1 Introduction
Algorithms designed to learn distributed sentence representations have been shown to be transferable across a range of tasks (Mou et al., 2016) and languages (Tiedemann, 2018). For example, Guu et al. (2017)
proposed to represent sentences as vectors that encode a notion similarity between sentence pairs, and showed that vector manipulations of the representation can result in meaningful change in semantics. The question we would like to explore is whether the semantic relationship between sentence pairs can be modeled in a more explicit manner. More specifically, we want to model the
logical relationship between sentences.Controlling the logical relationship between sentences has many direct applications. First of all, we can use it to provide a more clear definition of paraphrasing. To do so, we require two simultaneous conditions: (i) that the input sentence entails the output sentence; and (ii) that the output sentence entails the input sentence.
(1) 
The first requirement ensures the output sentence cannot be false if the input sentence is true, so that the output sentence can be considered a fact expressed by the input sentence. The second requirement ensures that the output contains at least the input’s information. The two requirements together can be used to define semantic equivalence between sentence.
Another interesting application is multidocument summarization. Traditionally, to summarize multiple documents, one would expect the model to abstract the most important part of the source documents, and this is usually measured by the amount of overlap that the output document has with the inputs. Informally, one finds the maximal amount of information that has the highest precision with each source document. Alternatively, if one wants to automate news aggregation, the ideal summary would need to contain the same number of facts as are contained in the union of all source documents. We can think of this second objective as requiring that the output document entail every single sentence across all source documents.
In this paper, we propose an approach to generating sentences, conditioned on an input sentence and a logical inference label. We do this by modeling the different possibilities for the output sentence as a distribution over the latent representation, which we train using an adversarial objective.
In particular, we differ from the usual adversarial training on text by using a differentiable global representation. Architecturewise, we also propose a Memory Operation Selection Module (MOSM) for encoding a sentence into a vector representation. Finally, we evaluate the quality and the diversity of our samples.
The rest of the paper is organized as follows: Sec. 2 will cover the related literature. Sec. 3 will detail the proposed model architecture, and Sec. 4 will describe and analyze the experiments run. Sec. 5 will then discuss the implications of being able to solve this task well, and the future research directions relating to this work. Finally, we conclude in Sec. 6.
2 Related Work
Many natural language tasks require reasoning capabiliities. The Recognising Textual Entailment (RTE) task requires the system to determine if the premise and hypothesis pair are (i) an entailment, (ii) contradicting each other or (iii) neutral to each other. The Natural language Inference (NLI) Task from Bowman et al. (2015a) introduces a large dataset with labeled pairs of sentences and their corresponding logical relationship. This dataset allows us to quantify how well current systems are able to be trained to recognise sentences with those relationships. Examples of the current stateoftheart for this task include Chen et al. (2017) and Gong et al. (2017).
Here we are interested in generating natural language that satisfies the given textual entailment class. Kolesnyk et al. (2016) has attempted this using only sentences from the entailment class, and focusing on generating a hypothesis given the premise. Going in this direction results in removal of information from the premise sentence. In this paper, we focus on going in the other direciton: generating a premise from a hypothesis. This requires adding additional details to the premise which have to make sense in context. In order to produce sentences with extra details and without some other details, we suggest that a natural way to model this kind of structure is to impose a distribution over an intermediate distribution representing the semantic space of the premise sentence.
In the realm of learning representations for sentences, Kiros et al. (2015) has a popular method for learning representations called “skipthought” vectors. These are trained by using the encoded sentence to predict the previous and next sentence in a passage. Conneau et al. (2017) specifically learned sentence representations from the SNLI dataset. They claim that using the supervised data from SNLI can outperform “skipthought” representations on different tasks. There have also been several efforts towards learning a distribution over sentence embeddings. Bowman et al. (2015b)
used Variational Autoencoders (VAEs) to learn Gaussian distributed word embeddings.
Hu et al. (2017) use a combined VAE/GAN objective to produce a disentangled representation that can be used to modify some attributes like sentiment and tense.There have also been forays into conditional distributions for sentences – which is what is required here. Both Gupta et al. (2017) and Guu et al. (2017) introduce models of the form , where is a paraphrase of , and represents the variability in the output sentence. Guu et al. (2017) introduces as an edit vector. However, because has to be paired with in order to generate the sentence, serves a very different purpose, and cannot be considered a sentence embedding in its own right. Ideally, what we want is a distribution over sentence representations, each one mapping to a set of semantically similar sentences. This is important if we want the distribution to model the possibilities of concepts that correspond to the right textual entailment with the hypothesis.
3 Method
Some approaches map a sentence to a distribution in the embedding space (Bowman et al., 2015b). The assumption when doing this is that there is some uncertainty over the latent space when mapping from the sentence. Some approaches, like Hu et al. (2017) attempt to disentangle factors in the learnt latent variable space, so that modifying each dimension in the latent representation modifies sentiment or tense in the original sentence.
If we consider plausible premise sentences given a hypothesis and an inference label , there are many possible solutions, of varying likelihoods. We can model this probabilistically as . In our model, we assume an underlying latent variable that accounts for the variation in possible output sentences,
Another assumption we make is that given , is independent of and . The resulting graphical model associated with the above dependency assumptions are depicted in Figure 1.
In our proposed model, we take inspiration from the Adversarial Autoencoder (Makhzani et al., 2015), however our prior is conditioned on and . Zhang et al. (2017)
also proposed a Conditional Adversarial Autoencoder for age progression prediction. In addition to the adversarial discriminator, our model includes a classifier on the representation and the hypothesis and label. A similar framework is also discussed in
Salimans et al. (2016).3.1 Architecture
The model consists of an encoder , a conditional prior, , a decoder , and a discriminator .
Autoencoder
The autoencoder comprises of two parts. An encoder that maps the given premise to a sentence representation , and a decoder that reconstructs from a given . In our model, the encoder reads the input premise using an RNN network:
(2) 
and
(3) 
where is a hidden state at time . is a vector generated from sequence of the hidden states. We will call the compression function.
The decoder is trained to predict the next word given the sentence representation and all the previously predicted words
. With an RNN, the conditional probability distribution of
is modeled as:(4) 
and
(5)  
(6) 
where is a nonlinear, potentially multilayered, function that outputs the probability of , is the hidden state of decoder RNN, and takes as the key to retrieve related information from . We note that other architectures such as a CNN or a transformer (Vaswani et al., 2017) can be used in place of the RNN. The details of the compression function and retrieval function will be discussed in Sec. 3.2.
Prior
We draw a sample, conditioned on , through the prior, which is described using following equations:
(7)  
(8)  
(9)  
(10) 
where is a random vector, ; is the label embedding and represents the concatenation of input vectors.
Classifier
This outputs the probability distribution over labels, taking as input the tuple , and is described using the following equations:
(11)  
(12)  
(13)  
(14)  
(15)  
(16)  
(17) 
where
refers to an elementwise pooling operator, and the activation function
for output layer is the softmax function. The architecture of the classifier is inspired by (Chen et al., 2017). Instead of doing attention over the sequence of hidden states for the premise, we use the retrieval function in Equation 12 to retrieve related information in for .Discriminator
The discriminator takes as input , and tries to determine if the in question comes from the encoder or prior. The architecture of the discriminator is similar to that of the classifier, with the exception that Equation 13 is replaced by:
(18) 
to pass label information to the discriminator. The sigmoid function is used as the activation for the output layer.
In our model the autoencoder, prior and classifier share the same parameters. The prior and the autoencoder share the same parameters. The classifier and the autoencoder share the same parameters. The discriminator does not share any parameters with the rest of model.
3.2 Compression and Retrieval Functions
The compression (Equation 3) and retrieval (Equation 6) functions can be modeled through many different mechanisms. Here, we introduce two different methods:
Mean Pooling
can be used to compress the sequence of the hidden states:
(19) 
and its retrieve counterpart directly returns :
(20) 
Memory Operation Selection Module (MOSM)
As an alternative to mean pooling, we use the architecture shown in Figure 3. A layer is defined as:
(21)  
(22)  
(23) 
where can be any activation function, is the input vector, is the control vector, are candidate weight matrices. For convenience, we denote the MOSM function as .
Thus, we can define the MOSM compression method as:
(24) 
The compression function uses as both control and input vector, to write themselves into . Because different s select different combinations of candidate matrices, we can have different mapping function each different at each time step.
(25) 
Retrieval functions use as control vectors to retrieve information from . Since the layer generates a different weight matrix for the feedforward path for different , we can output different for the same .
3.3 Model Learning
Like most adversarial networks, the conditional adversarial autoencoder is trained with a gradient descent based method in two phases: the generative phase and the discriminative phase.
In the generative phase, the autoencoder is updated to minimize the reconstruction error of the premise. The classifier and the encoder are updated to minimize the classification error of the premisehypothesis pair. The prior is also updated to optimize the classification error of , where is draw from the prior. The encoder and the prior are updated to confuse the discriminator.
In our initial experiments, we found that the samples from just the adversarial training alone results in wildly varied output sentences. To ameliorate this, we propose an auxiliary loss:
(26) 
where is the number of samples that are drawn from prior. The auxiliary loss measures how far our generated premises are from the true premise when conditioned on the hypothesis and label. As shown in experiment the model has better generating diversity, while more samples were drawn during training.
One can view this auxiliary loss as a ‘hard’ version of taking the log average of the probability of MonteCarlo samples,
(27)  
(28)  
(29)  
(30) 
Since is a constant, minimizing over the Equation 30 is the same as minimizing Equation 26.
In the discriminative phase, the discriminator is updated to tell apart the true (generated using the prior) from the generated samples (given by autoencoder).
4 Experiments
We use the Stanford Natural Language Inference (SNLI) corpus (Bowman et al., 2015a) to train and evaluate our models. From our experiments, we want to determine two things. First, do the sentences produced by the model form the correct textual entailment class on which it was conditioned on? Second, is there diversity among the sentences that are generated?
4.1 Baseline Methods
For comparison, we use a normal RNN encoderdecoder as a baseline method. The model uses a bidirectional LSTM network as encoder. The encoder reads the input hypothesis into a sequence of hidden states :
(31)  
(32) 
Where
can be the mean method or an MOSM. The distributed representation of label
and are concatenated together to feed into a normal MLP network, which output the sentence representation :(33) 
The decoder compute the conditional probability distribution with equations:
(34)  
(35) 
Thus, the baseline model share a similar architecture with prior and decoder in our model, while the randomness been toke out.
4.2 Experiment Settings
For all models, and are 2layers bidirectional LSTM (Hochreiter & Schmidhuber, 1997), are 2layers unidirectional LSTM. The dimension of hidden state, embeddings and latent representation are 300. When training, optimization is performed with Adam using learning rate , , and
. We carry out gradient clipping with maximum norm
. We train each model for 30 epoch. For each iteration, we randomly choose to run the generative phase or discriminative phase with probability
. Since we didn’t observe significant benefit from using Beam Search, all premises are generated using greedy search.4.3 Quality Evaluation
In order to evaluate the quality of the samples from our model, we trained two stateoftheart models for SNLI: (1) Densely Interactive Inference Network (DIIN)^{1}^{1}1https://github.com/YichenGong/DenselyInteractiveInferenceNetwork (Gong et al., 2017), (2) Enhanced Sequential Inference Model (ESIM)^{2}^{2}2https://github.com/lukecq1231/nli (Chen et al., 2017).
In our experiments, we found that it is possible to achieve an accuracy of 68% on SNLI label prediction by training a classifier using only the hypothesis as input. This calls into question how much the classification models rely on just the hypothesis for performing its task. To investigate this phenomena further, we randomly permuted the premises of the original test set and passed these new (random) permishypothesis pairs to the classifiers. The results are shown in the row labelled Random in Table 1. We were satisfied that at 42.7% and 41.1%, the classification models (both DIIN and ESIM) were not relying entirely on the hypothesis for prediction.
Model  DIIN  ESIM 

Random  42.7%  41.1% 
Baseline (Mean)  59.6%  59.6% 
Baseline (MOSM)  62.7%  62.6% 
MOSM (N=1, classifier)  67.2%  67.3% 
MOSM (auxiliary loss)  63.2%  60.6% 
Mean (N=1)  64.4%  62.4% 
Mean (N=10)  64.3%  62.3% 
MOSM (N=1)  76.1%  75.9% 
MOSM (N=10)  72.6%  71.8% 
We sampled 9845 hypotheses from the test set, and produced for each example with the given . The triplet was then passed to the classifiers and evaluated for accuracy. Both classification models perform at 88% accuracy, but, while they were not perfect, they provided a good probe for how well our models were generating the required sentences. Table 1 shows the accuracy of prediction on the respective models. Both the DIIN and ESIM models give similar results.
Our results show that using the MOSM gives an improvement over just taking the mean. Using the adversarial training also results in some gains, which suggests that training the model with the ‘awareness’ of the distribution over the representation space results in better quality samples. Using the adversarial training in conjunction with the MOSM layer gives us the model with the best performance. We also performed ablation tests, removing certain components of the model from the training to see how it affects the quality of samples. The difference between our best model against MOSM (, classifier) suggests that the classifier plays in important role in ensuring is a representation in the right class. In our experiment removing the auxiliary loss, we still achieve an accuracy 61%. However, looking at the samples for this iteration of the model, while having some concepts in common with the hypothesis, the sentences in general are more nonsensical in comparison to those trained with the auxiliary loss (See an example in Figure 6).
Label \Pred.  Ent.  Neut.  Cont. 

Entailment  67.8%  20.9%  11.4% 
Neutral  6.6%  76.7%  16.7% 
Contradiction  2.9%  12.8%  84.4% 
The confusion matrix for the samples from the best model
MOSM ()The confusion matrix produced when evaluating our best model (MOSM, ) on DIIN shows us where the classification model and our generative model agree (See Table 2). In our Random experiments, we find that the model has a bias towards predicting contradictions. This is observed here as well, with contradictions being the category with the highest agreement. We therefore cannot conclude that contradictions are easier for our model to generate. Also, using the original test set, the category in which DIIN performs the best is entailment, with a precision of 89.1% compared to 84.3% for neutral and 88.4% for contradiction. This suggests that generating suitable premises that entail the hypothesis is the hardest task for the model.
We also want to study how the classifier component of our model affects the generation of good samples. As shown in Figure 4, “Z precision” is higher then . This suggests that the classifier provides a strong regularization signal to the sentence representation . Because the autoencoder is not perfect, we do not observe the the same sample classification precision after is decoded. However, we still observe a synchronous improvement of both sample and valid precision. It is therefore reasonable to expect that a better classifier and a better autoencoder would result in better generated premises.
4.4 Diversity Evaluation
In order to evaluate the diversity of samples given by our model, we compute the BLEU score between to premises generated conditioned on the same hypothesis and label. In other words, given a triple from test set, we draw two different samples from the prior distribution . Then the decoder generates two premises using greedy search conditioned on
respectively. The similarity score between generated premises is then estimated by:
(36) 
For comparison, we also compute the BLEU score between real premise and generated premise . The average of diversity score between two generated premises is noted as , the one between real and generated premises is noted as
. Since it is not necessary have ngram match between premises, BLEU score can be inaccurate on some data points. We employ the Smoothing technique 2 described in
Chen & Cherry (2014).Model  

Baseline (Mean)  14.4  N/A 
Baseline (MOSM)  14.7  N/A 
MOSM (N=1, classifier)  14.4  46.7 
MOSM (auxiliary loss)  10.3  14.8 
Mean (N=1)  11.9  27.9 
Mean (N=10)  11.3  17.3 
MOSM (N=1)  14.2  38.9 
MOSM (N=10)  13.2  22.5 
As shown in Table 3, when we increase the number of samples in the auxiliary loss, the diversity of samples increases for both mean pooling and MOSM. This can serve as empirical evidence that the diversity of our model can be controlled by choosing a different hyperparameter . The higher given by MOSM method could be interpreted as real premise is more close to the center of mass of prior distribution. We also observe a gap between and . The gap shows that the sampled premise is still relatively similar between themselves. After removing the classifier, we observe an increase in . One possible explanation is that classifier prevents the prior from overfitting the training data. We observe an decrease in both BLEU scores, after removing the auxiliary loss. However, Table 1 and Figure 6 shows that removing auxiliary loss give low quality samples.
While the auxiliary loss is essential for the prior and the decoder to learn to cooperate, using an auxiliary loss where will collapse the prior distribution; instead of a distribution, the prior will learn to ignore the random input and deterministically predict . As shown in Figure 5, the auxiliary loss only passes gradients to the s in the left region of the distribution. As a result, samples drawn from right region have a significant lower chance receive gradient from decoder, while the entire region receives gradients from the discriminator and classifier. Therefore, the prior distribution can expand to more regions, but only those regulated by discriminator and classifier. This will increase the diversity of samples. However, we also observe that the precision slightly decreases in Table 1. This suggests that the discriminator and classifier in our model are not perfect for regularizing the prior distribution.
4.5 Samples
Figure 6 shows several examples generated by our model (MOSM, N=10). These example shows that our model can generate a variety of different premise while keep the correct semantic relation. Some of subjects in hypothesis are correctly replace by synonyms (e.g. “jocky” is replaced by “horse rider”, “human” is replaced by “person” and “woman”). The model also get some potential logical relation correct (e.g. “reading a book” is contradicted by “with his hands in his pockets”, “stands over a bread display” can either means “washing a window” or “preparing food in a kitchen”).
However, we also observe that the model tries to add “a blue shirt” for most “man”s in the sentences, which is one of the easiest way to add extra information into the model. The phenomenon aligned with wellknown model collapse failure case for most adversarial training based method. This observation give an explanation for the relatively higher BLEU between sample. The model also have some bias while generating premise (e.g. when hypothesis mention “a baby”, the premise automatically mention “a woman”), which aligns with the recent discovery that visual recognition tasks model tend to output biased predictions (Zhao et al., 2017).
5 Discussion
The broader vision of our project is to attain logical control for language, which we believe will allow us to perform better across many natural language applications. This is most easily achieved at the wordlevel, by adding or removing specific words to a sentence, using word generation rules based on languagespecific grammars. However, just as distributed word representations can be meaningfully combined (Mikolov et al., 2013) with good outcomes, we believe that sentencelevel representations are the way forward for manipulation of text.
The kind of control we seek to model, specifically, is characterized by the logical relationships between sentence pairs. Controlling semantic representation by modeling logical relationship between the input and output sentences has many potential use cases. Returning to the task of multidocument summarization discussed in the introduction, operating in the semantic space allows one to abstract the information of a document. Controlling the logical relationships among sentences provides a new way to think about what a summary is. Ideally, when multiple sources of information are given, we would like the output summary generated by a machine to be entailable by the union of inputs ^{3}^{3}3Here we assume there are no conflicting details.. This addresses the problem of precision: the resulting summary now has a subset of the information available in the union of all the given hypotheses.
To address the problem of recall, we need the resulting summary to entail each one of the individual hypotheses: Together, these two criteria form a clear formal definition for multidocument summarization,
which represents the set of all possible that fit the criteria.
In our paper, we toyed with the possibility of modeling the set by training a model with a distribution over different premises in the latent space . A good subsequent step would be modelling the first part of our logical description of multidocument summarisation,
This suggests a possible avenue for producing such a premise is finding the intersection of the distribution over for two given hypotheses that are likely enough to occur.
Future work can explore the possibility of this and determining the union of the hypotheses entailing the given premise.
6 Conclusion
We have proposed a model that generates premises from hypotheses with an intermediate latent space, which we interpret as different possible premises for a given hypothesis. This was trained using a Conditional Adversarial Autoencoder. This paper also proposed the Memory Operation Selection Module for encoding sentences to a distributed representation that uses attention over different operations in order to encode the input. The model was evaluated for quality and diversity. In terms of quality, we used two stateoftheart models for the RTE task on SNLI, and the samples generated by our best model were able to achieve an accuracy of 76.1%. For diversity, we compared the BLEU scores between the real premises and the generated premises, and the BLEU scores between the generated premises. In this regard, while our model is able to generate different premises for each hypothesis, there is still a gap between when compared to the similarities to the real premises. Looking at the samples, we note that the additional details that our model generates tend to repeat, and correspond to some type of mode collapse.
The task of performing reasoning well with natural language still remains a challenging problem. Our experiments demonstrate that while we can generate sentences with the logical entailment properties we desire, there is still much to be done in this direction. We hope with the new lens on some NLP tasks as natural language manipulation with logical control, new perspectives and methods will emerge to improve the field.
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