We show an example here on a classical XOR problem.

Neural Network

We create a simple neural network with one hidden layer. 

require "nn"
mlp = nn.Sequential();  -- make a multi-layer perceptron
inputs = 2; outputs = 1; HUs = 20; -- parameters
mlp:add(nn.Linear(inputs, HUs))
mlp:add(nn.Tanh())
mlp:add(nn.Linear(HUs, outputs))

Loss function

We choose the Mean Squared Error criterion. 

criterion = nn.MSECriterion()

Training

We create data on the fly and feed it to the neural network. 

require "lab"
for i = 1,2500 do
  -- random sample
  local input= lab.randn(2);     -- normally distributed example in 2d
  local output= torch.Tensor(1);
  if input[1]*input[2] > 0 then  -- calculate label for XOR function
    output[1] = -1
  else
    output[1] = 1
  end

  -- feed it to the neural network and the criterion
  criterion:forward(mlp:forward(input), output)

  -- train over this example in 3 steps
  -- (1) zero the accumulation of the gradients
  mlp:zeroGradParameters()
  -- (2) accumulate gradients
  mlp:backward(input, criterion:backward(mlp.output, output))
  -- (3) update parameters with a 0.01 learning rate
  mlp:updateParameters(0.01)
end

Test the network 

x = torch.Tensor(2)
x[1] =  0.5; x[2] =  0.5; print(mlp:forward(x))
x[1] =  0.5; x[2] = -0.5; print(mlp:forward(x))
x[1] = -0.5; x[2] =  0.5; print(mlp:forward(x))
x[1] = -0.5; x[2] = -0.5; print(mlp:forward(x))

You should see something like: 

> x = torch.Tensor(2)
> x[1] =  0.5; x[2] =  0.5; print(mlp:forward(x))

-0.6140
[torch.Tensor of dimension 1]

> x[1] =  0.5; x[2] = -0.5; print(mlp:forward(x))

 0.8878
[torch.Tensor of dimension 1]

> x[1] = -0.5; x[2] =  0.5; print(mlp:forward(x))

 0.8548
[torch.Tensor of dimension 1]

> x[1] = -0.5; x[2] = -0.5; print(mlp:forward(x))

-0.5498
[torch.Tensor of dimension 1]