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@@ -1,9 +1,10 @@
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# Improve performance of neural network
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-from lab import neural
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+import numpy as np
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+from lab import neural, io_mnist
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from copy import copy
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-def train(inputNetwork, learnRate, epochs):
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+def train(inputNetwork, learnRate, epochs, batchSize = 10):
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"""
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Create an improved network
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@@ -12,9 +13,63 @@ def train(inputNetwork, learnRate, epochs):
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return : a trained copy with improved performance
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"""
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- outputNetwork = copy(inputNetwork)
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+ net = copy(inputNetwork)
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- # TODO Training
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+ np_images, np_expected = io_mnist.load_training_samples()
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- return outputNetwork
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+ nbSamples = np_images.shape[1]
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+
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+ # Prepare variables
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+ a0 = np.empty((net.inputLength, batchSize))
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+
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+ w1 = net.layer1 # reference
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+ b1 = np.stack([net.bias1] * batchSize).transpose() # stack
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+
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+ z1 = np.empty(net.hiddenLength, batchSize)
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+ a1 = np.empty(net.hiddenLength, batchSize)
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+
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+ w2 = net.layer2 # reference
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+ b2 = np.stack([net.bias2] * batchSize).transpose() # stack
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+
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+ z2 = np.empty(net.outputLength, batchSize)
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+ a2 = np.empty(net.outputLength, batchSize)
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+
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+ y = np.empty((net.outputLength, batchSize))
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+
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+ g = net.activationFunction
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+ g_ = net.activationDerivative
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+
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+ d2 = np.empty(a2.shape)
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+ d1 = np.empty(a1.shape)
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+
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+ for epoch in range(epochs):
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+ # Create mini batches
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+ # TODO Shuffle samples
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+
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+ # Iterate over batches
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+ for batchIndex in range(0, nbSamples, batchSize):
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+ # Capture batch
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+ batchEndIndex = batchIndex + batchSize
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+ a0 = np_images[:, batchIndex:batchEndIndex]
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+ y = np_expected[:, batchIndex:batchEndIndex]
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+
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+ # Forward computation
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+ z1 = w1 @ a0 + b1
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+ a1 = g(z1)
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+
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+ z2 = w2 @ a1 + b2
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+ a2 = g(z2)
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+
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+ # Backward propagation
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+ d2 = a2 - y
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+ d1 = w2.transpose() @ d2 * g_(z1)
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+
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+ # Weight correction
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+ net.layer2 -= learnRate * d2 @ a1.transpose() / batchSize
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+ net.layer1 -= learnRate * d1 @ a0.transpose() / batchSize
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+
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+ net.bias2 -= learnRate * d2 @ np.ones(batchSize) / batchSize
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+ net.bias1 -= learnRate * d1 @ np.ones(batchSize) / batchSize
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+
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+ return net
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