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so you know being similar to what Francis told us about this morning weamp;#39;re interested in trying to understand something about the training and performance of neural networks and so Iamp;#39;ve got a diagram here thatamp;#39;s kind of similar to Francisamp;#39;s but I helpfully used all different notation just to keep you on your toes so weamp;#39;re interested in a network thatamp;#39;s going to take a d-dimensional input and an output a single real value and the way we think about this is the following all the parameters of this network is one giant vector that recall fado so this corresponds to the weight matrices that all the layers plus the final layer and we can think about the output of this network is some function H that is a function of the input X and is characterized by these these weights in theta so we take the input X we multiply at times the first weight matrix W 1 apply a nonlinear activation and and so forth and then finally when we want to train one of th