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Multilayer Perceptron Help (Regression Problem)
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Multilayer Perceptron Help (Regression Problem)
#1
Hello everyone,

I'm working on a project for my machine learning class and I really need help understanding what happens during backpropagation with a multilayer perceptron and how the network should be structured. The goal is for the perceptron to approximate the correct output of the function given values for x and y. Here is the assignment:



Investigate the use of the Multi-Layer Perceptron to approximate (a regression problem) the following function:

f(x,y)=sin⁡(pi*10*x+10/(1+y^2))+ln⁡(x^2+y^2), 1 ≤x,y ≤100 are real numbers

You may use any implementation of the MLP.

What to do:

Set up two sets of data, one for training and one for testing. Use the training set to compute the weights of the network. Evaluate the
approximation accuracy (the root-mean squared error) of the network on the test data. Use a variable number of hidden layers (1-2), each with a
variable number of neurons (0-19). Investigate how the network’s performance is affected by varying the number of hidden layers and the number of
hidden neurons in each layer. It is not necessary to try all 20 x 20 combinations of neurons in the two hidden layers; try only some of them.

Hint: If you use your own implementation:
Use two input neurons: one for x and one for y.
For the hidden neurons, use bipolar or unipolar sigmoid activation functions.
Use a single output neuron, with the identity (linear) activation function (read Sections 3.2.3 and 4.4.1 from textbook).
Do not forget to add a fixed input (-1) to each layer



Should the sigmoid function be used on the input layer?
When would I use the linear activation function?
How do I backpropagate through the network? Is there an equation for this?

I have coded a neural network for a project which solves the XOR problem, but this one is different as the inputs are not 0 or 1 and the output is not 0 or 1. I'm unsure of how to train the network given this problem and I cannot find a solution anywhere I look.
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