BI-GRU Capsule Networks for Student Answers Assessment
Nisrine Ait Khayi

Vasile Rus

Department of computer science
University of Memphis/IIS
Memphis TN USA
ntkhynyn@memphis.edu

Department of computer science
University of Memphis/IIS
Memphis TN USA
vrus@memphis.edu

ABSTRACT
Motivated by the good results of capsule networks in textclassification and other Natural Language Processing tasks, we
present in this paper a Bi-GRU Capsule Networks model toautomatically assess freely-generated student answers assessment
within the context of dialogue-based intelligent tutoring systems.
Our proposed model is composed of several important components:
an embedding layer, a Bi-GRU layer, a capsule layer and a SoftMax
layer. We have conducted a number of experiments considering abinary classification task: correct or incorrect answers. Our model
has reached a highest accuracy of 72.50 when using an Elmo wordembedding as detailed in the body of the paper.

KEYWORDS
Capsule networks, deep learning, intelligent tutoring systems,
semantic similarity.

1

Introduction

Automatically assessing open-ended short student responses is anextremely challenging task as students can express their responses
in numerous ways owing to different individual styles and varied
cognitive abilities and knowledge levels. This assessment plays avital role in improving the tutoring experience. The systemprovides hints and feedbacks for the struggling students withincorrect answers. Table 1 shows four answers, articulated by four
different college students, to a question asked by the state-of-theart intelligent tutoring system (ITS) DeepTutor (Rus et al., 2013).
It should be noted that all four student answers in Table 1 arecorrect answers to the tutor question. As can be seen from the table,some students write full sentences (student answer A4), someothers write very short answers (A3), and yet other students write
elaborate answers that include additional concepts relative to thereference answer (A1).
The widely adopted and scalable approach to assessing such openended student responses is semantic similarity in which a score,usually normalized, is computed between a target student answer
and an expert-provided reference answer (Banjade et al., 2016). If
the student answer has a high semantic similarity score to thereference answer we infer that the student answer has the same
correctness value as the reference answer. A low semantic
similarity score implies the student response is incorrect. It should

be noted that sometimes the reference answer may denote a
common misconception in which case a high-similarity score tosuch misconception means the student answer also indicates a
misconception, i.e., it is incorrect.
Problem description:
While speeding up, a large truck pushes a small compact car.
Tutor question:
How do the magnitudes of forces they exert on each othercompare?
Reference answer:
The forces from the truck and car are equal and opposite.
Student answers:
A1. The magnitudes of the forces are equal and opposite toeach other due to Newton’s third law of motion.
A2. they are equal and opposite in direction
A3. equal and opposite
A4. the truck applies an equal and opposite force to the car.
Table 1. Example of students’ answers
More broadly, the task of computing the semantic similarity of two
texts consists of determining, both quantitatively (e.g., normalized
score between 0 and 1) or qualitatively (are the two texts in aparaphrase, elaboration, or entailment relation) the degree ofsimilarity between the two texts. It is a widely used step in many
Natural Language Processing (NLP) applications such as text
summarization (Wong et al., 2008; Nenkova et al., 2011), question
answering (Vo et al., 2015) and machine translation (Corley and
Mihalcea, 2005). It should be noted that we can distinguish among
semantic similarity tasks and methods at various granularity levels:
word-to-word similarity (w2w), phrase-to-phrase(ph2ph),sentence-to-sentence (s2s), paragraph-to-paragraph (p2p), anddocument-to-document (d2d) similarities.
Several approaches have been proposed to automatically assess thesemantic similarity of short, sentence-level texts, which are our
focus. For instance, recently, NLP researchers have applied
extensively deep learning models, which have the advantage of notneeding hand-crafted features and other external resources, that is,just the raw sentences and the corresponding pre-trained wordembeddings are needed as input. Despite of this limited-resource
approach, many deep learning methods have provided state of artof performance. For example, Pontes and colleagues (2018)
proposed a deep learning model that combines convolution andrecurrent neural networks to measure the semantic similarity ofsentences. This combination of networks has been helpful incapturing the most relevant information of sentences, thus,
improving the computation of semantic similarity scores relative tostate-of-the-art systems. Other approaches worth-mentioning are:(1) the Non Linear Similarity approach (Tsubaki et al., 2016),
where word representations are inferred through the similarity
learning of sentences in high-dimensional space with kernel
functions, (2) Constituency Tree LSTM (Tai et al., 2015) which isa generalization to LSTMs to tree-structured network topologies,and (3) Skip-thought (Kiros et al. 2015), where an encoder-decoder
model is used to reconstruct the surrounded sentences. Then,sentences with common semantic and syntactic properties are
mapped to similar vector representations.
Furthermore, Bao et al. (2018) proposed an Attention SiameseLong Short-Term Memory (LSTM) model to measure the semantic
textual similarity. An attention mechanism has been used to capture
the high-level semantic information. The empirical experiments
have demonstrated the effectiveness of the model with animpressive performance.
Wang and colleagues (2018) presented an approach that combines
a Bidirectional Long Short-Term Memory Networks (BLSTM) andConvolutional Neural Networks to extract the semantic features ofa sentence. Then sentence representations are learned with wordlevel attention. Finally, an output layer that calculates the similarity
score was used. This proposed model was evaluated using the
Quora duplicate questions public dataset. The obtained results
showed that this model has outperformed many existing
approaches, such as Support Vector Machine (SVM),
Convolutional Neural Networks (CNN), Bidirectional Long ShortTerm Memory (BLSTM) and attention based BLSTM, with ahighest accuracy of 0.89.
Our approach is very different from these approaches except thefact that uses Deep Learning.
Our task of automatically assessing freely generated student
answers within a dialog system context is a special case of the moregeneral semantic similarity task. As shown in Figure 1, given two
inputs, the student answer and the reference answer, the assessment
model computes the correctness of the student answer. Typically,
the reference and student answer are domain specific as tutoringtargets specific science topics, e.g., Physics. Furthermore, theanswers are generated in the context of problem-solving
instructional activities in which students are asked to provide
solutions to various problems in the form of short essays, the essays
are evaluated and if incorrect and/or incomplete a tutorial dialogue
follows in which students provide short answers to tutoring
systems’ hints. For this work, we don’t capture domain specificinformation. This can be addressed in a future work.

Figure 1. students’ answers assessment problem statement

Motivated by the good results of deep learning models in similar
semantic similarity tasks, we present in this paper a Bi-GRU
Capsnet model to assess the students answers generated during
student-system dialogue-based interactions. Capsules have thecapability to express the semantic meanings in a wider space using
a vector instead of a scalar. Thus, these capsules are suitable toexpress a sentence as a vector (Kim. J et al.,2018). This generated
vector captures the instantiation parameters of the input such as theorder of the words and their semantic representation. On the other
hand, word embeddings also transform words into lower
dimensional vectors that preserve the contextual similarity ofwords. In general, the embedding vectors are fed into various deeplearning models. Our model consists of several importantcomponents. First, there is an embedding layer that transforms eachword of the input to a distributed vector representation. Second, theresulted embedding matrix is fed into a Bidirectional Gated
Recurrent Units layer (Bi-GRUs) (Cho et al., 2014) to encode theinput text into a fixed length representation. The fixed length
representation is then fed into a capsule network. Finally, thecapsule network is followed by a fully connected dense layer with
SoftMax activation for the classification. We evaluate theperformance of our model using the DT-Grade (Banjade et al.,2016) corpus.
The paper is organized as following: paragraph 2 represents therelated research work. The next section describes the modelarchitecture and its components. Section 4 depicts the conducted
experiments and results. The final section concludes the paper,summarizing the main contribution of this work and the possible
directions to improve the current results.

2

Related work

Capsule networks have been introduced by Geoffrey Hinton forimage classification to overcome the limitations of the Convolution
Neural Networks particularly in the pooling layer. These networks
are based on so called capsules and are trained using a dynamic
routing algorithm (Sabour et al., 2017). Each capsule encodes aparticular feature (e.g. local order of words, semantic
representations of words) that the network is looking for. The
magnitude of a capsule vector defines the probability of theexistence of that feature. The layers of capsule networks areconnected via computing a learned vector between each pair ofcapsules. Then, the routing algorithm is used to ensure that theoutput of the capsule, which is a vector, gets sent to an appropriate
parent in the layer above. The capsule computes a “prediction
vector” for each possible parent. This prediction vector is
calculated by multiplying the capsule ‘s own output by a weightmatrix. A top-down feedback is applied, in case the prediction
vector has a large scalar product with the output of a possible
parent. This is done to increase the coupling coefficient for thatparent and decrease it for other parents. In sum, this iterative
routing process decides the credit attribution between the nodes inlower and higher levels. Recently, several NLP researchers haveapplied Capsule Networks for various tasks such as text

classification and sentiment analysis. The obtained results werevery impressive and encouraging to further investigate these
networks in related tasks.
Zhao and colleagues (2018) used capsule networks with dynamic
routing algorithm for text classification. To boost performance,
they have applied three different strategies to stabilize the dynamic
routing process by decreasing some noise capsules. First, an
Orphan category has been added to the network to capture thebackground information such as stop words and the words that are
unrelated to specific categories. Second, a Leaky-SoftMax
approach has been used to update the connection strength between
the parent capsules and their children. Third, the connection
strength has been amended using the probability of the existence ofthe child capsules. To evaluate the performance of the proposed
approach, they have conducted several experiments using six
different datasets. The obtained results demonstrated theeffectiveness of capsule networks over many baseline methods.
Our approach is similar in the sense that we model the student
answer assessment task as a text classification task. However, thearchitecture of our proposed model is different. In fact, Zhao andcolleagues’ model consists of a convolutional layer after theembedding layer and our proposed model consists of a BI-GRU
layer instead.
Kim and colleagues (2018) have applied capsule networks for textclassification. They have used a simple dynamic routing algorithm
to boost the efficiency of the model. Their proposed model consistsof the following components: (1) an embedding layer, (2) a feature
map that use convolutions, (3) a convolutional capsule layer, and(4) a text capsule layer. The authors have conducted several
experiments using different datasets. The results demonstrated thepotential of the application of the capsule networks in the textclassification. This approach is similar to our work in the sense of
considering the student answer assessment task as a textclassification task. The main difference is using a BI-GRU layer
instead of convolutions after the embedding layer.
Capsule networks have been applied successfully in other NLP
tasks. Zhang and colleagues (2018) proposed a relation extraction
approach based on capsule networks with attention mechanism.
Wang and colleagues (2018) presented an attention-based BIGRU-CapsNet model to detect hypernymy relationship between
compound entities. Xia and colleagues (2018) proposed two
capsule-based architectures to solve the zero-shot intent detection
problem: the INTENT-CAPSNET that extracts semantic featuresfrom utterances and aggregate them to discriminate existing intents,
and INTENTCAPSNET to discriminate emerging intents via
knowledge transfer from existing intents.
Based on these successes of capsule networks on related tasks, wehave explored their potential for assessing student answers. To thebest of our knowledge, this is the first attempt at using capsule
networks for assessing student generated answers in conversational
intelligent tutoring systems.

3

Bi-GRU Capsnet Model

Our proposed model (figure 2) consists four major components: (1)an embedding layer that transforms each word to a distributed
vector with a dimension d, (2) a bidirectional- GRU encoder, (3) acapsule network that generates semantic representations of thestudent and reference answers using a dynamic routing algorithm,(4) a SoftMax layer that computes the probabilities of thecorrectness classes.

3.1 Embedding layer
Given a student answer 𝑋 and a reference answer 𝑋 ′ , we tokenize
them into a sequence of words: 𝑋 = [𝑤1 , . . . , 𝑤𝑛 ] and 𝑋 ′ =[𝑤 ′ 1 , … , 𝑤 ′ 𝑚 ] . Afterwards, each token is converted into a ddimensional vector through the embedding layer. In this work, we
consider the following word embeddings approaches: Glove,
Word2vec and ELMo.
•••

Glove embedding has been proposed by Pennington et al.
(2014). It is a “count b-based” model where the word cooccurrence count matrix is pre-processed by normalizing
the counts and log-smoothing operation. This matrix isthen factorized to get lower dimensional representations.
Word2vec embedding has been proposed by Mikolov
and colleagues (2013). Two models have been proposed:
CBOW and skip-gram. CBOW computes the probabilityof a target word given the context surrounding words
within a window. Skip-gram is the opposite of CBOW
model where the probability of the surrounding words iscomputed given the target word.
ELMo (Peters et al. ,2018) method produces wordembeddings for each context where the word is used, thus
allowing different representations for the same word. The
mechanism of ELMo is based on the representation
obtained from a bidirectional language model(biLM). It
consists of two language models (LM): forward LM andbackward LM. The use of ELMo embedding has boosted
the performance of several deep learning models.

Figure 3. Capsule structure
Given the input vectors 𝑢1 , 𝑢2 and 𝑢3 from the previous layers, alearned transformation matrix 𝑊𝑖𝑗 is applied to generate thepredictors vectors 𝑢̂𝑖 as following:𝑢̂𝑗|𝑖 = 𝑊𝑖𝑗 𝑢𝑖(5)Then, in the higher layer, a capsule 𝑠𝑗 is computed by the linear
combination of all the prediction vectors with weights 𝑐𝑖𝑗 asfollowing:𝑠𝑗 = ∑𝑖 𝑐𝑖𝑗 𝑢𝑗|𝑖(6)
where 𝑐𝑖𝑗 are coupling coefficients computed the dynamic routing
algorithm described in figure 4.
Figure 2. Bi-Gru-Capsnet model architecture

Routing Algorithm

3.3.2 Bi-GRU layer
A GRU model is a variant of the Recurrent Neural Network (RNN).
GRU has two gates: un update gate z and a reset gate r. The update
gate determines how much memory of previous cell to keep alive,
and the rest gate determines how to combine the input of new cellwith the previous memory. For each position 𝑡, GRU computes ℎ𝑡
with input 𝑥𝑡 and previous state ℎ𝑡−1 , as:
𝑟𝑡 = 𝜎(𝑊𝑟 𝑥𝑡 + 𝑈𝑟 ℎ𝑡−1 )𝑢𝑡 = 𝜎(𝑊𝑢 𝑥𝑡 + 𝑈𝑢 ℎ𝑡−1 )ℎ̃𝑡 = tanh(𝑊𝑐 𝑥𝑡 + 𝑈(𝑟𝑡 ∙ ℎ𝑡 − 1))ℎ𝑡 = (1 − 𝑢𝑡 ) ∙ ℎ𝑡−1 + 𝑢𝑡 ∙ ℎ̃𝑡

(1)
(2)
(3)
(4)

Where ℎ𝑡 , 𝑟𝑡 and 𝑢𝑡 are d-dimensional hidden state, reset gate,
and update gate. 𝑊𝑟 , 𝑊𝑢 , 𝑊𝑐 and 𝑈𝑟 , 𝑈𝑢 and 𝑈 are theparameters of the GRU model. 𝜎 is the sigmoid function, and . isthe element-wise production.
The outputs vectors ℎ𝑡 and ℎ𝑡 ′ are fed into the capsule layer.

3.3

1: procedure ROUTING (𝑢̂𝑗|𝑖 , 𝑟, 𝑙 )2: for all capsule 𝑖 in layer 𝑙 and capsule 𝑗 in layer 𝑙 + 1:
𝑏𝑖𝑗 ← 0
3: for 𝑟 iterations do
4: for all capsule 𝑖 in layer 𝑙 :𝑐𝑖 ← 𝑠𝑜𝑓𝑡𝑚𝑎𝑥(𝑏𝑖 )SoftMax computes Eq.3
5: for all capsule 𝑗 in layer (𝑙 + 1): 𝑠𝑗 ← ∑𝑖 𝑐𝑖𝑗 𝑢̂𝑗|𝑖
6: for all capsule 𝑗 in layer (𝑙 + 1):
𝑣𝑗 ← 𝑠𝑞𝑢𝑎𝑠ℎ(𝑠𝑗 )squash computes Eq.1
7: for all capsule 𝑖 in layer 𝑙 and capsule 𝑗 in layer (𝑙 + 1) :𝑏𝑖𝑗 ← 𝑏𝑖𝑗 + 𝑢̂𝑗|𝑖 ∙ 𝑣𝑗
return 𝒗𝒋
Figure 4. the routing algorithm
As stated before, the output of a capsule represents the probability
that the input has the entity that the capsule describes. So, the rangeof the activation vector should be in the [0,1] interval. For thispurpose, a squash function is applied to generate the final output
vector 𝑣𝑗 as following:

Capsule layer

The assumption behind capsule networks is that there are capsules(group of neurons) that tell whether certain entities are present in
an image. A capsule as shown in figure 3 has an activation vector
that represents the instantiation parameters of an entity and whose
length represents the probability of the existence of that entity.

𝒗𝒋 =

‖𝒔𝒋 ‖

𝟐

𝒔𝒋

𝟏+‖𝒔𝒋 ‖ ‖𝒔𝒋 ‖𝟐(7)

The final outputs of the capsule layers for the given students’answers are activation vectors 𝑣1 and 𝑣2 .

Afterwards, we concatenate these vectors as [𝑣1 , 𝑣2 ] and we feed
this concatenation into a SoftMax layer that computes theprobability for each correctness class.

4

Experiments and Results

Our experiments were conducted in the context of student
generated answers in response to hints (in the form of questions) inconversational intelligent tutoring systems. To this end, we haveused a previously annotated dataset as described next.

4.1 The DT-Grade Dataset
The DT-Grade dataset consists of 900 instances of student answers
extracted from logged tutorial interactions between 40 junior level
college students and the state-of-the-art intelligent tutoring system
DeepTutor. Each annotation example (See table 1) consists of thefollowing attributes: (1) problem description, (2) tutor question, (3)student answer and (4) reference answers. In addition, the data
includes the correctness class of each student answer. There are
four classes: correct, correct but incomplete, incorrect andcontradictory.
In this work, we consider two classes: correct and incorrect. The
correct answers are those labeled as “correct“ in the DT-Gradedataset. All the other instances are considered as belonging to the“incorrect” class.

Problem Description:
A car windshield collides with a mosquito, squashing it.
Question:
How does Newton's third law apply to this situation?
Student Answer:
the windshield will apply a force to the mosquito equal the force
applied by the mosquito to the windshield
Reference answer
1: Since the windshield exerts a force on the mosquito, which
we can call action, the mosquito exerts an equal and opposite
force on the windshield, called the reaction.
Table 3. Annotation example of the DT-Grade dataset

4.2 Results
Several experiments have been conducted with different capsnet
neural networks (see table 4) varying the embedding
representations and the number of capsules to evaluate theperformance of our proposed model using the DT-Grade dataset.

Model

Accuracy %F1 Measure

61

0.61

60.62

0.55

58.75

0.6

55

0.59

56.25

0.57

52.25

0.47

69.37

0.68

66.25

0.66

72.5

0.7

56.25
60

0.56
0.6

Bi-GRU-capsnet(Glove,10)
Bi-GRU-capsnet(Glove,15)
Bi-GRU-capsnet(Glove,20)
Bi-GRU-capsnet(Word2vec,10)
Bi-GRU-capsnet(Word2vec,15)
Bi-GRU-capsnet(Word2vec,20)
Bi-GRU-capsnet(Elmo,20)
Bi-GRU-capsnet(Elmo,15)
Bi-GRU-capsnet(Elmo,10)
Bi-GRU (Glove)
LSTM (Glove)

Table4. The performance results of various models.
A first set of experiments have been conducted using thepretrained Glove embeddings with 100 dimension and threedifferent values of the number of capsules. Based on the literature,
we have started with a value of 10 and added two other values: 15
and 20. This has been done to test the impact of different
expressiveness levels of the capsule network layer on theperformance. A second set of experiments have been conductedusing word2vec embeddings with 100 dimensions while using thesame different values of the number of capsules. Another set ofexperiments have been run using ELMo embeddings with 300
dimensions, which are the state of art of embeddings, while using
the same values of the number of capsules. To compare theperformance of our model with existing ones, we have empiricallyexperimented the following baseline deep learning models: (1) An
LSTM (Long Short-Term Memory) neural network that consists ofa Glove embedding and 240 cells. (2) A Bi-GRU network thatconsists of Glove embedding with 50 units.
During the experiments, we used 80% of data set for training and
20% for testing. The distribution of classes, as shown in Table 5, intraining and testing is imbalanced. To overcome this problem, we
adjusted the class weights in the model during the training.

DatasetCorrect (%)

Training
Testing41
41.58

Incorrect (%)
59
58.41

Table5. the distribution of classes in training and testing data

Table5 represents the distribution of classes in the training and test
dataset. As mentioned previously, we have considered data withcorrect label as correct and anything else as incorrect.
Hyperparameters. In all the experiments, we used a Bi-GRU layer
with 50 units. Several numbers of units have been tested and thisvalue has led to higher accuracy. We also added a 0.2 Dropout tothe Bi-GRU layer to prevent over-fitting. For the capsule layer, weused 3 iterations for the routing algorithm and 16 for the capsuledimension. We also added a 0.2 Dropout to prevent over-fitting.
For optimization, we use the Adam optimizer (Kimgma andBa,2014) with a learning rate of 0.0001. The gradients are clipped
to 0.5 to prevent exploding gradients. We trained our model for 100
epochs to obtain the results. The increase of epochs, particularly
when using the ELMo embedding, showed an increase in theoverall accuracy and F1-measure values.

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Table 4 shows the results on the DT-Grade dataset. Our Bi-GRU
capsnet model outperforms the baselines deep learning models,particularly the Bi-Gru and LSTM models. The results show that
our model reaches the highest accuracy of 72.5 and 0.7 of F1measure when using the ELMo embedding particularly. This is nota surprising result. Several research works have demonstrated that
ELMo embeddings boost the performance of deep learning models
in various NLP tasks. However, the accuracy and F1 score
decreased significantly when using the word2vec embedding
approach. 72.5 accuracy is considered a very good result for the
DT-Grade dataset due to its small size in comparison with larger
NLP datasets.

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5. Conclusions
In this paper, we proposed a Bi-GRU-Capsnet model to assess thecorrectness of the students answers within the intelligent tutoring
system DeepTutor. We have chosen this deep learning model to getbenefits from its no requirements of hands -crafted features andexternal resources. Added to this, Capsule networks have thecapability to express the semantic meanings in a wider space using
a vector that captures the instantiation parameters of the input suchas the order of words and their semantic representation . The
experimental results show that our model reached the state of art ofperformance on the DT-Grade dataset. Particularly, our model
reached the highest accuracy when using the ELMo embeddings.
In the future, we plan to investigate more deep learning models toimprove the current results.

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ACKNOWLEDGMENTS
To be added later – removed during the blind review process.

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