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# CS 224n Assignment #3: Dependency Parsing

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CS 224n Assignment #3: Dependency Parsing
In this assignment, you will build a neural dependency parser using PyTorch. For a review of the fundamentals of PyTorch, please check out the PyTorch review session on Canvas. In Part 1, you will learn about two
general neural network techniques (Adam Optimization and Dropout). In Part 2, you will implement and
train a dependency parser using the techniques from Part 1, before analyzing a few erroneous dependency
parses.
1. Machine Learning & Neural Networks (8 points)
Recall the standard Stochastic Gradient Descent update rule:
θ ← θ − α∇θ
Jminibatch(θ)
where θ is a vector containing all of the model parameters, J is the loss function, ∇θ
Jminibatch(θ)
is the gradient of the loss function with respect to the parameters on a minibatch of data, and α is
the learning rate. Adam Optimization1 uses a more sophisticated update rule with two additional
steps.2
i. (2 points) First, Adam uses a trick called momentum by keeping track of m, a rolling average
m ← β1m + (1 − β1)∇θ
Jminibatch(θ)
θ ← θ − αm
where β1 is a hyperparameter between 0 and 1 (often set to 0.9). Briefly explain in 2-4 sentences
(you don’t need to prove mathematically, just give an intuition) how using m stops the updates
from varying as much and why this low variance may be helpful to learning, overall.
ii. (2 points) Adam extends the idea of momentum with the trick of adaptive learning rates by
keeping track of v, a rolling average of the magnitudes of the gradients:
m ← β1m + (1 − β1)∇θ
Jminibatch(θ)
v ← β2v + (1 − β2)(∇θ
Jminibatch(θ) ∇θ
Jminibatch(θ))
θ ← θ − αm/

v
where and / denote elementwise multiplication and division (so zz is elementwise squaring)
and β2 is a hyperparameter between 0 and 1 (often set to 0.99). Since Adam divides the update
by √
v, which of the model parameters will get larger updates? Why might this help with
learning?
(b) (4 points) Dropout3
is a regularization technique. During training, dropout randomly sets units
in the hidden layer h to zero with probability pdrop (dropping different units each minibatch), and
then multiplies h by a constant γ. We can write this as:
hdrop = γd h
where d ∈ {0, 1}
Dh (Dh is the size of h) is a mask vector where each entry is 0 with probability
pdrop and 1 with probability (1 − pdrop). γ is chosen such that the expected value of hdrop is h:
Epdrop [hdrop]i = hi
for all i ∈ {1, . . . , Dh}.
1Kingma and Ba, 2015, https://arxiv.org/pdf/1412.6980.pdf
2The actual Adam update uses a few additional tricks that are less important, but we won’t worry about them here. If you
3Srivastava et al., 2014, https://www.cs.toronto.edu/˜hinton/absps/JMLRdropout.pdf
1
CS 224n Assignment 3 Page 2 of 8
i. (2 points) What must γ equal in terms of pdrop? Briefly justify your answer or show your math
derivation using the equations given above.
ii. (2 points) Why should dropout be applied during training? Why should dropout NOT be applied during evaluation? (Hint: it may help to look at the paper linked above in the write-up.)
CS 224n Assignment 3 Page 3 of 8
2. Neural Transition-Based Dependency Parsing (44 points)
In this section, you’ll be implementing a neural-network based dependency parser with the goal of maximizing performance on the UAS (Unlabeled Attachment Score) metric.
We will be using PyTorch 1.7.1 from https://pytorch.org/get-started/locally/ with the
CUDA option set to None, and the tqdm package – which produces progress bar visualizations throughout your training process. The official PyTorch website is a great resource that includes tutorials for
understanding PyTorch’s Tensor library and neural networks.
A dependency parser analyzes the grammatical structure of a sentence, establishing relationships between
head words, and words which modify those heads. There are multiple types of dependency parsers,
including transition-based parsers, graph-based parsers, and feature-based parsers. Your implementation
will be a transition-based parser, which incrementally builds up a parse one step at a time. At every step
it maintains a partial parse, which is represented as follows:
• A stack of words that are currently being processed.
• A buffer of words yet to be processed.
• A list of dependencies predicted by the parser.
Initially, the stack only contains ROOT, the dependencies list is empty, and the buffer contains all words
of the sentence in order. At each step, the parser applies a transition to the partial parse until its buffer
is empty and the stack size is 1. The following transitions can be applied:
• SHIFT: removes the first word from the buffer and pushes it onto the stack.
• LEFT-ARC: marks the second (second most recently added) item on the stack as a dependent of
the first item and removes the second item from the stack, adding a first word → second word
dependency to the dependency list.
• RIGHT-ARC: marks the first (most recently added) item on the stack as a dependent of the second
item and removes the first item from the stack, adding a second word → first word dependency to
the dependency list.
On each step, your parser will decide among the three transitions using a neural network classifier.
(a) (4 points) Go through the sequence of transitions needed for parsing the sentence “I parsed this
sentence correctly”. The dependency tree for the sentence is shown below. At each step, give the
configuration of the stack and buffer, as well as what transition was applied this step and what new
dependency was added (if any). The first three steps are provided below as an example.
ROOT I parsed this sentence correctly
Stack Buffer New dependency Transition
[ROOT] [I, parsed, this, sentence, correctly] Initial Configuration
[ROOT, I] [parsed, this, sentence, correctly] SHIFT
[ROOT, I, parsed] [this, sentence, correctly] SHIFT
[ROOT, parsed] [this, sentence, correctly] parsed→I LEFT-ARC
CS 224n Assignment 3 Page 4 of 8
(b) (2 points) A sentence containing n words will be parsed in how many steps (in terms of n)? Briefly
explain in 1-2 sentences why.
(c) (6 points) Implement the init and parse step functions in the PartialParse class in
parser transitions.py. This implements the transition mechanics your parser will use. You
can run basic (non-exhaustive) tests by running python parser transitions.py part c.
(d) (8 points) Our network will predict which transition should be applied next to a partial parse. We
could use it to parse a single sentence by applying predicted transitions until the parse is complete.
However, neural networks run much more efficiently when making predictions about batches of data
at a time (i.e., predicting the next transition for any different partial parses simultaneously). We
can parse sentences in minibatches with the following algorithm.
Algorithm 1 Minibatch Dependency Parsing
Input: sentences, a list of sentences to be parsed and model, our model that makes parse decisions
Initialize partial parses as a list of PartialParses, one for each sentence in sentences
Initialize unfinished parses as a shallow copy of partial parses
while unfinished parses is not empty do
Take the first batch size parses in unfinished parses as a minibatch
Use the model to predict the next transition for each partial parse in the minibatch
Perform a parse step on each partial parse in the minibatch with its predicted transition
Remove the completed (empty buffer and stack of size 1) parses from unfinished parses
end while
Return: The dependencies for each (now completed) parse in partial parses.
Implement this algorithm in the minibatch parse function in parser transitions.py. You
can run basic (non-exhaustive) tests by running python parser transitions.py part d.
Note: You will need minibatch parse to be correctly implemented to evaluate the model you will
build in part (e). However, you do not need it to train the model, so you should be able to complete
most of part (e) even if minibatch parse is not implemented yet.
(e) (12 points) We are now going to train a neural network to predict, given the state of the stack,
buffer, and dependencies, which transition should be applied next.
First, the model extracts a feature vector representing the current state. We will be using the feature
set presented in the original neural dependency parsing paper: A Fast and Accurate Dependency
Parser using Neural Networks.
4 The function extracting these features has been implemented for
you in utils/parser utils.py. This feature vector consists of a list of tokens (e.g., the last
word in the stack, first word in the buffer, dependent of the second-to-last word in the stack if there
is one, etc.). They can be represented as a list of integers w = [w1, w2, . . . , wm] where m is the
number of features and each 0 ≤ wi < |V | is the index of a token in the vocabulary (|V | is the
vocabulary size). Then our network looks up an embedding for each word and concatenates them
into a single input vector:
x = [Ew1
, …, Ewm] ∈ R
dm
where E ∈ R
|V |×d
is an embedding matrix with each row Ew as the vector for a particular word w.
4Chen and Manning, 2014, http://cs.stanford.edu/people/danqi/papers/emnlp2014.pdf
CS 224n Assignment 3 Page 5 of 8
We then compute our prediction as:
h = ReLU(xW + b1)
l = hU + b2
yˆ = softmax(l)
where h is referred to as the hidden layer, l is referred to as the logits, yˆ is referred to as the
predictions, and ReLU(z) = max(z, 0)). We will train the model to minimize cross-entropy loss:
J(θ) = CE(y, yˆ) = −
X
3
i=1
yi
log ˆyi
To compute the loss for the training set, we average this J(θ) across all training examples.
We will use UAS score as our evaluation metric. UAS refers to Unlabeled Attachment Score, which
is computed as the ratio between number of correctly predicted dependencies and the number of
total dependencies despite of the relations (our model doesn’t predict this).
In parser model.py you will find skeleton code to implement this simple neural network using
PyTorch. Complete the init , embedding lookup and forward functions to implement the
model. Then complete the train for epoch and train functions within the run.py file.
Finally execute python run.py to train your model and compute predictions on test data from
Penn Treebank (annotated with Universal Dependencies).
Note:
• For this assignment, you are asked to implement Linear layer and Embedding layer. Please
DO NOT use torch.nn.Linear or torch.nn.Embedding module in your code, otherwise
you will receive deductions for this problem.
• Please follow the naming requirements in our TODO if there are any, e.g. if there are explicit
are free to declare other variable names if not explicitly required.
Hints:
• Each of the variables you are asked to declare (self.embed to hidden weight,
self.embed to hidden bias, self.hidden to logits weight,
self.hidden to logits bias) corresponds to one of the variables above (W, b1, U, b2).
• It may help to work backwards in the algorithm (start from yˆ) and keep track of the matrix/vector sizes.
• Once you have implemented embedding lookup (e) or forward (f) you can call python
parser model.py with flag -e or -f or both to run sanity checks with each function. These
sanity checks are fairly basic and passing them doesn’t mean your code is bug free.
• When debugging, you can add a debug flag: python run.py -d. This will cause the code
to run over a small subset of the data, so that training the model won’t take as long. Make
sure to remove the -d flag to run the full model once you are done debugging.
• When running with debug mode, you should be able to get a loss smaller than 0.2 and a UAS
larger than 65 on the dev set (although in rare cases your results may be lower, there is some
randomness when training).
• It should take about 1 hour to train the model on the entire the training dataset, i.e., when
debug mode is disabled.
CS 224n Assignment 3 Page 6 of 8
• When debug mode is disabled, you should be able to get a loss smaller than 0.08 on the train set
and an Unlabeled Attachment Score larger than 87 on the dev set. For comparison, the model
in the original neural dependency parsing paper gets 92.5 UAS. If you want, you can tweak
the hyperparameters for your model (hidden layer size, hyperparameters for Adam, number of
epochs, etc.) to improve the performance (but you are not required to do so).
Deliverables:
• Working implementation of the transition mechanics that the neural dependency parser uses in
parser transitions.py.
• Working implementation of minibatch dependency parsing in parser transitions.py.
• Working implementation of the neural dependency parser in parser model.py. (We’ll look
at and run this code for grading).
• Working implementation of the functions for training in run.py. (We’ll look at and run this
• Report the best UAS your model achieves on the dev set and the UAS it achieves on the test
(f) (12 points) We’d like to look at example dependency parses and understand where parsers like ours
might be wrong. For example, in this sentence:
Moscow sent troops into Afghanistan .
PROPN VERB NOUN ADP PROPN PUNCT
nsubj dobj
root
nmod
case
punct
the dependency of the phrase into Afghanistan is wrong, because the phrase should modify sent (as
in sent into Afghanistan) not troops (because troops into Afghanistan doesn’t make sense). Here is
the correct parse:
Moscow sent troops into Afghanistan .
PROPN VERB NOUN ADP PROPN PUNCT
nsubj dobj
root
nmod
case
punct
More generally, here are four types of parsing error:
• Prepositional Phrase Attachment Error: In the example above, the phrase into Afghanistan
is a prepositional phrase5
. A Prepositional Phrase Attachment Error is when a prepositional
phrase is attached to the wrong head word (in this example, troops is the wrong head word and
sent is the correct head word). More examples of prepositional phrases include with a rock,
before midnight and under the carpet.
• Verb Phrase Attachment Error: In the sentence Leaving the store unattended, I went
outside to watch the parade, the phrase leaving the store unattended is a verb phrase6
. A Verb
Phrase Attachment Error is when a verb phrase is attached to the wrong head word (in this
example, the correct head word is went).
• Modifier Attachment Error: In the sentence I am extremely short, the adverb extremely is
a modifier of the adjective short. A Modifier Attachment Error is when a modifier is attached
to the wrong head word (in this example, the correct head word is short).
5For examples of prepositional phrases, see: https://www.grammarly.com/blog/prepositional-phrase/
6For examples of verb phrases, see: https://examples.yourdictionary.com/verb-phrase-examples.html
CS 224n Assignment 3 Page 7 of 8
• Coordination Attachment Error: In the sentence Would you like brown rice or garlic naan?,
the phrases brown rice and garlic naan are both conjuncts and the word or is the coordinating
conjunction. The second conjunct (here garlic naan) should be attached to the first conjunct
(here brown rice). A Coordination Attachment Error is when the second conjunct is attached
to the wrong head word (in this example, the correct head word is rice). Other coordinating
conjunctions include and, but and so.
In this question are four sentences with dependency parses obtained from a parser. Each sentence
has one error type, and there is one example of each of the four types above. For each sentence,
state the type of error, the incorrect dependency, and the correct dependency. While each sentence
should have a unique error type, there may be multiple possible correct dependencies for some of
the sentences. To demonstrate: for the example above, you would write:
• Error type: Prepositional Phrase Attachment Error
• Incorrect dependency: troops → Afghanistan
• Correct dependency: sent → Afghanistan
Note: There are lots of details and conventions for dependency annotation. If you want to
org7 or the short introductory slides at: http://people.cs.georgetown.edu/nschneid/
p/UD-for-English.pdf. Note that you do not need to know all these details in order to do
this question. In each of these cases, we are asking about the attachment of phrases and it should
be sufficient to see if they are modifying the correct head. In particular, you do not need to look at
the labels on the the dependency edges – it suffices to just look at the edges themselves.
i.
I disembarked and was heading to a wedding fearing my death .
PRON VERB CCONJ AUX VERB ADP DET NOUN VERB PRON NOUN PUNCT
nsubj
root
cc
aux
conj
case
det
nmod
acl amod
dobj
punct
ii.
It makes me want to rush out and rescue people from dilemmas of their own making .
nsubj
root
nsubj
ccomp
mark
xcomp
conj
dobj case
nmod case
nmod:poss
amod
nmod
punct
iii.
7But note that in the assignment we are actually using UDv1, see: http://universaldependencies.org/docsv1/
CS 224n Assignment 3 Page 8 of 8
It is on loan from a guy named Joe O’Neill in Midland , Texas .
nsubj
cop
case
root
case
det
nmod
acl xcomp flat case
nmod
punct
appos
punct
iv.
Brian has been one of the most crucial elements to the success of Mozilla software .
nsubj
aux
aux
root
case
det
amod
nmod
case
det
nmod
case
compound
nmod
punct
Submission Instructions
You shall submit this assignment on GradeScope as two submissions – one for “Assignment 3 [coding]” and
another for ‘Assignment 3 [written]”:
1. Run the collect submission.sh script to produce your assignment3.zip file.