[Chainer] Learning XOR with multi-layer perceptron

Introduction

I want to use Chainer. But I'm not sure. Yes, let's start by learning XOR with a multi-layer perceptron.

** * This article is written on the assumption that the environment where Chainer can be used is in place. ** **

** Code used in this article **

• GitHub/ichiroex/xor-mlp-chainer

environment

--python 2.7 series

• chainer 1.6.2.1

Training data

# Prepare dataset
source = [[0, 0], [1, 0], [0, 1], [1, 1]]
target = [[0], [1], [1], [0]]
dataset = {}
dataset['source'] = np.array(source, dtype=np.float32)
dataset['target'] = np.array(target, dtype=np.float32)

Model definition

The model used this time is 2 inputs and 1 output.

N = len(source) # train data size

in_units  = 2   #Number of units in the input layer
n_units   = 2   #Number of hidden layer units
out_units = 1   #Number of units in the output layer

#Model definition
model = chainer.Chain(l1=L.Linear(in_units, n_units),
                      l2=L.Linear(n_units , out_units))

Forward propagation

def forward(x, t):
    h1 = F.sigmoid(model.l1(x))
    return model.l2(h1)

Learning

Repeat until the training error is less than 0.00001 or epoch is greater than or equal to n_epoch.

# Setup optimizer
optimizer = optimizers.Adam()
optimizer.setup(model)

# Learning loop
loss_val = 100
epoch = 0
while loss_val > 1e-5:

    # training
    x = chainer.Variable(xp.asarray(dataset['source'])) #source
    t = chainer.Variable(xp.asarray(dataset['target'])) #target
    
    model.zerograds()       #Zero initialization of gradient
    y    = forward(x, t)    #Forward propagation

    loss = F.mean_squared_error(y, t) #Mean squared error
    
    loss.backward()              #Error back propagation
    optimizer.update()           #optimisation
    
    #Display the result on the way
    if epoch % 1000 == 0:
        #Calculate error and accuracy rate
        loss_val = loss.data

        print 'epoch:', epoch
        print 'x:\n', x.data
        print 't:\n', t.data
        print 'y:\n', y.data

        print('train mean loss={}'.format(loss_val)) #Training error,Correct answer rate
        print ' - - - - - - - - - '
    
    # n_It ends when it becomes epoch or more
    if epoch >= n_epoch:
        break

    epoch += 1

#Save model and optimizer
print 'save the model'
serializers.save_npz('xor_mlp.model', model)
print 'save the optimizer'
serializers.save_npz('xor_mlp.state', optimizer)

Execution result

I am learning as a regression problem. When predicting, it is necessary to set the threshold value such as 1 if it is 0.5 or more and 0 if it is less than 0.5.

$ python train_xor.py --gpu 1
epoch: 0
x:
[[ 0.  0.]
 [ 1.  0.]
 [ 0.  1.]
 [ 1.  1.]]
t:
[[ 0.]
 [ 1.]
 [ 1.]
 [ 0.]]
y:
[[-0.62479508]  #I want you to get closer to 0
 [-0.85900736]  #I want you to get closer to 1
 [-0.4117983 ]  #I want you to get closer to 1
 [-0.62129647]] #I want you to get closer to 0
train mean loss=1.55636525154  #Training error(I want you to be smaller)
 - - - - - - - - -
epoch: 1000
x:
[[ 0.  0.]
 [ 1.  0.]
 [ 0.  1.]
 [ 1.  1.]]
t:
[[ 0.]
 [ 1.]
 [ 1.]
 [ 0.]]
y:
[[ 0.39130747]
 [ 0.40636665]
 [ 0.50217605]
 [ 0.52426183]]
train mean loss=0.257050335407
 - - - - - - - - -

...


 - - - - - - - - -
epoch: 8000
x:
[[ 0.  0.]
 [ 1.  0.]
 [ 0.  1.]
 [ 1.  1.]]
t:
[[ 0.]
 [ 1.]
 [ 1.]
 [ 0.]]
y:
[[ 0.00557911]
 [ 0.98262894]
 [ 0.98446763]
 [ 0.02371788]]
train mean loss=0.000284168170765
 - - - - - - - - -
epoch: 9000
x:
[[ 0.  0.]
 [ 1.  0.]
 [ 0.  1.]
 [ 1.  1.]]
t:
[[ 0.]
 [ 1.]
 [ 1.]
 [ 0.]]
y:
[[  5.99622726e-05] #Approached 0
 [  9.99812365e-01] #Approached 1
 [  9.99832511e-01] #Approached 1
 [  2.56299973e-04]] #Approached 0
train mean loss=3.31361960093e-08
 - - - - - - - - -
save the model
save the optimizer

Reference article

-Learning XOR -Let's learn neural network with chainer (Neural network with chainer 2)