def one_hot(x, m=None):
"""One-hot representation of integer vector.
Given a vector of integers from 0 to m-1, returns a matrix
with a one-hot representation, where each row corresponds
to an element of x.
Parameters
----------
x : integer vector
The integer vector to convert to a one-hot representation.
m : int, optional
The number of different columns for the one-hot representation. This
needs to be strictly greater than the maximum value of `x`.
Defaults to ``max(x) + 1``.
Returns
-------
Theano tensor variable
A Theano tensor variable of shape (``n``, `m`), where ``n`` is the
length of `x`, with the one-hot representation of `x`.
Notes
-----
If your integer vector represents target class memberships, and you wish to
compute the cross-entropy between predictions and the target class
memberships, then there is no need to use this function, since the function
:func:`lasagne.objectives.categorical_crossentropy()` can compute the
cross-entropy from the integer vector directly.
"""
if m is None:
m = T.cast(T.max(x) + 1, 'int32')
return T.eye(m)[T.cast(x, 'int32')]
def _linspace(start, stop, num):
# Theano linspace. Behaves similar to np.linspace
start = T.cast(start, theano.config.floatX)
stop = T.cast(stop, theano.config.floatX)
num = T.cast(num, theano.config.floatX)
step = (stop-start)/(num-1)
return T.arange(num, dtype=theano.config.floatX)*step+start
def _transform(theta, input, downsample_factor):
num_batch, num_channels, height, width = input.shape
theta = T.reshape(theta, (-1, 2, 3))
# grid of (x_t, y_t, 1), eq (1) in ref [1]
out_height = T.cast(height / downsample_factor[0], 'int64')
out_width = T.cast(width / downsample_factor[1], 'int64')
grid = _meshgrid(out_height, out_width)
# Transform A x (x_t, y_t, 1)^T -> (x_s, y_s)
T_g = T.dot(theta, grid)
x_s = T_g[:, 0]
y_s = T_g[:, 1]
x_s_flat = x_s.flatten()
y_s_flat = y_s.flatten()
# dimshuffle input to (bs, height, width, channels)
input_dim = input.dimshuffle(0, 2, 3, 1)
input_transformed = _interpolate(
input_dim, x_s_flat, y_s_flat,
out_height, out_width)
output = T.reshape(
input_transformed, (num_batch, out_height, out_width, num_channels))
output = output.dimshuffle(0, 3, 1, 2) # dimshuffle to conv format
return output
def _interpolate(im, x, y, out_height, out_width):
# *_f are floats
num_batch, height, width, channels = im.shape
height_f = T.cast(height, theano.config.floatX)
width_f = T.cast(width, theano.config.floatX)
# clip coordinates to [-1, 1]
x = T.clip(x, -1, 1)
y = T.clip(y, -1, 1)
# scale coordinates from [-1, 1] to [0, width/height - 1]
x = (x + 1) / 2 * (width_f - 1)
y = (y + 1) / 2 * (height_f - 1)
# obtain indices of the 2x2 pixel neighborhood surrounding the coordinates;
# we need those in floatX for interpolation and in int64 for indexing. for
# indexing, we need to take care they do not extend past the image.
x0_f = T.floor(x)
y0_f = T.floor(y)
x1_f = x0_f + 1
y1_f = y0_f + 1
x0 = T.cast(x0_f, 'int64')
y0 = T.cast(y0_f, 'int64')
x1 = T.cast(T.minimum(x1_f, width_f - 1), 'int64')
y1 = T.cast(T.minimum(y1_f, height_f - 1), 'int64')
# The input is [num_batch, height, width, channels]. We do the lookup in
# the flattened input, i.e [num_batch*height*width, channels]. We need
# to offset all indices to match the flat version
dim2 = width
dim1 = width*height
base = T.repeat(
T.arange(num_batch, dtype='int64')*dim1, out_height*out_width)
base_y0 = base + y0*dim2
base_y1 = base + y1*dim2
idx_a = base_y0 + x0
idx_b = base_y1 + x0
idx_c = base_y0 + x1
idx_d = base_y1 + x1
# use indices to lookup pixels for all samples
im_flat = im.reshape((-1, channels))
Ia = im_flat[idx_a]
Ib = im_flat[idx_b]
Ic = im_flat[idx_c]
Id = im_flat[idx_d]
# calculate interpolated values
wa = ((x1_f-x) * (y1_f-y)).dimshuffle(0, 'x')
wb = ((x1_f-x) * (y-y0_f)).dimshuffle(0, 'x')
wc = ((x-x0_f) * (y1_f-y)).dimshuffle(0, 'x')
wd = ((x-x0_f) * (y-y0_f)).dimshuffle(0, 'x')
output = T.sum([wa*Ia, wb*Ib, wc*Ic, wd*Id], axis=0)
return output
def main(model='mlp', num_epochs=500):
# Load the dataset
print("Loading data...")
X_train, y_train, X_val, y_val, X_test, y_test = load_dataset()
# Prepare Theano variables for inputs and targets
input_var = T.tensor4('inputs', fixed_shape=(128,) + X_train.shape[1:])
target_var = T.ivector('targets')
# Create neural network model (depending on first command line parameter)
print("Building model and compiling functions...")
if model == 'mlp':
network = build_mlp(input_var)
elif model.startswith('custom_mlp:'):
depth, width, drop_in, drop_hid = model.split(':', 1)[1].split(',')
network = build_custom_mlp(input_var, int(depth), int(width),
float(drop_in), float(drop_hid))
elif model == 'cnn':
network = build_cnn(input_var)
else:
print("Unrecognized model type %r." % model)
return
# Create a loss expression for training, i.e., a scalar objective we want
# to minimize (for our multi-class problem, it is the cross-entropy loss):
prediction = lasagne.layers.get_output(network)
loss = lasagne.objectives.categorical_crossentropy(prediction, target_var)
loss = T.mean(loss)
# We could add some weight decay as well here, see lasagne.regularization.
# Create update expressions for training, i.e., how to modify the
# parameters at each training step. Here, we'll use Stochastic Gradient
# Descent (SGD) with Nesterov momentum, but Lasagne offers plenty more.
params = lasagne.layers.get_all_params(network, trainable=True)
updates = lasagne.updates.nesterov_momentum(
loss, params, learning_rate=0.01, momentum=0.9)
# Create a loss expression for validation/testing. The crucial difference
# here is that we do a deterministic forward pass through the network,
# disabling dropout layers.
test_prediction = lasagne.layers.get_output(network, deterministic=True)
test_loss = lasagne.objectives.categorical_crossentropy(test_prediction,
target_var)
test_loss = T.mean(test_loss)
# As a bonus, also create an expression for the classification accuracy:
test_acc = T.mean(T.cast(T.eq(
T.cast(T.argmax(test_prediction, axis=1), 'int32'),
T.cast(target_var, 'int32')
), theano.config.floatX))
# Compile a function performing a training step on a mini-batch (by giving
# the updates dictionary) and returning the corresponding training loss:
train_fn = theano.function([input_var, target_var], loss, updates=updates)
# Compile a second function computing the validation loss and accuracy:
val_fn = theano.function([input_var, target_var], [test_loss, test_acc])
# Finally, launch the training loop.
print("Starting training...")
# We iterate over epochs:
for epoch in range(num_epochs):
# In each epoch, we do a full pass over the training data:
train_err = 0
train_batches = 0
start_time = time.time()
for batch in iterate_minibatches(X_train, y_train, 128, shuffle=True):
inputs, targets = batch
train_err += train_fn(inputs, targets)
train_batches += 1
# And a full pass over the validation data:
val_err = 0
val_acc = 0
val_batches = 0
for batch in iterate_minibatches(X_val, y_val, 128, shuffle=False):
inputs, targets = batch
err, acc = val_fn(inputs, targets)
val_err += err
val_acc += acc
val_batches += 1
# Then we print the results for this epoch:
print("Epoch {} of {} took {:.3f}s".format(
epoch + 1, num_epochs, time.time() - start_time))
print(" training loss:\t\t{:.6f}".format(train_err / train_batches))
print(" validation loss:\t\t{:.6f}".format(val_err / val_batches))
print(" validation accuracy:\t\t{:.2f} %".format(
val_acc / val_batches * 100))
# After training, we compute and print the test error:
test_err = 0
test_acc = 0
test_batches = 0
for batch in iterate_minibatches(X_test, y_test, 128, shuffle=False):
inputs, targets = batch
err, acc = val_fn(inputs, targets)
test_err += err
test_acc += acc
test_batches += 1
print("Final results:")
print(" test loss:\t\t\t{:.6f}".format(test_err / test_batches))
print(" test accuracy:\t\t{:.2f} %".format(
test_acc / test_batches * 100))
