Introduction
Modelling the relationship between sequences is extremely significant in most retrieval or classification problems involving two sequences. Traditionally, in Siamese networks, Hadamard product or concatenation have been used to fuse two vector representations of two input sequences to form a final representation for tasks like semantic similarity, passage retrieval. This representation, subsequently, has been used to compute similarity scores which has been used in a variety of training objectives like margin loss for ranking or cross-entropy error in classification.
We have also witnessed word or phrase level similarity to create alignment matrices between two sequences BIBREF0 , BIBREF1 . These alignment matrices has proved to be very useful to model the relationship between two word representations as well fuse the relevant information of one sequence into another. Empirical evidences have shown this alignment procedures have significantly performed better then simple concatenation or element-wise multiplication, especially for long sentences or paragraphs.
Attention works on creating neural alignment matrix using learnt weights without pre-computing alignment matrix and using them as features. The main objective of any attentive or alignment process is to look for matching words or phrases between two sequences and assign a high weight to the most similar pairs and vice-versa. The notion of matching or similarity maybe not semantic similarity but based on whatever task we have at hand. For example, for a task that requires capturing semantic similarity between two sequences like "how rich is tom cruise" and "how much wealth does tom cruise have", an attentive model shall discover the high similarity between "rich" and "wealthy" and assign a high weight value to the pair. Likewise, for a different task like question answering, a word "long" in a question like "how long does it take to recover from a mild fever" might be aligned with the phrase "a week" from the candidate answer "it takes almost a week to recover fully from a fever". Thus, attention significantly aids in better understanding the relevance of a similar user query in a similar measurement task or a candidate answer in a question answering task. The final prediction score is dependent on how well the relationship between two sequences are modeled and established.
The general process of matching one sequence with another through attention includes computing the alignment matrix containing weight value between every pair of word representations belonging to both of the sequences. Subsequently, softmax function is applied on all the elements of one of the two dimensions of the matrix to represent the matching probabilities of all the word of a sequence with respect to one particular word in the other sequence.
Since attention always looks for matching word representations, it operates under the assumption that there is always a match to be found inside the sequences. We provide a theoretical limitation to it and propose another technique called conflict that looks for contrasting relationship between words in two sequences. We empirically verify that our proposed conflict mechanism combined with attention can outperform the performance of attention working solely.
Related Work
Bahdanau et al. BIBREF2 introduced attention first in neural machine translation. It used a feed-forward network over addition of encoder and decoder states to compute alignment score. Our work is very similar to this except we use element wise difference instead of addition to build our conflict function. BIBREF3 came up with a scaled dot-product attention in their Transformer model which is fast and memory-efficient. Due to the scaling factor, it didn't have the issue of gradients zeroing out. On the other hand, BIBREF4 has experimented with global and local attention based on the how many hidden states the attention function takes into account. Their experiments have revolved around three attention functions - dot, concat and general. Their findings include that dot product works best for global attention. Our work also belongs to the global attention family as we consider all the hidden states of the sequence.
Attention has been widely used in pair-classification problems like natural language inference. Wang et al. BIBREF5 introduced BIMPM which matched one sequence with another in four different fashion but one single matching function which they used as cosine. Liu et al. BIBREF6 proposed SAN for language inference which also used dot-product attention between the sequences.
Summarizing, attention has helped in achieving state-of-the-art results in NLI and QA. Prior work in attention has been mostly in similarity based approaches while our work focuses on non-matching sequences.
How attention works
Let us consider that we have two sequences INLINEFORM0 and INLINEFORM1 each with M and N words respectively. The objective of attention is two-fold: compute alignment scores (or weight) between every word representation pairs from INLINEFORM2 and INLINEFORM3 and fuse the matching information of INLINEFORM4 with INLINEFORM5 thus computing a new representation of INLINEFORM6 conditioned on INLINEFORM7 .
The word representations that attention operates on can be either embeddings like GloVe or hidden states from any recurrent neural network. We denote these representations as u = INLINEFORM0 and v = INLINEFORM1 . We provide a mathematical working of how a general attention mechanism works between two sequences, followed by a explanation in words: DISPLAYFORM0
Explanation: Both are sequences are non-linearly projected into two different spaces (eqn.1) and each word representation in INLINEFORM0 is matched with that in INLINEFORM1 by computing a dot-product (eqn.2). INLINEFORM2 is a M X N matrix that stores the alignment scores between word INLINEFORM3 and INLINEFORM4 (eqn.2). Since, the scores are not normalized, a softmax function is applied on each row to convert them to probabilities (eqn. 3). Thus, each row contains relative importance of words in INLINEFORM5 to a particular word INLINEFORM6 . Weighted sum of INLINEFORM7 is taken (eqn. 4) and fused with the word representation INLINEFORM8 using concatenation (eqn.5).
Limits of using only Attention
Attention operates by using dot product or sometimes addition followed by linear projection to a scalar which models the similarity between two vectors. Subsequently, softmax is applied which gives high probabilities to most matching word representations. This assumes that there is some highly matched word pairs already existing and high scores will be assigned to them. Given a vector INLINEFORM0 =( INLINEFORM1 ,..., INLINEFORM2 ) on which softmax function is applied, each INLINEFORM3 INLINEFORM4 (0, 1). It is observable that the average value of INLINEFORM5 is always INLINEFORM6 . In other words, it is impossible to produce a vector having all INLINEFORM7 < INLINEFORM8 when two sequences have no matching at all.
In cases, where one or more word pairs from two different sequences are highly dissimilar, it is impossible to assign a very low probability to it without increasing the probability of some other pair somewhere else since INLINEFORM0 = 1.
For example, when we consider two sequences "height of tom cruise" and "age of sun", while computing the attention weights between the word "height" and all the words in the second sequence it can be observed that their no matching word in the latter. In this case, a standard dot-product based attention with softmax won't be able to produce weights which is below 0.33 (=1/3) for all the words in the second sequence with respect to the word "height" in the first sequence.
Conflict model
We propose a different mechanism that does the opposite of what attention does that is computing how much two sequences repel each other. This works very similar to how attention works but inversely.
We demonstrate a general model but we also realize that there can be other variants of it which may be worked out to perform better. Our approach consists of using element wise difference between two vectors followed by a linear transformation to produce a scalar weight. The remaining of the process acts similar to how attention works. Mathematically, we can express it as: DISPLAYFORM0
where INLINEFORM0 INLINEFORM1 INLINEFORM2 is a parameter that we introduce to provide a weight for the pair. The two word representations INLINEFORM3 and INLINEFORM4 are projected to a space where their element wise difference can be used to model their dissimilarity and softmax applied on them can produce high probability to more dissimilar word pairs.
It is good to note that conflict suffers from the same limitation that attention suffers from. This is when a pair of sentences are highly matching especially with multiple associations. But when the two methods work together, each compensates for the other's shortcomings.
Combination of attention and conflict
We used two weighted representations of INLINEFORM0 using weights of attention and conflict as computed in Eqn. (4) and (8) respectively. Our final representation of a word representation INLINEFORM1 conditioned on INLINEFORM2 can be expressed as: DISPLAYFORM0
where A and C denote that they are from attention and conflict models respectively.
Relation to Multi-Head attention
Multi-head attention, as introduced in BIBREF3 , computes multiple identical attention mechanism parallelly on multiple linear projections of same inputs. The parameters of each attention and projections are different in each head. Finally, they concatenate all the attentions which is similar to how we concatenate conflict and attention. However, they use dot-product to compute each of the attention.
Our combined model that contains both attention and conflict can be thought of as a 2-head attention model but both heads are different. Our conflict head explicitly captures difference between the inputs.
Visualizing attention and conflict
We observe how our conflict model learns the dissimilarities between word representations. We achieve that by visualizing the heatmap of the weight matrix INLINEFORM0 for both attention and conflict from eqns. (3) and (8). While attention successfully learns the alignments, conflict matrix also shows that our approach models the contradicting associations like "animal" and "lake" or "australia" and "world". These two associations are the unique pairs which are instrumental in determining that the two queries are not similar.
The model
We create two models both of which constitutes of three main parts: encoder, interaction and classifier and take two sequences as input. Except interaction, all the other parts are exactly identical between the two models. The encoder is shared among the sequences simply uses two stacked GRU layers. The interaction part consists of only attention for one model while for the another one it consists of attention and conflict combined as shown in (eqn.11) . The classifier part is simply stacked fully-connected layers. Figure 3 shows a block diagram of how our model looks like.
Task 1: Quora Duplicate Question Pair Detection
The dataset includes pairs of questions labelled as 1 or 0 depending on whether a pair is duplicate or not respectively. This is a popular pair-level classification task on which extensive work has already been done before like BIBREF7 , BIBREF8 . For this task, we make the output layer of our model to predict two probabilities for non-duplicate and duplicate. We sample the data from the original dataset so that it contains equal positive and negative classes. Original dataset has some class imbalance but for sake simplicity we don't consider it. The final data that we use has roughly 400,000 question pairs and we split this data into train and test using 8:2 ratio.
We train all our models for roughly 2 epochs with a batch size of 64. We use a hidden dimension of 150 throughout the model. The embedding layer uses ELMO BIBREF9 which has proven to be very useful in various downstream language understanding tasks. Our FC layers consists of four dense layers with INLINEFORM0 activation after each layer. The dropout rate is kept as 0.2 for every recurrent and FC linear layers. We use Adam optimizer in our experiment with epsilon=1e-8, beta=0.9 and learning rate=1e-3.
Task 2: Ranking questions in Bing's People Also Ask
People Also Ask is a feature in Bing search result page where related questions are recommended to the user. User may click on a question to view the answer. Clicking is a positive feedback that shows user's interest in the question. We use this click logs to build a question classifier using the same model in Figure 3. The problem statement is very similar to BIBREF10 where they use logistic regression to predict whether an user would click on ad. Our goal is to classify if a question is potential high-click question or not for a given query. For this, we first create a labelled data set using the click logs where any question having CTR lower than 0.3 is labelled as 0 and a question having CTR more than 0.7 as 1.
Our final data resembles that of a pair-level classifier, as in Task 1, where user query and candidate questions are input. With these data set, we train a binary classifier to detect high-click and low-click questions.
Quantitative Analysis
For both tasks, we compute classification accuracy using three model variants and report the results in Table 1 and Table 2. We observe that model with both attention and conflict combined gives the best results.
We also show the training loss curve for both the models having attention and attention combined with conflict respectively. Figure 4 and 5 shows these curves for Task 1 and Task 2 respectively. The curves are smoothed using moving average having an window size of 8. We notice that the conflict model has much steeper slope and converges to a much better minima in both the tasks. It can also be noticed that in the training procedure for the model which has both attention and conflict, the updates are much smoother.
Qualitative Comparison
We also show qualitative results where we can observe that our model with attention and conflict combined does better on cases where pairs are non-duplicate and has very small difference. We have observed that the conflict model is very sensitive to even minor differences and compensates in such cases where attention poses high bias towards similarities already there in the sequences.
Sequence 1: What are the best ways to learn French ?
Sequence 2: How do I learn french genders ?
Attention only: 1
Attention+Conflict: 0
Ground Truth: 0
Sequence 1: How do I prevent breast cancer ?
Sequence 2: Is breast cancer preventable ?
Attention only: 1
Attention+Conflict: 0
Ground Truth: 0
We provide two examples with predictions from the models with only attention and combination of attention and conflict. Each example is accompanied by the ground truth in our data.
Analyzing the gains
We analyzed the gains in Task 1 which we get from the attention-conflict model in order to ensure that they are not due to randomness in weight initialization or simply additional parameters. We particularly focused on the examples which were incorrectly marked in attention model but correctly in attention-conflict model. We saw that 70% of those cases are the ones where the pair was incorrectly marked as duplicate in the previous model but our combined model correctly marked them as non-duplicate.
Conclusion
In this work, we highlighted the limits of attention especially in cases where two sequences have a contradicting relationship based on the task it performs. To alleviate this problem and further improve the performance, we propose a conflict mechanism that tries to capture how two sequences repel each other. This acts like the inverse of attention and, empirically, we show that how conflict and attention together can improve the performance.
Future research work should be based on alternative design of conflict mechanism using other difference operators other than element wise difference which we use.

Question: On which tasks do they test their conflict method?
Answer: Task 1: Quora Duplicate Question Pair Detection, Task 2: Ranking questions
Quora Duplicate Question Pair Detection, Ranking questions in Bing's People Also Ask