Python neural network library that provides the following network types:
- feed-forward neural network
- recurrent (Elman) neural network
It supports the following activations functions:
- linear
- sigmoid
- tanh
- softmax
It supports the following cost functions:
- sum of squared errors (SSE)
- cross entropy (CE)
And it supports an arbitrary number of hidden layers and arbitrary batch size for gradient descent algorithm.
To learn XOR function (see code for this and other examples in test folder):
from neuron.neuralnet import NN
inputs = [[0,0], [0,1], [1,0], [1,1]]
targets = [[0], [1], [1], [0]]
nn = NN([2, 2, 1], ["sigmoid", "sigmoid"], cost_function="ce")
nn.train(inputs, targets, batch_size=4, alpha=1, lamda=0.0, iterations=3000)
preds = []
for index, inp in enumerate(inputs):
pred = nn.predict(inp)
preds.append(pred)
print "%s -> %s" % (inp, pred)
The output looks like:
[0, 0] -> [ 0.00903832] [0, 1] -> [ 0.99312] [1, 0] -> [ 0.99327432] [1, 1] -> [ 0.00975482]
To learn (some nonsense) function using softmax output layer and two hidden layers:
inputs = [[0, 0, 1], [1, 0, 0], [0, 1, 0]]
targets = [[1, 0, 0], [0, 0, 1], [0, 1, 0]]
nn = NN([3, 3, 5, 3], ["sigmoid", "tanh", "softmax"], cost_function="softmax_ce")
nn.train(inputs, targets, batch_size=4, alpha=1, lamda=0.0, iterations=1000)
preds = []
for index, inp in enumerate(inputs):
pred = nn.predict(inp)
preds.append(pred)
print "%s -> %s" % (inp, pred)
The output looks like:
[0, 0, 1] -> [ 9.99473157e-01 2.26014879e-04 3.00828353e-04] [1, 0, 0] -> [ 2.29435307e-04 2.89636262e-04 9.99480928e-01] [0, 1, 0] -> [ 1.68368019e-04 9.99476531e-01 3.55100544e-04]
Approximating the sine function using Recurrent network:
from neuron.recurrent import Recurrent
import pylab as pl
import numpy as np
size = 100
np.random.seed(0)
inputs = np.linspace(-7, 7, 20)
targets = np.sin(inputs) * 0.5
inputs.resize((size, 1))
targets.resize((size, 1))
nn = Recurrent([1, 10, 1], ["tanh", "linear"], cost_function="sse")
epoch_errors = nn.train(inputs, targets, batch_size=1, alpha=0.1, lamda=0.0, iterations=500, calculate_errors=True)
pl.subplot(211)
pl.plot(epoch_errors)
pl.xlabel('Epoch number')
pl.ylabel('error (default SSE)')
output = []
for index, inp in enumerate(inputs):
pred = nn.predict(inp)
output.append(pred)
x2 = np.linspace(-6.0,6.0,150)
x2.resize((size, 1))
output1 = []
for index, inp in enumerate(x2):
pred = nn.predict(inp)
output1.append(pred)
pl.subplot(212)
pl.plot(inputs , targets, '.', inputs, output, 'p')
pl.show()
You can use findparameters.find function to try to find the optimal hyperparameters. For example for recognition of handwritten digits (see digits.py and digits_findparameters.py in test folder):
import scipy.io
from neuron import findparameters
training_data = scipy.io.loadmat('../data/digits/ex4data1.mat')
X = training_data.get("X")
y = training_data.get("y")
targets = []
for j in y:
t = [0] * 10
t[j-1] = 1
targets.append(t)
def evaluate(nn, inputs, targets):
wrong = 0
right = 0
for jindex, x in enumerate(inputs):
p = nn.predict(x)
maxind = p.argmax() + 1
if maxind == y[jindex]:
right += 1
else:
wrong += 1
#print "right: %s, wrong: %s" % (right, wrong)
acc = right / float(len(y))
return acc
findparameters.find(evaluate, X, targets, net_type="feedforward", input_size=400, output_size=10,
output_activation="sigmoid", cost_function="ce")
You should get accuracy for a bunch of different hyperparameters configurations, some of them:
hidden_size: 250, activation: tanh, alpha: 0.1, lambda: 0, iter: 1, batch_size: 5 ---- 0.9104 hidden_size: 250, activation: tanh, alpha: 0.1, lambda: 0, iter: 1, batch_size: 50 ---- 0.9292 hidden_size: 250, activation: tanh, alpha: 0.1, lambda: 0, iter: 5, batch_size: 5 ---- 0.9784 hidden_size: 250, activation: tanh, alpha: 0.1, lambda: 0, iter: 5, batch_size: 50 ---- 0.9878 hidden_size: 250, activation: tanh, alpha: 0.1, lambda: 0, iter: 10, batch_size: 5 ---- 0.9994