# How to perform back-propagation in Decoupled Neural Interfaces?

I am attempting to create a fully decoupled feed-forward neural network by using decoupled neural interfaces (DNIs) as explained in the paper Decoupled Neural Interfaces using Synthetic Gradients (2017) by Max Jaderberg et al. As in the paper, the DNI is able to produce a synthetic error gradient that reflects the error with respect the output:

$$\frac{\partial L}{\partial h_{i}}$$

I can then use this to update the current layer's parameters by multiplying by the parameters to get the loss with respect to the parameters:

$$\frac{\partial L}{\partial \theta}=\frac{\partial L}{\partial h_{i}} * \frac{\partial h_{i}}{\partial \theta}$$

In the paper, the layer's model is then updated based on the next layer sending the true error backwards.

My question is, given that I am able to calculate the error with respect to the current output, how do I use this to calculate the loss with respect to the previous layer's output?