def SGD_train(minibatch_size, data, labels, alpha, momentum, epochs):
"""Train the network with stochastic gradient descent
:type minibatch_size: an integer
:param minibatch_size: the size of the minibatches (usually something like 256)
:type data: 3D matrix height x width x num training data pts.
:param data: A 3D matrix that contains all of the training data points of the set
:type labels: num training data pts x 1 vector
:param labels: the labels for each image
:type alpha: float
:param alpha: the learning rate
:type momentum: float
:param momentum: the momentum
:type epochs: an integer
:param epochs: the number of epochs (ie. iterations) through the training
"""
it = 0
# convolutional layer, taking in a 28x28 image, using 2 9x9 filters
# output should be 2 28-9+1x28-9+1 = 2 20x20 feature maps in a (20, 20, 2) form
layer0 = ConvLayer((28, 28, 1), (9,9,2))
print "initialized convolutional layer"
# pooling layer, taking in 2 20x20 feature maps
# output should be 2 10x10 feature maps
layer1 = PoolingLayer((20, 20, 2))
print "initialized pooling layer"
# fully-connected softmax layer, taking in 2 10x10 feature maps (if downsampled by 2)
# flattened into a long input vector
layer2 = FullyConnectedLayer(200, 10)
print "initialized fully-connected layer"
params = np.concatenate((layer0.W.flatten(), layer0.bias.flatten(), layer2.W.flatten(), layer2.bias.flatten()))
velocity = np.zeros(params.shape)
for i in range(0, epochs):
correct_class = 0
cost = 0.0
# shuffle the dataset--shuffle_vec will be used as indices
shuffle_vec = rand.permutation(data.shape[2])
for j in range(0, data.shape[2] - minibatch_size + 1, minibatch_size):
# perform gradient descent w/each batch
it += 1
if it == 20:
# increase momentum after 20 iterations
momentum = 0.9
# gradient should be an unrolled vector of the avg. sum of the 256 gradients gotten
# from the forward pass and backprop
for k in range(0, minibatch_size):
layer0.forwardprop(data[:,:,shuffle_vec[j+k]].reshape((28,28,1)))
layer1.downsample(layer0.output, (20,20,2))
layer2_input = layer1.output.flatten()
layer2.softmax_output(layer2_input.reshape((layer2_input.size, 1)))
cost += J(layer2.output, labels[shuffle_vec[j+k]])
# print "%d %d" % (np.argmax(layer2.output), labels[shuffle_vec[j+k]])
if np.argmax(layer2.output) == labels[shuffle_vec[j+k]]:
correct_class += 1
# backprop
layer2.backprop(0, 0, encode_label(labels[shuffle_vec[j+k]]))
layer1.upsample(layer2, 0)
layer0.backprop(layer1)
# flatten the gradient vector
if k == 0:
grad = np.concatenate((layer0.gradient_w.flatten(), layer0.gradient_b.flatten(), layer2.gradient_w.flatten(), layer2.gradient_b.flatten()))
else:
grad += np.concatenate((layer0.gradient_w.flatten(), layer0.gradient_b.flatten(), layer2.gradient_w.flatten(), layer2.gradient_b.flatten()))
grad /= minibatch_size
# update velocity vector
velocity = momentum*velocity + alpha*grad
params = params - velocity
# update the parameters
layer0.W = params[0:layer0.W.flatten().size].reshape(layer0.W.shape)
next_begin = layer0.W.flatten().size
layer0.bias = params[next_begin:next_begin+layer0.bias.flatten().size].reshape(layer0.bias.shape)
next_begin += layer0.bias.flatten().size
layer2.W = params[next_begin:next_begin+layer2.W.flatten().size].reshape(layer2.W.shape)
next_begin += layer2.W.flatten().size
layer2.bias = params[next_begin:].reshape(layer2.bias.shape)
# reduce learning rate by half after each epoch
alpha /= 2.0
print "%d correct classifications" % correct_class
print "cost function is ", cost/(minibatch_size*(data.shape[2] - minibatch_size + 1))
def testGradient():
"""Test the backprop implementation by checking the gradients on a small network"""
# load the training data
images, labels = load_mnist()
images /= 255.0
grad_images = images[:,:,0:10] #use 10 image subset for gradient checking
grad_labels = labels[0,0:10] #respective labels for the images--going to have to encode these labels
# create a small network, 1 conv layer + 1 pooling layer + 1 fully connected softmax
# convolutional layer, taking in a 28x28 image, using 2 9x9 filters
# output should be 2 28-9+1x28-9+1 = 2 20x20 feature maps in a (20, 20, 2) form
layer0 = ConvLayer(grad_images[:,:,0].reshape((28,28,1)), (28, 28, 1), (9, 9, 2, 1))
print "initalized convolutional layer"
layer0.forwardprop(grad_images[:,:,0].reshape((28,28,1)))
print "finished forward pass of convolutional layer"
# pooling layer, taking in 2 20x20 feature maps
# output should be 2 10x10 feature maps (though may want to downsample 5x for gradient check)
layer1 = PoolingLayer(layer0.output, (20, 20, 2))
print "initialized pooling layer"
layer1.downsample(layer0.output, (20, 20, 2))
print "finished forward pass of pooling layer"
# fully-connected softmax layer, taking in 2 10x10 feature maps (if downsampled by 2)
# or taking in 2 4x4 feature maps (if downsampled by 5)
# either way, flattened into a long input vector
full_conn_input = layer1.output.flatten()
layer2 = FullyConnectedLayer(full_conn_input.reshape((full_conn_input.size, 1)), full_conn_input.size, 10)
print "initialized fully-conn layer"
layer2.softmax_output(full_conn_input.reshape((full_conn_input.size, 1)))
print "finished forward pass of fully-conn layer"
# perform backpropagation
target = np.zeros((10,1))
for i in range(0, 10):
if grad_labels[i] == 1:
target[i] = 1
layer2.backprop(0, 0, target)
print "finished layer 2 backprop"
layer1.upsample(layer2, 0)
print "finished layer 1 backprop"
layer0.backprop(layer1)
print "finished layer 0 backprop"
# # after initialization, finish training
# for i in range(1, grad_labels.size):
# # forward propagation
# layer0.forwardprop(grad_images[:,:,i].reshape((28,28,1)))
# layer1.downsample(layer0.output, (20,20,2))
# full_conn_input = layer1.output.flatten()
# layer2.softmax_output(full_conn_input.reshape((full_conn_input.size, 1)))
#
# # backpropagation
# target = np.zeros((10,1))
# for j in range(0,10):
# if grad_labels[i] == 1:
# target[i] = 1
# layer2.backprop(0, 0, target)
# layer1.upsample(layer2, 0)
# layer0.backprop(layer1)
# check the gradient
epsilon = 1.0e-4
layer0_check = layer0
layer1_check = layer1
layer2_check = layer2
layer0_w_vec = layer0.W.flatten()
layer0_bias_vec = layer0.bias.flatten()
layer0_gradw = layer0.gradient_w.flatten()
layer0_gradb = layer0.gradient_b.flatten()
layer2_w_vec = layer2.W.flatten()
layer2_bias_vec = layer2.bias.flatten()
layer2_gradw = layer2.gradient_w.flatten()
layer2_gradb = layer2.gradient_b.flatten()
w_vec = np.concatenate((layer0_w_vec, layer0_bias_vec, layer2_w_vec, layer2_bias_vec))
backprop_vec = np.concatenate((layer0_gradw, layer0_gradb, layer2_gradw, layer2_gradb))
print layer0_gradw
gradient_check = np.zeros(w_vec.size)
for i in range(0, w_vec.size):
pos = w_vec
pos[i] += epsilon
neg = w_vec
neg[i] -= epsilon
# feed-forward to get J(w+e), J(w-e), subtract and calculate gradient
# J(w+e)
layer0_check.W = pos[0:layer0_w_vec.size].reshape(layer0.filter_shape)
layer0_check.bias = pos[layer0_w_vec.size : layer0_w_vec.size+layer0_bias_vec.size].reshape(layer0.bias_shape)
layer2_check.W = pos[layer0_w_vec.size+layer0_bias_vec.size : layer0.W.size+layer0.bias.size+layer2_w_vec.size].reshape(layer2.W.shape)
layer2_check.bias = pos[layer0.W.size+layer0.bias.size+layer2_w_vec.size:].reshape(layer2.bias.shape)
layer0_check.forwardprop(grad_images[:,:,0].reshape((28,28,1)))
layer1_check.downsample(layer0_check.output, (20,20,2))
full_conn_input = layer1.output.flatten()
layer2_check.softmax_output(full_conn_input.reshape((full_conn_input.size, 1)))
pos_out = J(layer2_check.output, grad_labels[0])
# J(w-e)
layer0_check.W = neg[0:layer0_w_vec.size].reshape(layer0.filter_shape)
layer0_check.bias = neg[layer0_w_vec.size : layer0_w_vec.size+layer0_bias_vec.size].reshape(layer0.bias_shape)
layer2_check.W = neg[layer0_w_vec.size+layer0_bias_vec.size : layer0.W.size+layer0.bias.size+layer2_w_vec.size].reshape(layer2.W.shape)
layer2_check.bias = neg[layer0.W.size+layer0.bias.size+layer2_w_vec.size:].reshape(layer2.bias.shape)
layer0_check.forwardprop(grad_images[:,:,0].reshape((28,28,1)))
layer1_check.downsample(layer0_check.output, (20,20,2))
full_conn_input = layer1.output.flatten()
layer2_check.softmax_output(full_conn_input.reshape((full_conn_input.size, 1)))
neg_out = J(layer2_check.output, grad_labels[0])
# compute gradient for i
gradient_check[i] = (pos_out - neg_out)/(2*epsilon)
# print gradient_check
print gradient_check[0:layer0_w_vec.size]