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A Neural Network in just a Few Lines of Code

The following 2 code snippets show the same neural network implementation in both Neureka and Numpy!

Neureka (Groovy) Numpy (Python) 
var X = Tensor.of(Double, [[0, 0, 1], [0, 1, 1], [1, 0, 1], [1, 1, 1] ])
var y = Tensor.of(Double, [[0,1,1,0]]).T
var W1 = Tensor.ofRandom(Double, 3,4)
var W2 = Tensor.ofRandom(Double, 4,1)
60_000.times {
    var l1 = Tensor.of('sig(',X.dot(W1),')')
    var l2 = Tensor.of('sig(',l1.dot(W2),')')
    var l2_delta = (y - l2)*(l2*(-l2+1))
    var l1_delta = l2_delta.dot(W2.T) * (l1 * (-l1+1))
    W2 += l1.T.dot(l2_delta)
    W1 += X.T.dot(l1_delta)
}
 
X = np.array([ [0,0,1],[0,1,1],[1,0,1],[1,1,1] ])
y = np.array([[0,1,1,0]]).T
W1 = 2*np.random.random((3,4)) - 1
W2 = 2*np.random.random((4,1)) - 1
for j in xrange(60000):
    l1 = 1/(1+np.exp(-(np.dot(X,W1))))
    l2 = 1/(1+np.exp(-(np.dot(l1,W2))))
    l2_delta = (y - l2)*(l2*(1-l2))
    l1_delta = l2_delta.dot(W2.T) * (l1 * (1-l1))
    W2 += l1.T.dot(l2_delta)
    W1 += X.T.dot(l1_delta)

But wait! It gets even better!

All of this l1_delta and l2_delta stuff looks really complicated and is really distracting from the actual architecture of the network... That is why Neureka has this part of building a neural network automated for you! You simply specify which tensors require gradients, and then you send the error values through the backward method to your weights (and their gradients). After each pass you tell your weights to apply their gradients. Done!

Neureka (Groovy) Numpy (Python) 
var X = Tensor.of(Double, [[0, 0, 1], [0, 1, 1], [1, 0, 1], [1, 1, 1]])
var y = Tensor.of(Double, [[0, 1, 1, 0]]).T
var W1 = Tensor.ofRandom(Double, 3, 4).setRqsGradient(true)
var W2 = Tensor.ofRandom(Double, 4, 1).setRqsGradient(true)
60_000.times {
    var l2 = Tensor.of('sig(',Tensor.of('sig(',X.dot(W1),')').dot(W2),')')
    l2.backward(y - l2) // Back-propagating the error!
    W1.applyGradient(); W2.applyGradient()
}
 
X = np.array([ [0,0,1],[0,1,1],[1,0,1],[1,1,1] ])
y = np.array([[0,1,1,0]]).T
W1 = 2*np.random.random((3,4)) - 1
W2 = 2*np.random.random((4,1)) - 1
for j in xrange(60000):
    l1 = 1/(1+np.exp(-(np.dot(X,W1))))
    l2 = 1/(1+np.exp(-(np.dot(l1,W2))))
    l2_delta = (y - l2)*(l2*(1-l2))
    l1_delta = l2_delta.dot(W2.T) * (l1 * (1-l1))
    W2 += l1.T.dot(l2_delta)
    W1 += X.T.dot(l1_delta)