In the simple example where I have n input neurons, I can consider this to be a point in a n-dimensional space.If the output layer is just one neuron with value 0 or 1, if I get convergence, the neural net should define a hyperplane dividing the two classes of points - those mapped to 0 and those mapped to 1. How do I calculate this hyperplane using the (n,1) matrix of weights I calculated?
How to draw a hyperplane using the weights calculated
neural network
If you have only an input layer, one set of weights, and an output layer, you can solve this directly with $$ X \cdot w = threshold $$However if you add in hidden layers, you no longer necessarily have a hyperplane, as in order to be a hyperplane it must be able to be expressed as the solution of a single algebraic equation of degree 1.Even if you can't solve directly, you can still get a sense for the response surface by evaluating your network's output over a wide range of inputs. 