_1\circledast h_2)$$
It is possible to apply the associative property if the first or both layers have a non-linear activation function (in the case above ReLU, but it could be any activation function)? I don't think so. Any idea or related paper or some kind of approach?