使用修改后的 mnist.py（Lasagne 的主要示例）进入 Lasagne 和 Theano，以训练一个非常简单的 XOR。
import numpy as np
import theano
import theano.tensor as T
import time
import lasagne
X_train = [[[[0, 0], [0, 1], [1, 0], [1, 1]]]] # (1)
y_train = [[[[1, 0], [0, 1], [0, 1], [1, 0]]]]
# [0, 1, 1, 0]
X_train = np.array(X_train).astype(np.uint8)
y_train = np.array(y_train).astype(np.uint8)
print X_train.shape
X_val = X_train
y_val = y_train
X_test = X_train
y_test = y_train
def build_mlp(input_var=None):
# This creates an MLP of two hidden layers of 800 units each, followed by
# a softmax output layer of 10 units. It applies 20% dropout to the input
# data and 50% dropout to the hidden layers.
# Input layer, specifying the expected input shape of the network
# (unspecified batchsize, 1 channel, 28 rows and 28 columns) and
# linking it to the given Theano variable `input_var`, if any:
l_in = lasagne.layers.InputLayer(shape=(None, 1, 4, 2), # (2)
input_var=input_var)
# Apply 20% dropout to the input data:
# l_in_drop = lasagne.layers.DropoutLayer(l_in, p=0.2)
# Add a fully-connected layer of 800 units, using the linear rectifier, and
# initializing weights with Glorot's scheme (which is the default anyway):
l_hid1 = lasagne.layers.DenseLayer(
l_in, num_units=4,
nonlinearity=lasagne.nonlinearities.rectify,
W=lasagne.init.GlorotUniform())
# Finally, we'll add the fully-connected output layer, of 10 softmax units:
l_out = lasagne.layers.DenseLayer(
l_hid1, num_units=2,
nonlinearity=lasagne.nonlinearities.softmax)
# Each layer is linked to its incoming layer(s), so we only need to pass
# the output layer to give access to a network in Lasagne:
return l_out
# Prepare Theano variables for inputs and targets
input_var = T.tensor4('inputs')
target_var = T.ivector('targets')
network = build_mlp(input_var)
# 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 = loss.mean()
# 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 = test_loss.mean()
# As a bonus, also create an expression for the classification accuracy:
test_acc = T.mean(T.eq(T.argmax(test_prediction, axis=1), target_var),
dtype=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])
# ############################# Batch iterator ###############################
# This is just a simple helper function iterating over training data in
# mini-batches of a particular size, optionally in random order. It assumes
# data is available as numpy arrays. For big datasets, you could load numpy
# arrays as memory-mapped files (np.load(..., mmap_mode='r')), or write your
# own custom data iteration function. For small datasets, you can also copy
# them to GPU at once for slightly improved performance. This would involve
# several changes in the main program, though, and is not demonstrated here.
def iterate_minibatches(inputs, targets, batchsize, shuffle=False):
assert len(inputs) == len(targets)
if shuffle:
indices = np.arange(len(inputs))
np.random.shuffle(indices)
for start_idx in range(0, len(inputs) - batchsize + 1, batchsize):
if shuffle:
excerpt = indices[start_idx:start_idx + batchsize]
else:
excerpt = slice(start_idx, start_idx + batchsize)
yield inputs[excerpt], targets[excerpt]
else:
if shuffle:
excerpt = indices[0:len(inputs)]
else:
excerpt = slice(0, len(inputs))
yield inputs[excerpt], targets[excerpt]
num_epochs = 4
# 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, 4, shuffle=True):
inputs, targets = batch
print inputs.shape, targets.shape, input_var.shape, input_var.ndim, inputs.ndim
train_err += train_fn(inputs, targets) # (3)
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, 4, 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, 500, 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))
# Optionally, you could now dump the network weights to a file like this:
# np.savez('model.npz', lasagne.layers.get_all_param_values(network))
在 (1) 处定义训练集，在 (2) 处将输入修改为新维度，并在 (3) 处得到异常：
Traceback (most recent call last):
File "test.py", line 139, in <module>
train_err += train_fn(inputs, targets)
File "/usr/local/lib/python2.7/site-packages/theano/compile/function_module.py", line 513, in __call__
allow_downcast=s.allow_downcast)
File "/usr/local/lib/python2.7/site-packages/theano/tensor/type.py", line 169, in filter
data.shape))
TypeError: ('Bad input argument to theano function with name "test.py:91" at index 1(0-based)', 'Wrong number of dimensions: expected 1, got 4 with shape (1, 1, 4, 2).')
而且我不知道我做错了什么。当我打印尺寸（或程序的输出直到异常）时，我得到了这个
(1, 1, 4, 2)
Starting training...
(1, 1, 4, 2) (1, 1, 4, 2) Shape.0 4 4
这似乎是完美的。我做错了什么以及必须如何形成阵列才能工作？