We show an example here on a classical XOR problem.

Dataset

We first need to create a dataset, following the conventions described in StochasticGradient. 

require "lab"
dataset={};
function dataset:size() return 100 end -- 100 examples
for i=1,dataset:size() do 
  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
  dataset[i] = {input, output}
end

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))

Training

We choose the Mean Squared Error criterion and train the beast. 

criterion = nn.MSECriterion()  
trainer = nn.StochasticGradient(mlp, criterion)
trainer.learningRate = 0.01
trainer:train(dataset)

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))

-0.3490
[torch.Tensor of dimension 1]

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

 1.0561
[torch.Tensor of dimension 1]

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

 0.8640
[torch.Tensor of dimension 1]

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

-0.2941
[torch.Tensor of dimension 1]