Schematics of the Back-Propagation process, where the error of each neuron δ is computed first from the error in the output layer (panel a), through all the hidden layers (panel b). The weights and bias are updated accordingly. Panel a: schematic of how the error is computed for the output neuron (Eq. (14)). We note that in this study we use the identity function for the activation function of the output, . Panel b: schematic of how the error of neuron j in hidden layer l is computed from the error of the m_l + 1 neurons in layer l + 1 (Eq. (15)).