In [1]:
# we assume that we have the dynet module in your path.
import dynet as dy
An (1-layer) RNN can be thought of as a sequence of cells, $h_1,...,h_k$, where $h_i$ indicates the time dimenstion.
Each cell $h_i$ has an input $x_i$ and an output $r_i$. In addition to $x_i$, cell $h_i$ receives as input also $r_{i-1}$.
In a deep (multi-layer) RNN, we don't have a sequence, but a grid. That is we have several layers of sequences:
Let $r_i^j$ be the output of cell $h_i^j$. Then:
The input to $h_i^1$ is $x_i$ and $r_{i-1}^1$.
The input to $h_i^2$ is $r_i^1$ and $r_{i-1}^2$, and so on.
In [2]:
pc = dy.ParameterCollection()
NUM_LAYERS=2
INPUT_DIM=50
HIDDEN_DIM=10
builder = dy.LSTMBuilder(NUM_LAYERS, INPUT_DIM, HIDDEN_DIM, pc)
# or:
# builder = dy.SimpleRNNBuilder(NUM_LAYERS, INPUT_DIM, HIDDEN_DIM, pc)
Note that when we create the builder, it adds the internal RNN parameters to the ParameterCollection.
We do not need to care about them, but they will be optimized together with the rest of the network's parameters.
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s0 = builder.initial_state()
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x1 = dy.vecInput(INPUT_DIM)
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s1=s0.add_input(x1)
y1 = s1.output()
# here, we add x1 to the RNN, and the output we get from the top is y (a HIDEN_DIM-dim vector)
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y1.npvalue().shape
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s2=s1.add_input(x1) # we can add another input
y2=s2.output()
If our LSTM/RNN was one layer deep, y2 would be equal to the hidden state. However, since it is 2 layers deep, y2 is only the hidden state (= output) of the last layer.
If we were to want access to the all the hidden state (the output of both the first and the last layers), we could use the .h() method, which returns a list of expressions, one for each layer:
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print(s2.h())
The same interface that we saw until now for the LSTM, holds also for the Simple RNN:
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# create a simple rnn builder
rnnbuilder=dy.SimpleRNNBuilder(NUM_LAYERS, INPUT_DIM, HIDDEN_DIM, pc)
# initialize a new graph, and a new sequence
rs0 = rnnbuilder.initial_state()
# add inputs
rs1 = rs0.add_input(x1)
ry1 = rs1.output()
print("all layers:", s1.h())
In [10]:
print(s1.s())
To summarize, when calling .add_input(x) on an RNNState what happens is that the state creates a new RNN/LSTM column, passing it:
xThe state is then returned, and we can call it's output() method to get the output y, which is the output at the top of the column. We can access the outputs of all the layers (not only the last one) using the .h() method of the state.
.s() The internal state of the RNN may be more involved than just the outputs $h$. This is the case for the LSTM, that keeps an extra "memory" cell, that is used when calculating $h$, and which is also passed to the next column. To access the entire hidden state, we use the .s() method.
The output of .s() differs by the type of RNN being used. For the simple-RNN, it is the same as .h(). For the LSTM, it is more involved.
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rnn_h = rs1.h()
rnn_s = rs1.s()
print("RNN h:", rnn_h)
print("RNN s:", rnn_s)
lstm_h = s1.h()
lstm_s = s1.s()
print("LSTM h:", lstm_h)
print("LSTM s:", lstm_s
)
As we can see, the LSTM has two extra state expressions (one for each hidden layer) before the outputs h.
Stack LSTM The RNN's are shaped as a stack: we can remove the top and continue from the previous state.
This is done either by remembering the previous state and continuing it with a new .add_input(), or using
we can access the previous state of a given state using the .prev() method of state.
Initializing a new sequence with a given state When we call builder.initial_state(), we are assuming the state has random /0 initialization. If we want, we can specify a list of expressions that will serve as the initial state. The expected format is the same as the results of a call to .final_s(). TODO: this is not supported yet.
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s2=s1.add_input(x1)
s3=s2.add_input(x1)
s4=s3.add_input(x1)
# let's continue s3 with a new input.
s5=s3.add_input(x1)
# we now have two different sequences:
# s0,s1,s2,s3,s4
# s0,s1,s2,s3,s5
# the two sequences share parameters.
assert(s5.prev() == s3)
assert(s4.prev() == s3)
s6=s3.prev().add_input(x1)
# we now have an additional sequence:
# s0,s1,s2,s6
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s6.h()
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s6.s()
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The RNNState interface is convenient, and allows for incremental input construction.
However, sometimes we know the sequence of inputs in advance, and care only about the sequence of
output expressions. In this case, we can use the add_inputs(xs) method, where xs is a list of Expression.
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state = rnnbuilder.initial_state()
xs = [x1,x1,x1]
states = state.add_inputs(xs)
outputs = [s.output() for s in states]
hs = [s.h() for s in states]
print(outputs, hs)
This is convenient.
What if we do not care about .s() and .h(), and do not need to access the previous vectors? In such cases
we can use the transduce(xs) method instead of add_inputs(xs).
transduce takes in a sequence of Expressions, and returns a sequence of Expressions.
As a consequence of not returning RNNStates, trnasduce is much more memory efficient than add_inputs or a series of calls to add_input.
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state = rnnbuilder.initial_state()
xs = [x1,x1,x1]
outputs = state.transduce(xs)
print(outputs)
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import random
from collections import defaultdict
from itertools import count
import sys
LAYERS = 1
INPUT_DIM = 50
HIDDEN_DIM = 50
characters = list("abcdefghijklmnopqrstuvwxyz ")
characters.append("<EOS>")
int2char = list(characters)
char2int = {c:i for i,c in enumerate(characters)}
VOCAB_SIZE = len(characters)
In [18]:
pc = dy.ParameterCollection()
srnn = dy.SimpleRNNBuilder(LAYERS, INPUT_DIM, HIDDEN_DIM, pc)
lstm = dy.LSTMBuilder(LAYERS, INPUT_DIM, HIDDEN_DIM, pc)
# add parameters for the hidden->output part for both lstm and srnn
params_lstm = {}
params_srnn = {}
for params in [params_lstm, params_srnn]:
params["lookup"] = pc.add_lookup_parameters((VOCAB_SIZE, INPUT_DIM))
params["R"] = pc.add_parameters((VOCAB_SIZE, HIDDEN_DIM))
params["bias"] = pc.add_parameters((VOCAB_SIZE))
# return compute loss of RNN for one sentence
def do_one_sentence(rnn, params, sentence):
# setup the sentence
dy.renew_cg()
s0 = rnn.initial_state()
R = params["R"]
bias = params["bias"]
lookup = params["lookup"]
sentence = ["<EOS>"] + list(sentence) + ["<EOS>"]
sentence = [char2int[c] for c in sentence]
s = s0
loss = []
for char,next_char in zip(sentence,sentence[1:]):
s = s.add_input(lookup[char])
probs = dy.softmax(R*s.output() + bias)
loss.append( -dy.log(dy.pick(probs,next_char)) )
loss = dy.esum(loss)
return loss
# generate from model:
def generate(rnn, params):
def sample(probs):
rnd = random.random()
for i,p in enumerate(probs):
rnd -= p
if rnd <= 0: break
return i
# setup the sentence
dy.renew_cg()
s0 = rnn.initial_state()
R = params["R"]
bias = params["bias"]
lookup = params["lookup"]
s = s0.add_input(lookup[char2int["<EOS>"]])
out=[]
while True:
probs = dy.softmax(R*s.output() + bias)
probs = probs.vec_value()
next_char = sample(probs)
out.append(int2char[next_char])
if out[-1] == "<EOS>": break
s = s.add_input(lookup[next_char])
return "".join(out[:-1]) # strip the <EOS>
# train, and generate every 5 samples
def train(rnn, params, sentence):
trainer = dy.SimpleSGDTrainer(pc)
for i in range(200):
loss = do_one_sentence(rnn, params, sentence)
loss_value = loss.value()
loss.backward()
trainer.update()
if i % 5 == 0:
print("%.10f" % loss_value, end="\t")
print(generate(rnn, params))
Notice that:
do_one_sentence over and over again.
We must re-use the same rnn-builder, as this is where the shared parameters are kept.dy.renew_cg() before each sentence -- because we want to have a new graph (new network) for this sentence.
The parameters will be shared through the model and the shared rnn-builder.
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sentence = "a quick brown fox jumped over the lazy dog"
train(srnn, params_srnn, sentence)
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sentence = "a quick brown fox jumped over the lazy dog"
train(lstm, params_lstm, sentence)
The model seem to learn the sentence quite well.
Somewhat surprisingly, the Simple-RNN model learn quicker than the LSTM! (If you increase the number of layers, this difference will be even more pronounced)
How can that be?
The answer is that we are cheating a bit. The sentence we are trying to learn has each letter-bigram exactly once. This means a simple trigram model can memorize it very well.
Try it out with more complex sequences.
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train(srnn, params_srnn, "these pretzels are making me thirsty")