7 Analysis of neural networks: a random matrix approach The inherent intractability of neural network performances,which mainly originates from the non linearity of the neural activations (as well as from learning by back-propagation of the error). With this observation in mind,we propose here a theoretical study of the performance of large dimensional neural networks (in the sense of large datasets and number of neurons)The inherent intractability of neural network performances, which mainly originates from the non linearity of the neural activations (as well as from learning by back-propagation of the error). 7 Analysis of neural networks: a random matrix approach With this observation in mind, we propose here a theoretical study of the performance of large dimensional neural networks (in the sense of large datasets and number of neurons)