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Consider a 1-layer neural net with three input units, 1 output unit, no hidden units and no bias terms. Suppose that the output unit uses a sigmoid activation function, i.e., y = 1/(1 + e−z), where z is the total input to the unit. Let y be the computed output of the neural net, let d be the desired output, and let C = −d log y − (1 − d) log (1 − y) be the cross entropy error.Write down the equations for a single step of weight updates by gradient descent (based on a single data sample), and derive all the necessary derivatives. Simplify your answers, and be sure to clearly identify all the variables you use.

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  • Gradient Descent with one neuron:… Backpropagation with one neuron:… I think those two would be enough, but if not, please do not hesitate to ask specifics. – Ugur MULUK Dec 4 at 11:54

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