Basic neural network

Basic neural network

Before you begin...

Download and install Titus. This article was tested with Titus 0.7.1; newer versions should work with no modification. Python >= 2.6 and < 3.0 is required.

Launch a Python prompt and import the following:

Python 2.7.6
Type "help", "copyright", "credits" or "license" for more information.
>>> import titus.prettypfa
>>> from titus.genpy import PFAEngine

The basic form

The model.neural.simpleLayers function assumes that the topology of the neural network is arranged in layers. We chose the m.link.logit activation function from the link function library.

pfaDocument = titus.prettypfa.jsonNode('''
types:
  Layer = record(Layer,
                 weights: array(array(double)),
                 bias: array(double))

input: array(double)
output: double
cells:
  neuralnet(array(Layer)) = []
action:
  var activation = model.neural.simpleLayers(input, neuralnet, fcn(x: double -> double) m.link.logit(x));
  m.link.logit(activation[0])
''')

Producing a model

The model parameters for a layered neural network is just a set of transition matricies and bias vectors.

neuralnet = [{"weights": [[ -6.0, -8.0],
                          [-25.0, -30.0]], "bias": [4.0, 50.0]},
             {"weights": [[-12.0, 30.0]], "bias": [-25.0]}]

Insert the model into PFA

pfaDocument["cells"]["neuralnet"]["init"] = neuralnet

Test it!

engine, = PFAEngine.fromJson(pfaDocument)

data_xor = [[0, 0],
            [1, 0],
            [0, 1],
            [1, 1]]
y = [0.0,
     1.0,
     1.0,
     0.0]

for i in range(4):
    print "{0:.3f} vs {1}".format(engine.action(data_xor[i]), y[i])