Layers are basically a set of functions that are used on hidden layers of a network.

We will go through the following details about layers in this chapter −

• Understanding layer
• Creating Layer using Pybrain

Understanding layers

We have seen examples earlier where we have used layers as follows −

• TanhLayer
• SoftmaxLayer

Example using TanhLayer

Below is one example where we have used TanhLayer for building a network −

testnetwork.py

from pybrain.tools.shortcuts import buildNetwork
from pybrain.structure import TanhLayer
from pybrain.datasets import SupervisedDataSet
from pybrain.supervised.trainers import BackpropTrainer

# Create a network with two inputs, three hidden, and one output
nn = buildNetwork(2, 3, 1, bias=True, hiddenclass=TanhLayer)

# Create a dataset that matches network input and output sizes:
norgate = SupervisedDataSet(2, 1)

# Create a dataset to be used for testing.
nortrain = SupervisedDataSet(2, 1)

# Add input and target values to dataset
# Values for NOR truth table
norgate.addSample((0, 0), (1,))
norgate.addSample((0, 1), (0,))
norgate.addSample((1, 0), (0,))
norgate.addSample((1, 1), (0,))

# Add input and target values to dataset
# Values for NOR truth table
nortrain.addSample((0, 0), (1,))
nortrain.addSample((0, 1), (0,))
nortrain.addSample((1, 0), (0,))
nortrain.addSample((1, 1), (0,))

#Training the network with dataset norgate.
trainer = BackpropTrainer(nn, norgate)

# will run the loop 1000 times to train it.
for epoch in range(1000):
   trainer.train()
trainer.testOnData(dataset=nortrain, verbose = True)

Output

The output for the above code is as follows −

python testnetwork.py

C:pybrainpybrainsrc>python testnetwork.py
Testing on data:
(''out: '', ''[0.887 ]'')
(''correct:'', ''[1 ]'')
error: 0.00637334
(''out: '', ''[0.149 ]'')
(''correct:'', ''[0 ]'')
error: 0.01110338
(''out: '', ''[0.102 ]'')
(''correct:'', ''[0 ]'')
error: 0.00522736
(''out: '', ''[-0.163]'')
(''correct:'', ''[0 ]'')
error: 0.01328650
(''All errors:'', [0.006373344564625953, 0.01110338071737218, 
   0.005227359234093431, 0.01328649974219942])
(''Average error:'', 0.008997646064572746)
(''Max error:'', 0.01328649974219942, ''Median error:'', 0.01110338071737218)

Example using SoftMaxLayer

Below is one example where we have used SoftmaxLayer for building a network −

from pybrain.tools.shortcuts import buildNetwork
from pybrain.structure.modules import SoftmaxLayer
from pybrain.datasets import SupervisedDataSet
from pybrain.supervised.trainers import BackpropTrainer

# Create a network with two inputs, three hidden, and one output
nn = buildNetwork(2, 3, 1, bias=True, hiddenclass=SoftmaxLayer)

# Create a dataset that matches network input and output sizes:
norgate = SupervisedDataSet(2, 1)

# Create a dataset to be used for testing.
nortrain = SupervisedDataSet(2, 1)

# Add input and target values to dataset
# Values for NOR truth table
norgate.addSample((0, 0), (1,))
norgate.addSample((0, 1), (0,))
norgate.addSample((1, 0), (0,))
norgate.addSample((1, 1), (0,))

# Add input and target values to dataset
# Values for NOR truth table
nortrain.addSample((0, 0), (1,))
nortrain.addSample((0, 1), (0,))
nortrain.addSample((1, 0), (0,))
nortrain.addSample((1, 1), (0,))

#Training the network with dataset norgate.
trainer = BackpropTrainer(nn, norgate)

# will run the loop 1000 times to train it.
for epoch in range(1000):
trainer.train()
trainer.testOnData(dataset=nortrain, verbose = True)

Output

The output is as follows −

C:pybrainpybrainsrc>python example16.py
Testing on data:
(''out: '', ''[0.918 ]'')
(''correct:'', ''[1 ]'')
error: 0.00333524
(''out: '', ''[0.082 ]'')
(''correct:'', ''[0 ]'')
error: 0.00333484
(''out: '', ''[0.078 ]'')
(''correct:'', ''[0 ]'')
error: 0.00303433
(''out: '', ''[-0.082]'')
(''correct:'', ''[0 ]'')
error: 0.00340005
(''All errors:'', [0.0033352368788838365, 0.003334842961037291, 
   0.003034328685718761, 0.0034000458892589056])
(''Average error:'', 0.0032761136037246985)
(''Max error:'', 0.0034000458892589056, ''Median error:'', 0.0033352368788838365)

Creating Layer in Pybrain

In Pybrain, you can create your own layer as follows −

To create a layer, you need to use NeuronLayer class as the base class to create all type of layers.

Example

from pybrain.structure.modules.neuronlayer import NeuronLayer
class LinearLayer(NeuronLayer):
   def _forwardImplementation(self, inbuf, outbuf):
      outbuf[:] = inbuf
   def _backwardImplementation(self, outerr, inerr, outbuf, inbuf):
      inerr[:] = outer

To create a Layer, we need to implement two methods: _forwardImplementation() and _backwardImplementation().

The _forwardImplementation() takes in 2 arguments inbuf and outbuf, which are Scipy arrays. Its size is dependent on the layers’ input and output dimensions.

The _backwardImplementation() is used to calculate the derivative of the output with respect to the input given.

So to implement a layer in Pybrain, this is the skeleton of the layer class −

from pybrain.structure.modules.neuronlayer import NeuronLayer
class NewLayer(NeuronLayer):
   def _forwardImplementation(self, inbuf, outbuf):
      pass
   def _backwardImplementation(self, outerr, inerr, outbuf, inbuf):
      pass

In case you want to implement a quadratic polynomial function as a layer, we can do so as follows −

Consider we have a polynomial function as −

f(x) = 3x2

The derivative of the above polynomial function will be as follows −

f(x) = 6 x

The final layer class for the above polynomial function will be as follows −

testlayer.py

from pybrain.structure.modules.neuronlayer import NeuronLayer
class PolynomialLayer(NeuronLayer):
   def _forwardImplementation(self, inbuf, outbuf):
      outbuf[:] = 3*inbuf**2
   def _backwardImplementation(self, outerr, inerr, outbuf, inbuf):
      inerr[:] = 6*inbuf*outerr

Now let us make use of the layer created as shown below −

testlayer1.py

from testlayer import PolynomialLayer
from pybrain.tools.shortcuts import buildNetwork
from pybrain.tests.helpers import gradientCheck

n = buildNetwork(2, 3, 1, hiddenclass=PolynomialLayer)
n.randomize()

gradientCheck(n)

GradientCheck() will test whether the layer is working fine or not.We need to pass the network where the layer is used to gradientCheck(n).It will give the output as “Perfect Gradient” if the layer is working fine.

Output

C:pybrainpybrainsrc>python testlayer1.py
Perfect gradient