@author: Jonathan Raiman @date: December 10th 2014
Implements most of the great things that came out in 2014 concerning recurrent neural networks, and some good optimizers for these types of networks.
Note: Dropout causes gradient issues with theano if placed in scan, so it should be set to 0 for now, and will be fixed in the future.
This module contains several Layer types that are useful for prediction and modeling from sequences:
- A non-recurrent Layer, with a connection matrix W, and bias b
- A recurrent RNN Layer that takes as input its previous hidden activation and has an initial hidden activation
- A recurrent LSTM Layer that takes as input its previous hidden activation and memory cell values, and has initial values for both of those
- An Embedding layer that contains an embedding matrix and takes integers as input and returns slices from its embedding matrix (e.g. word vectors)
This module also contains the SGD, AdaGrad, and AdaDelta gradient descent methods that are constructed using an objective function and a set of theano variables, and returns an updates dictionary to pass to a theano function (see below).
Here is an example of usage with stacked LSTM units, using Adadelta to optimize, and using a scan op.
# bug for now forces us to use 0.0 with scan,
dropout = 0.0
model = StackedCells(4, layers=[20, 20], activation=T.tanh, celltype=LSTM)
model.layers[0].in_gate2.activation = lambda x: x
model.layers.append(Layer(20, 2, lambda x: T.nnet.softmax(x)[0]))
# in this example dynamics is a random function that takes our
# output along with the current state and produces an observation
# for t + 1
def step(x, *prev_hiddens):
new_states = stacked_rnn.forward(x, prev_hiddens, dropout)
return [dynamics(x, new_states[-1])] + new_states[:-1]
initial_obs = T.vector()
timesteps = T.iscalar()
result, updates = theano.scan(step,
n_steps=timesteps,
outputs_info=[dict(initial=initial_obs, taps=[-1])] + [dict(initial=layer.initial_hidden_state, taps=[-1]) for layer in model.layers if hasattr(layer, 'initial_hidden_state')])
target = T.vector()
cost = (result[0][:,[0,2]] - target[[0,2]]).norm(L=2) / timesteps
updates, gsums, xsums, lr, max_norm = \
create_optimization_updates(cost, model.params, method='adadelta')
update_fun = theano.function([initial_obs, target, timesteps], cost, updates = updates, allow_input_downcast=True)
predict_fun = theano.function([initial_obs, timesteps], result[0], allow_input_downcast=True)
for example, label in training_set:
c = update_fun(example, label, 10)
Suppose you now have many sequences (of equal length -- we'll generalize this later). Then training can be done in batches:
model = StackedCells(4, layers=[20, 20], activation=T.tanh, celltype=LSTM)
model.layers[0].in_gate2.activation = lambda x: x
model.layers.append(Layer(20, 2, lambda x: T.nnet.softmax(x)[0]))
# in this example dynamics is a random function that takes our
# output along with the current state and produces an observation
# for t + 1
def step(x, *prev_hiddens):
new_states = stacked_rnn.forward(x, prev_hiddens, dropout)
return [dynamics(x, new_states[-1])] + new_states[:-1]
# switch to a matrix of observations:
initial_obs = T.imatrix()
timesteps = T.iscalar()
result, updates = theano.scan(step,
n_steps=timesteps,
outputs_info=[dict(initial=initial_obs, taps=[-1])] + [dict(initial=layer.initial_hidden_state, taps=[-1]) for layer in model.layers if hasattr(layer, 'initial_hidden_state')])
target = T.ivector()
cost = (result[0][:,:,[0,2]] - target[:,[0,2]]).norm(L=2) / timesteps
updates, gsums, xsums, lr, max_norm = \
create_optimization_updates(cost, model.params, method='adadelta')
update_fun = theano.function([initial_obs, target, timesteps], cost, updates = updates, allow_input_downcast=True)
predict_fun = theano.function([initial_obs, timesteps], result[0], allow_input_downcast=True)
for minibatch, labels in minibatches:
c = update_fun(minibatch, label, 10)
This is particularly useful to make sure of the GPU and other embarassingly parallel parts of an optimization.
Generalization can be made to different sequence length if we accept the minor cost of forward-propagating parts of our graph we don't care about. To do this we make all sequences the same length by padding the end of the shorter ones with some symbol. Then use a binary matrix of the same size than all your minibatch sequences. The matrix has a 1 in areas when the error should be calculated, and zero otherwise. Elementwise mutliply this mask with your output, and then apply your objective function to this masked output. The error will be obtained everywhere, but will be zero in areas that were masked, yielding the correct error function.
While there is some waste computation, the parallelization can offset this cost and make the overall computation faster.
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