prompt_front: You are given a scientific article and a question. Answer the question as concisely as you can, using a single phrase or sentence if possible. If the question cannot be answered based on the information in the article, write "unanswerable". If the question is a yes/no question, answer "yes", "no", or "unanswerable". Do not provide any explanation.

Please answer the questions based on the text provided below. What are the baseline models?
Context 1: Introduction
In the kitchen, we increasingly rely on instructions from cooking websites: recipes  A cook with a predilection for Asian cuisine may wish to prepare chicken curry, but may not know all necessary ingredients apart from a few basics  These users with limited knowledge cannot rely on existing recipe generation approaches that focus on creating coherent recipes given all ingredients and a recipe name BIBREF0  Such models do not address issues of personal preference (e g  culinary tastes, garnish choices) and incomplete recipe details  We propose to approach both problems via personalized generation of plausible, user-specific recipes using user preferences extracted from previously consumed recipes 
Our work combines two important tasks from natural language processing and recommender systems: data-to-text generation BIBREF1 and personalized recommendation BIBREF2  Our model takes as user input the name of a specific dish, a few key ingredients, and a calorie level  We pass these loose input specifications to an encoder-decoder framework and attend on user profiles—learned latent representations of recipes previously consumed by a user—to generate a recipe personalized to the user's tastes  We fuse these `user-aware' representations with decoder output in an attention fusion layer to jointly determine text generation  Quantitative (perplexity, user-ranking) and qualitative analysis on user-aware model outputs confirm that personalization indeed assists in generating plausible recipes from incomplete ingredients 
While personalized text generation has seen success in conveying user writing styles in the product review BIBREF3, BIBREF4 and dialogue BIBREF5 spaces, we are the first to consider it for the problem of recipe generation, where output quality is heavily dependent on the content of the instructions—such as ingredients and cooking techniques 
To summarize, our main contributions are as follows:
We explore a new task of generating plausible and personalized recipes from incomplete input specifications by leveraging historical user preferences;
We release a new dataset of 180K+ recipes and 700K+ user reviews for this task;
We introduce new evaluation strategies for generation quality in instructional texts, centering on quantitative measures of coherence  We also show qualitatively and quantitatively that personalized models generate high-quality and specific recipes that align with historical user preferences 
Related Work
Large-scale transformer-based language models have shown surprising expressivity and fluency in creative and conditional long-text generation BIBREF6, BIBREF7  Recent works have proposed hierarchical methods that condition on narrative frameworks to generate internally consistent long texts BIBREF8, BIBREF9, BIBREF10  Here, we generate procedurally structured recipes instead of free-form narratives 
Recipe generation belongs to the field of data-to-text natural language generation BIBREF1, which sees other applications in automated journalism BIBREF11, question-answering BIBREF12, and abstractive summarization BIBREF13, among others  BIBREF14, BIBREF15 model recipes as a structured collection of ingredient entities acted upon by cooking actions  BIBREF0 imposes a `checklist' attention constraint emphasizing hitherto unused ingredients during generation  BIBREF16 attend over explicit ingredient references in the prior recipe step  Similar hierarchical approaches that infer a full ingredient list to constrain generation will not help personalize recipes, and would be infeasible in our setting due to the potentially unconstrained number of ingredients (from a space of 10K+) in a recipe  We instead learn historical preferences to guide full recipe generation 
A recent line of work has explored user- and item-dependent aspect-aware review generation BIBREF3, BIBREF4  This work is related to ours in that it combines contextual language generation with personalization  Here, we attend over historical user preferences from previously consumed recipes to generate recipe content, rather than writing styles 
Approach
Our model's input specification consists of: the recipe name as a sequence of tokens, a partial list of ingredients, and a caloric level (high, medium, low)  It outputs the recipe instructions as a token sequence: $\mathcal {W}_r=\lbrace w_{r,0}, \dots , w_{r,T}\rbrace $ for a recipe $r$ of length $T$  To personalize output, we use historical recipe interactions of a user $u \in \mathcal {U}$ 
Encoder: Our encoder has three embedding layers: vocabulary embedding $\mathcal {V}$, ingredient embedding $\mathcal {I}$, and caloric-level embedding $\mathcal {C}$  Each token in the (length $L_n$) recipe name is embedded via $\mathcal {V}$; the embedded token sequence is passed to a two-layered bidirectional GRU (BiGRU) BIBREF17, which outputs hidden states for names $\lbrace \mathbf {n}_{\text{enc},j} \in \mathbb {R}^{2d_h}\rbrace $, with hidden size $d_h$  Similarly each of the $L_i$ input ingredients is embedded via $\mathcal {I}$, and the embedded ingredient sequence is passed to another two-layered BiGRU to output ingredient hidden states as $\lbrace \mathbf {i}_{\text{enc},j} \in \mathbb {R}^{2d_h}\rbrace $  The caloric level is embedded via $\mathcal {C}$ and passed through a projection layer with weights $W_c$ to generate calorie hidden representation $\mathbf {c}_{\text{enc}} \in \mathbb {R}^{2d_h}$ 
Ingredient Attention: We apply attention BIBREF18 over the encoded ingredients to use encoder outputs at each decoding time step  We define an attention-score function $\alpha $ with key $K$ and query $Q$:
with trainable weights $W_{\alpha }$, bias $\mathbf {b}_{\alpha }$, and normalization term $Z$  At decoding time $t$, we calculate the ingredient context $\mathbf {a}_{t}^{i} \in \mathbb {R}^{d_h}$ as:
Decoder: The decoder is a two-layer GRU with hidden state $h_t$ conditioned on previous hidden state $h_{t-1}$ and input token $w_{r, t}$ from the original recipe text  We project the concatenated encoder outputs as the initial decoder hidden state:
To bias generation toward user preferences, we attend over a user's previously reviewed recipes to jointly determine the final output token distribution  We consider two different schemes to model preferences from user histories: (1) recipe interactions, and (2) techniques seen therein (defined in data)  BIBREF19, BIBREF20, BIBREF21 explore similar schemes for personalized recommendation 
Prior Recipe Attention: We obtain the set of prior recipes for a user $u$: $R^+_u$, where each recipe can be represented by an embedding from a recipe embedding layer $\mathcal {R}$ or an average of the name tokens embedded by $\mathcal {V}$  We attend over the $k$-most recent prior recipes, $R^{k+}_u$, to account for temporal drift of user preferences BIBREF22  These embeddings are used in the `Prior Recipe' and `Prior Name' models, respectively 
Given a recipe representation $\mathbf {r} \in \mathbb {R}^{d_r}$ (where $d_r$ is recipe- or vocabulary-embedding size depending on the recipe representation) the prior recipe attention context $\mathbf {a}_{t}^{r_u}$ is calculated as
Prior Technique Attention: We calculate prior technique preference (used in the `Prior Tech` model) by normalizing co-occurrence between users and techniques seen in $R^+_u$, to obtain a preference vector $\rho _{u}$  Each technique $x$ is embedded via a technique embedding layer $\mathcal {X}$ to $\mathbf {x}\in \mathbb {R}^{d_x}$  Prior technique attention is calculated as
where, inspired by copy mechanisms BIBREF23, BIBREF24, we add $\rho _{u,x}$ for technique $x$ to emphasize the attention by the user's prior technique preference 
Attention Fusion Layer: We fuse all contexts calculated at time $t$, concatenating them with decoder GRU output and previous token embedding:
We then calculate the token probability:
and maximize the log-likelihood of the generated sequence conditioned on input specifications and user preferences  fig:ex shows a case where the Prior Name model attends strongly on previously consumed savory recipes to suggest the usage of an additional ingredient (`cilantro') 
Recipe Dataset: Food com
We collect a novel dataset of 230K+ recipe texts and 1M+ user interactions (reviews) over 18 years (2000-2018) from Food com  Here, we restrict to recipes with at least 3 steps, and at least 4 and no more than 20 ingredients  We discard users with fewer than 4 reviews, giving 180K+ recipes and 700K+ reviews, with splits as in tab:recipeixnstats 
Our model must learn to generate from a diverse recipe space: in our training data, the average recipe length is 117 tokens with a maximum of 256  There are 13K unique ingredients across all recipes  Rare words dominate the vocabulary: 95% of words appear $<$100 times, accounting for only 1 65% of all word usage  As such, we perform Byte-Pair Encoding (BPE) tokenization BIBREF25, BIBREF26, giving a training vocabulary of 15K tokens across 19M total mentions  User profiles are similarly diverse: 50% of users have consumed $\le $6 recipes, while 10% of users have consumed $>$45 recipes 
We order reviews by timestamp, keeping the most recent review for each user as the test set, the second most recent for validation, and the remainder for training (sequential leave-one-out evaluation BIBREF27)  We evaluate only on recipes not in the training set 
We manually construct a list of 58 cooking techniques from 384 cooking actions collected by BIBREF15; the most common techniques (bake, combine, pour, boil) account for 36 5% of technique mentions  We approximate technique adherence via string match between the recipe text and technique list 
Experiments and Results
For training and evaluation, we provide our model with the first 3-5 ingredients listed in each recipe  We decode recipe text via top-$k$ sampling BIBREF7, finding $k=3$ to produce satisfactory results  We use a hidden size $d_h=256$ for both the encoder and decoder  Embedding dimensions for vocabulary, ingredient, recipe, techniques, and caloric level are 300, 10, 50, 50, and 5 (respectively)  For prior recipe attention, we set $k=20$, the 80th %-ile for the number of user interactions  We use the Adam optimizer BIBREF28 with a learning rate of $10^{-3}$, annealed with a decay rate of 0 9 BIBREF29  We also use teacher-forcing BIBREF30 in all training epochs 
In this work, we investigate how leveraging historical user preferences can improve generation quality over strong baselines in our setting  We compare our personalized models against two baselines  The first is a name-based Nearest-Neighbor model (NN)  We initially adapted the Neural Checklist Model of BIBREF0 as a baseline; however, we ultimately use a simple Encoder-Decoder baseline with ingredient attention (Enc-Dec), which provides comparable performance and lower complexity  All personalized models outperform baseline in BPE perplexity (tab:metricsontest) with Prior Name performing the best  While our models exhibit comparable performance to baseline in BLEU-1/4 and ROUGE-L, we generate more diverse (Distinct-1/2: percentage of distinct unigrams and bigrams) and acceptable recipes  BLEU and ROUGE are not the most appropriate metrics for generation quality  A `correct' recipe can be written in many ways with the same main entities (ingredients)  As BLEU-1/4 capture structural information via n-gram matching, they are not correlated with subjective recipe quality  This mirrors observations from BIBREF31, BIBREF8 
We observe that personalized models make more diverse recipes than baseline  They thus perform better in BLEU-1 with more key entities (ingredient mentions) present, but worse in BLEU-4, as these recipes are written in a personalized way and deviate from gold on the phrasal level  Similarly, the `Prior Name' model generates more unigram-diverse recipes than other personalized models and obtains a correspondingly lower BLEU-1 score 
Qualitative Analysis: We present sample outputs for a cocktail recipe in tab:samplerecipes, and additional recipes in the appendix  Generation quality progressively improves from generic baseline output to a blended cocktail produced by our best performing model  Models attending over prior recipes explicitly reference ingredients  The Prior Name model further suggests the addition of lemon and mint, which are reasonably associated with previously consumed recipes like coconut mousse and pork skewers 
Personalization: To measure personalization, we evaluate how closely the generated text corresponds to a particular user profile  We compute the likelihood of generated recipes using identical input specifications but conditioned on ten different user profiles—one `gold' user who consumed the original recipe, and nine randomly generated user profiles  Following BIBREF8, we expect the highest likelihood for the recipe conditioned on the gold user  We measure user matching accuracy (UMA)—the proportion where the gold user is ranked highest—and Mean Reciprocal Rank (MRR) BIBREF32 of the gold user  All personalized models beat baselines in both metrics, showing our models personalize generated recipes to the given user profiles  The Prior Name model achieves the best UMA and MRR by a large margin, revealing that prior recipe names are strong signals for personalization  Moreover, the addition of attention mechanisms to capture these signals improves language modeling performance over a strong non-personalized baseline 
Recipe Level Coherence: A plausible recipe should possess a coherent step order, and we evaluate this via a metric for recipe-level coherence  We use the neural scoring model from BIBREF33 to measure recipe-level coherence for each generated recipe  Each recipe step is encoded by BERT BIBREF34  Our scoring model is a GRU network that learns the overall recipe step ordering structure by minimizing the cosine similarity of recipe step hidden representations presented in the correct and reverse orders  Once pretrained, our scorer calculates the similarity of a generated recipe to the forward and backwards ordering of its corresponding gold label, giving a score equal to the difference between the former and latter  A higher score indicates better step ordering (with a maximum score of 2)  tab:coherencemetrics shows that our personalized models achieve average recipe-level coherence scores of 1 78-1 82, surpassing the baseline at 1 77 
Recipe Step Entailment: Local coherence is also crucial to a user following a recipe: it is crucial that subsequent steps are logically consistent with prior ones  We model local coherence as an entailment task: predicting the likelihood that a recipe step follows the preceding  We sample several consecutive (positive) and non-consecutive (negative) pairs of steps from each recipe  We train a BERT BIBREF34 model to predict the entailment score of a pair of steps separated by a [SEP] token, using the final representation of the [CLS] token  The step entailment score is computed as the average of scores for each set of consecutive steps in each recipe, averaged over every generated recipe for a model, as shown in tab:coherencemetrics 
Human Evaluation: We presented 310 pairs of recipes for pairwise comparison BIBREF8 (details in appendix) between baseline and each personalized model, with results shown in tab:metricsontest  On average, human evaluators preferred personalized model outputs to baseline 63% of the time, confirming that personalized attention improves the semantic plausibility of generated recipes  We also performed a small-scale human coherence survey over 90 recipes, in which 60% of users found recipes generated by personalized models to be more coherent and preferable to those generated by baseline models 
Conclusion
In this paper, we propose a novel task: to generate personalized recipes from incomplete input specifications and user histories  On a large novel dataset of 180K recipes and 700K reviews, we show that our personalized generative models can generate plausible, personalized, and coherent recipes preferred by human evaluators for consumption  We also introduce a set of automatic coherence measures for instructional texts as well as personalization metrics to support our claims  Our future work includes generating structured representations of recipes to handle ingredient properties, as well as accounting for references to collections of ingredients (e g  “dry mix") 
Acknowledgements  This work is partly supported by NSF #1750063  We thank all reviewers for their constructive suggestions, as well as Rei M , Sujoy P , Alicia L , Eric H , Tim S , Kathy C , Allen C , and Micah I  for their feedback 
Appendix ::: Food com: Dataset Details
Our raw data consists of 270K recipes and 1 4M user-recipe interactions (reviews) scraped from Food com, covering a period of 18 years (January 2000 to December 2018)  See tab:int-stats for dataset summary statistics, and tab:samplegk for sample information about one user-recipe interaction and the recipe involved 
Appendix ::: Generated Examples
See tab:samplechx for a sample recipe for chicken chili and tab:samplewaffle for a sample recipe for sweet waffles 
Human Evaluation
We prepared a set of 15 pairwise comparisons per evaluation session, and collected 930 pairwise evaluations (310 per personalized model) over 62 sessions  For each pair, users were given a partial recipe specification (name and 3-5 key ingredients), as well as two generated recipes labeled `A' and `B'  One recipe is generated from our baseline encoder-decoder model and one recipe is generated by one of our three personalized models (Prior Tech, Prior Name, Prior Recipe)  The order of recipe presentation (A/B) is randomly selected for each question  A screenshot of the user evaluation interface is given in fig:exeval  We ask the user to indicate which recipe they find more coherent, and which recipe best accomplishes the goal indicated by the recipe name  A screenshot of this survey interface is given in fig:exeval2 
Context 2: Introduction
Language modelling in its inception had one-hot vector encoding of words  However, it captures only alphabetic ordering but not the word semantic similarity  Vector space models helps to learn word representations in a lower dimensional space and also captures semantic similarity  Learning word embedding aids in natural language processing tasks such as question answering and reasoning BIBREF0, stance detection BIBREF1, claim verification BIBREF2 
Recent models BIBREF3, BIBREF4 work on the basis that words with similar context share semantic similarity  BIBREF4 proposes a neural probabilistic model which models the target word probability conditioned on the previous words using a recurrent neural network  Word2Vec models BIBREF3 such as continuous bag-of-words (CBOW) predict the target word given the context, and skip-gram model works in reverse of predicting the context given the target word  While, GloVe embeddings were based on a Global matrix factorization on local contexts BIBREF5  However, the aforementioned models do not handle words with multiple meanings (polysemies) 
BIBREF6 proposes a neural network approach considering both local and global contexts in learning word embeddings (point estimates)  Their multiple prototype model handles polysemous words by providing apriori heuristics about word senses in the dataset  BIBREF7 proposes an alternative to handle polysemous words by a modified skip-gram model and EM algorithm  BIBREF8 presents a non-parametric based alternative to handle polysemies  However, these approaches fail to consider entailment relations among the words  BIBREF9 learn a Gaussian distribution per word using the expected likelihood kernel  However, for polysemous words, this may lead to word distributions with larger variances as it may have to cover various senses 
BIBREF10 proposes multimodal word distribution approach  It captures polysemy  However, the energy based objective function fails to consider asymmetry and hence entailment  Textual entailment recognition is necessary to capture lexical inference relations such as causality (for example, mosquito $\rightarrow $ malaria), hypernymy (for example, dog $\models $ animal) etc 
In this paper, we propose to obtain multi-sense word embedding distributions by using a variant of max margin objective based on the asymmetric KL divergence energy function to capture textual entailment  Multi-sense distributions are advantageous in capturing polysemous nature of words and in reducing the uncertainty per word by distributing it across senses  However, computing KL divergence between mixtures of Gaussians is intractable, and we use a KL divergence approximation based on stricter upper and lower bounds  While capturing textual entailment (asymmetry), we have also not compromised on capturing symmetrical similarity between words (for example, funny and hilarious) which will be elucidated in Section $3 1$  We also show the effectiveness of the proposed approach on the benchmark word similarity and entailment datasets in the experimental section 
Methodology ::: Word Representation
Probabilistic representation of words helps one model uncertainty in word representation, and polysemy  Given a corpus $V$, containing a list of words each represented as $w$, the probability density for a word $w$ can be represented as a mixture of Gaussians with $C$ components BIBREF10 
Here, $p_{w,j}$ represents the probability of word $w$ belonging to the component $j$, $\operatorname{\mathbf {\mu }}_{w,j}$ represents $D$ dimensional word representation corresponding to the $j^{th}$ component sense of the word $w$, and $\Sigma _{w,j}$ represents the uncertainty in representation for word $w$ belonging to component $j$ 
Objective function
The model parameters (means, covariances and mixture weights) $\theta $ can be learnt using a variant of max-margin objective BIBREF11 
Here $E_\theta (\cdot , \cdot )$ represents an energy function which assigns a score to the pair of words, $w$ is a particular word under consideration, $c$ its positive context (same context), and $c^{\prime }$ the negative context  The objective aims to push the margin of the difference between the energy function of a word $w$ to its positive context $c$ higher than its negative context $c$ by a threshold of $m$  Thus, word pairs in the same context gets a higher energy than the word pairs in the dissimilar context  BIBREF10 consider the energy function to be an expected likelihood kernel which is defined as follows 
This is similar to the cosine similarity metric over vectors and the energy between two words is maximum when they have similar distributions  But, the expected likelihood kernel is a symmetric metric which will not be suitable for capturing ordering among words and hence entailment 
Objective function ::: Proposed Energy function
As each word is represented by a mixture of Gaussian distributions, KL divergence is a better choice of energy function to capture distance between distributions  Since, KL divergence is minimum when the distributions are similar and maximum when they are dissimilar, energy function is taken as exponentiated negative KL divergence 
However, computing KL divergence between Gaussian mixtures is intractable and obtaining exact KL value is not possible  One way of approximating the KL is by Monte-Carlo approximation but it requires large number of samples to get a good approximation and is computationally expensive on high dimensional embedding space 
Alternatively, BIBREF12 presents a KL approximation between Gaussian mixtures where they obtain an upper bound through product of Gaussian approximation method and a lower bound through variational approximation method  In BIBREF13, the authors combine the lower and upper bounds from approximation methods of BIBREF12 to provide a stricter bound on KL between Gaussian mixtures  Lets consider Gaussian mixtures for the words $w$ and $v$ as follows 
The approximate KL divergence between the Gaussian mixture representations over the words $w$ and $v$ is shown in equation DISPLAY_FORM8  More details on approximation is included in the Supplementary Material 
where $EL_{ik}(w,w) = \int f_{w,i} (\operatorname{\mathbf {x}}) f_{w,k} (\operatorname{\mathbf {x}}) d\operatorname{\mathbf {x}}$ and $EL_{ij}(w,v) = \int f_{w,i} (\operatorname{\mathbf {x}}) f_{v,k} (\operatorname{\mathbf {x}}) d\operatorname{\mathbf {x}}$  Note that the expected likelihood kernel appears component wise inside the approximate KL divergence derivation 
One advantage of using KL as energy function is that it enables to capture asymmetry in entailment datasets  For eg , let us consider the words 'chair' with two senses as 'bench' and 'sling', and 'wood' with two senses as 'trees' and 'furniture'  The word chair ($w$) is entailed within wood ($v$), i e

ground_truth: name-based Nearest-Neighbor model (NN), Encoder-Decoder baseline with ingredient attention (Enc-Dec)

prompt_front: You are given a scientific article and a question. Answer the question as concisely as you can, using a single phrase or sentence if possible. If the question cannot be answered based on the information in the article, write "unanswerable". If the question is a yes/no question, answer "yes", "no", or "unanswerable". Do not provide any explanation.

Please answer the questions based on the text provided below. How does this approach compare to other WSD approaches employing word embeddings?
Context 2:  chair $\models $ wood  Now, minimizing the KL divergence necessitates maximizing $\log {\sum _j p_{v,j} \exp ({-KL(f_{w,i} (\operatorname{\mathbf {x}})||f_{v,j}(\operatorname{\mathbf {x}}))})}$ which in turn minimizes $KL(f_{w,i}(\operatorname{\mathbf {x}})||f_{v,j}(\operatorname{\mathbf {x}}))$  This will result in the support of the $i^{th}$ component of $w$ to be within the $j^{th}$ component of $v$, and holds for all component pairs leading to the entailment of $w$ within $v$  Consequently, we can see that bench $\models $ trees, bench $\models $ furniture, sling $\models $ trees, and sling $\models $ furniture  Thus, it introduces lexical relationship between the senses of child word and that of the parent word  Minimizing the KL also necessitates maximizing $\log {\sum _j {p_{v,j}} EL_{ij}(w,v)}$ term for all component pairs among $w$ and $v$  This is similar to maximizing expected likelihood kernel, which brings the means of $f_{w,i}(\operatorname{\mathbf {x}})$ and $f_{v,j}(\operatorname{\mathbf {x}})$ closer (weighted by their co-variances) as discussed in BIBREF10  Hence, the proposed approach captures the best of both worlds, thereby catering to both word similarity and entailment 
We also note that minimizing the KL divergence necessitates minimizing $\log {\sum _k p_{w,k} \exp ({-KL(f_{w,i}||f_{w,k})})}$ which in turn maximizes $KL(f_{w,i}||f_{w,k})$  This prevents the different mixture components of a word converging to single Gaussian and encourages capturing different possible senses of the word  The same is also achieved by minimizing $\sum _k {p_{w,k}} EL_{ik}(w,w)$ term and act as a regularization term which promotes diversity in learning senses of a word 
Experimentation and Results
We train our proposed model GM$\_$KL (Gaussian Mixture using KL Divergence) on the Text8 dataset BIBREF14 which is a pre-processed data of $17M$ words from wikipedia  Of which, 71290 unique and frequent words are chosen using the subsampling trick in BIBREF15  We compare GM$\_$KL with the previous approaches w2g BIBREF9 ( single Gaussian model) and w2gm BIBREF10 (mixture of Gaussian model with expected likelihood kernel)  For all the models used for experimentation, the embedding size ($D$) was set to 50, number of mixtures to 2, context window length to 10, batch size to 128  The word embeddings were initialized using a uniform distribution in the range of $[-\sqrt{\frac{3}{D}}$, $\sqrt{\frac{3}{D}}]$ such that the expectation of variance is 1 and mean 0 BIBREF16  One could also consider initializing the word embeddings using other contextual representations such as BERT BIBREF17 and ELMo BIBREF18 in the proposed approach  In order to purely analyze the performance of $\emph {GM\_KL}$ over the other models, we have chosen initialization using uniform distribution for experiments  For computational benefits, diagonal covariance is used similar to BIBREF10  Each mixture probability is constrained in the range $[0,1]$, summing to 1 by optimizing over unconstrained scores in the range $(-\infty ,\infty )$ and converting scores to probability using softmax function  The mixture scores are initialized to 0 to ensure fairness among all the components  The threshold for negative sampling was set to $10^{-5}$, as recommended in BIBREF3  Mini-batch gradient descent with Adagrad optimizer BIBREF19 was used with initial learning rate set to $0 05$ 
Table TABREF9 shows the qualitative results of GM$\_$KL  Given a query word and component id, the set of nearest neighbours along with their respective component ids are listed  For eg , the word `plane' in its 0th component captures the `geometry' sense and so are its neighbours, and its 1st component captures `vehicle' sense and so are its corresponding neighbours  Other words such as `rock' captures both the `metal' and `music' senses, `star' captures `celebrity' and `astronomical' senses, and `phone' captures `telephony' and `internet' senses 
We quantitatively compare the performance of the GM$\_$KL, w2g, and w2gm approaches on the SCWS dataset BIBREF6  The dataset consists of 2003 word pairs of polysemous and homonymous words with labels obtained by an average of 10 human scores  The Spearman correlation between the human scores and the model scores are computed  To obtain the model score, the following metrics are used:
MaxCos: Maximum cosine similarity among all component pairs of words $w$ and $v$:
AvgCos: Average component-wise cosine similarity between the words $w$ and $v$ 
KL$\_$approx: Formulated as shown in (DISPLAY_FORM8) between the words $w$ and $v$ 
KL$\_$comp: Maximum component-wise negative KL between words $w$ and $v$:
Table TABREF17 compares the performance of the approaches on the SCWS dataset  It is evident from Table TABREF17 that GM$\_$KL achieves better correlation than existing approaches for various metrics on SCWS dataset 
Table TABREF18 shows the Spearman correlation values of GM$\_$KL model evaluated on the benchmark word similarity datasets: SL BIBREF20, WS, WS-R, WS-S BIBREF21, MEN BIBREF22, MC BIBREF23, RG BIBREF24, YP BIBREF25, MTurk-287 and MTurk-771 BIBREF26, BIBREF27, and RW BIBREF28  The metric used for comparison is 'AvgCos'  It can be seen that for most of the datasets, GM$\_$KL achieves significantly better correlation score than w2g and w2gm approaches  Other datasets such as MC and RW consist of only a single sense, and hence w2g model performs better and GM$\_$KL achieves next better performance  The YP dataset have multiple senses but does not contain entailed data and hence could not make use of entailment benefits of GM$\_$KL 
Table TABREF19 shows the evaluation results of GM$\_$KL model on the entailment datasets such as entailment pairs dataset BIBREF29 created from WordNet with both positive and negative labels, a crowdsourced dataset BIBREF30 of 79 semantic relations labelled as entailed or not and annotated distributionally similar nouns dataset BIBREF31  The 'MaxCos' similarity metric is used for evaluation and the best precision and best F1-score is shown, by picking the optimal threshold  Overall, GM$\_$KL performs better than both w2g and w2gm approaches 
Conclusion
We proposed a KL divergence based energy function for learning multi-sense word embedding distributions modelled as Gaussian mixtures  Due to the intractability of the Gaussian mixtures for the KL divergence measure, we use an approximate KL divergence function  We also demonstrated that the proposed GM$\_$KL approaches performed better than other approaches on the benchmark word similarity and entailment datasets 
tocsectionAppendices
Approximation for KL divergence between mixtures of gaussians
KL between gaussian mixtures $f_{w}(\operatorname{\mathbf {x}})$ and $f_{v}(\operatorname{\mathbf {x}})$ can be decomposed as:
BIBREF12 presents KL approximation between gaussian mixtures using
product of gaussian approximation method where KL is approximated using product of component gaussians and
variational approximation method where KL is approximated by introducing some variational parameters 
The product of component gaussian approximation method using Jensen's inequality provides upper bounds as shown in equations DISPLAY_FORM23 and  
The variational approximation method provides lower bounds as shown in equations DISPLAY_FORM24 and DISPLAY_FORM25 
where $H$ represents the entropy term and the entropy of $i^{th}$ component of word $w$ with dimension $D$ is given as
In BIBREF13, the authors combine the lower and upper bounds from approximation methods of BIBREF12 to formulate a stricter bound on KL between gaussian mixtures 
From equations DISPLAY_FORM23 and DISPLAY_FORM25, a stricter lower bound for KL between gaussian mixtures is obtained as shown in equation DISPLAY_FORM26
From equations and DISPLAY_FORM24, a stricter upper bound for KL between gaussian mixtures is obtained as shown in equation DISPLAY_FORM27
Finally, the KL between gaussian mixtures is taken as the mean of KL upper and lower bounds as shown in equation DISPLAY_FORM28 
Context 3: Introduction
This work is licenced under a Creative Commons Attribution 4 0 International Licence  Licence details: http://creativecommons org/licenses/by/4 0/
In the spirit of the brevity of social media's messages and reactions, people have got used to express feelings minimally and symbolically, as with hashtags on Twitter and Instagram  On Facebook, people tend to be more wordy, but posts normally receive more simple “likes” than longer comments  Since February 2016, Facebook users can express specific emotions in response to a post thanks to the newly introduced reaction feature (see Section SECREF2 ), so that now a post can be wordlessly marked with an expression of say “joy" or “surprise" rather than a generic “like” 
It has been observed that this new feature helps Facebook to know much more about their users and exploit this information for targeted advertising BIBREF0 , but interest in people's opinions and how they feel isn't limited to commercial reasons, as it invests social monitoring, too, including health care and education BIBREF1   However, emotions and opinions are not always expressed this explicitly, so that there is high interest in developing systems towards their automatic detection  Creating manually annotated datasets large enough to train supervised models is not only costly, but also—especially in the case of opinions and emotions—difficult, due to the intrinsic subjectivity of the task BIBREF2 , BIBREF3   Therefore, research has focused on unsupervised methods enriched with information derived from lexica, which are manually created BIBREF3 , BIBREF4   Since go2009twitter have shown that happy and sad emoticons can be successfully used as signals for sentiment labels, distant supervision, i e  using some reasonably safe signals as proxies for automatically labelling training data BIBREF5 , has been used also for emotion recognition, for example exploiting both emoticons and Twitter hashtags BIBREF6 , but mainly towards creating emotion lexica  mohammad2015using use hashtags, experimenting also with highly fine-grained emotion sets (up to almost 600 emotion labels), to create the large Hashtag Emotion Lexicon  Emoticons are used as proxies also by hallsmarmulti, who use distributed vector representations to find which words are interchangeable with emoticons but also which emoticons are used in a similar context 
We take advantage of distant supervision by using Facebook reactions as proxies for emotion labels, which to the best of our knowledge hasn't been done yet, and we train a set of Support Vector Machine models for emotion recognition  Our models, differently from existing ones, exploit information which is acquired entirely automatically, and achieve competitive or even state-of-the-art results for some of the emotion labels on existing, standard evaluation datasets  For explanatory purposes, related work is discussed further and more in detail when we describe the benchmarks for evaluation (Section SECREF3 ) and when we compare our models to existing ones (Section SECREF5 )  We also explore and discuss how choosing different sets of Facebook pages as training data provides an intrinsic domain-adaptation method 
Facebook reactions as labels
For years, on Facebook people could leave comments to posts, and also “like” them, by using a thumbs-up feature to explicitly express a generic, rather underspecified, approval  A “like” could thus mean “I like what you said", but also “I like that you bring up such topic (though I find the content of the article you linked annoying)" 
In February 2016, after a short trial, Facebook made a more explicit reaction feature available world-wide  Rather than allowing for the underspecified “like” as the only wordless response to a post, a set of six more specific reactions was introduced, as shown in Figure FIGREF1 : Like, Love, Haha, Wow, Sad and Angry  We use such reactions as proxies for emotion labels associated to posts 
We collected Facebook posts and their corresponding reactions from public pages using the Facebook API, which we accessed via the Facebook-sdk python library  We chose different pages (and therefore domains and stances), aiming at a balanced and varied dataset, but we did so mainly based on intuition (see Section SECREF4 ) and with an eye to the nature of the datasets available for evaluation (see Section SECREF5 )  The choice of which pages to select posts from is far from trivial, and we believe this is actually an interesting aspect of our approach, as by using different Facebook pages one can intrinsically tackle the domain-adaptation problem (See Section SECREF6 for further discussion on this)  The final collection of Facebook pages for the experiments described in this paper is as follows: FoxNews, CNN, ESPN, New York Times, Time magazine, Huffington Post Weird News, The Guardian, Cartoon Network, Cooking Light, Home Cooking Adventure, Justin Bieber, Nickelodeon, Spongebob, Disney 
Note that thankful was only available during specific time spans related to certain events, as Mother's Day in May 2016 
For each page, we downloaded the latest 1000 posts, or the maximum available if there are fewer, from February 2016, retrieving the counts of reactions for each post  The output is a JSON file containing a list of dictionaries with a timestamp, the post and a reaction vector with frequency values, which indicate how many users used that reaction in response to the post (Figure FIGREF3 )  The resulting emotion vectors must then be turned into an emotion label 
In the context of this experiment, we made the simple decision of associating to each post the emotion with the highest count, ignoring like as it is the default and most generic reaction people tend to use  Therefore, for example, to the first post in Figure FIGREF3 , we would associate the label sad, as it has the highest score (284) among the meaningful emotions we consider, though it also has non-zero scores for other emotions  At this stage, we didn't perform any other entropy-based selection of posts, to be investigated in future work 
Emotion datasets
Three datasets annotated with emotions are commonly used for the development and evaluation of emotion detection systems, namely the Affective Text dataset, the Fairy Tales dataset, and the ISEAR dataset  In order to compare our performance to state-of-the-art results, we have used them as well  In this Section, in addition to a description of each dataset, we provide an overview of the emotions used, their distribution, and how we mapped them to those we obtained from Facebook posts in Section SECREF7   A summary is provided in Table TABREF8 , which also shows, in the bottom row, what role each dataset has in our experiments: apart from the development portion of the Affective Text, which we used to develop our models (Section SECREF4 ), all three have been used as benchmarks for our evaluation 
Affective Text dataset
Task 14 at SemEval 2007 BIBREF7 was concerned with the classification of emotions and valence in news headlines  The headlines where collected from several news websites including Google news, The New York Times, BBC News and CNN  The used emotion labels were Anger, Disgust, Fear, Joy, Sadness, Surprise, in line with the six basic emotions of Ekman's standard model BIBREF8   Valence was to be determined as positive or negative  Classification of emotion and valence were treated as separate tasks  Emotion labels were not considered as mututally exclusive, and each emotion was assigned a score from 0 to 100  Training/developing data amounted to 250 annotated headlines (Affective development), while systems were evaluated on another 1000 (Affective test)  Evaluation was done using two different methods: a fine-grained evaluation using Pearson's r to measure the correlation between the system scores and the gold standard; and a coarse-grained method where each emotion score was converted to a binary label, and precision, recall, and f-score were computed to assess performance  As it is done in most works that use this dataset BIBREF3 , BIBREF4 , BIBREF9 , we also treat this as a classification problem (coarse-grained)  This dataset has been extensively used for the evaluation of various unsupervised methods BIBREF2 , but also for testing different supervised learning techniques and feature portability BIBREF10  
Fairy Tales dataset
This is a dataset collected by alm2008affect, where about 1,000 sentences from fairy tales (by B  Potter, H C  Andersen and Grimm) were annotated with the same six emotions of the Affective Text dataset, though with different names: Angry, Disgusted, Fearful, Happy, Sad, and Surprised  In most works that use this dataset BIBREF3 , BIBREF4 , BIBREF9 , only sentences where all annotators agreed are used, and the labels angry and disgusted are merged  We adopt the same choices 
ISEAR
The ISEAR (International Survey on Emotion Antecedents and Reactions BIBREF11 , BIBREF12 ) is a dataset created in the context of a psychology project of the 1990s, by collecting questionnaires answered by people with different cultural backgrounds  The main aim of this project was to gather insights in cross-cultural aspects of emotional reactions  Student respondents, both psychologists and non-psychologists, were asked to report situations in which they had experienced all of seven major emotions (joy, fear, anger, sadness, disgust, shame and guilt)  In each case, the questions covered the way they had appraised a given situation and how they reacted  The final dataset contains reports by approximately 3000 respondents from all over the world, for a total of 7665 sentences labelled with an emotion, making this the largest dataset out of the three we use 
Overview of datasets and emotions
We summarise datasets and emotion distribution from two viewpoints  First, because there are different sets of emotions labels in the datasets and Facebook data, we need to provide a mapping and derive a subset of emotions that we are going to use for the experiments  This is shown in Table TABREF8 , where in the “Mapped” column we report the final emotions we use in this paper: anger, joy, sadness, surprise  All labels in each dataset are mapped to these final emotions, which are therefore the labels we use for training and testing our models 
Second, the distribution of the emotions for each dataset is different, as can be seen in Figure FIGREF9  
In Figure FIGREF9 we also provide the distribution of the emotions anger, joy, sadness, surprise per Facebook page, in terms of number of posts (recall that we assign to a post the label corresponding to the majority emotion associated to it, see Section SECREF2 )

ground_truth: GM$\_$KL achieves better correlation than existing approaches for various metrics on SCWS dataset.

prompt_front: You are given a scientific article and a question. Answer the question as concisely as you can, using a single phrase or sentence if possible. If the question cannot be answered based on the information in the article, write "unanswerable". If the question is a yes/no question, answer "yes", "no", or "unanswerable". Do not provide any explanation.

Please answer the questions based on the text provided below. Which existing benchmarks did they compare to?
Context 3:  We can observe that for example pages about news tend to have more sadness and anger posts, while pages about cooking and tv-shows have a high percentage of joy posts  We will use this information to find the best set of pages for a given target domain (see Section SECREF5 ) 
Model
There are two main decisions to be taken in developing our model: (i) which Facebook pages to select as training data, and (ii) which features to use to train the model, which we discuss below  Specifically, we first set on a subset of pages and then experiment with features  Further exploration of the interaction between choice of pages and choice of features is left to future work, and partly discussed in Section SECREF6   For development, we use a small portion of the Affective data set described in Section SECREF4 , that is the portion that had been released as development set for SemEval's 2007 Task 14 BIBREF7 , which contains 250 annotated sentences (Affective development, Section SECREF4 )  All results reported in this section are on this dataset  The test set of Task 14 as well as the other two datasets described in Section SECREF3 will be used to evaluate the final models (Section SECREF4 ) 
Selecting Facebook pages
Although page selection is a crucial ingredient of this approach, which we believe calls for further and deeper, dedicated investigation, for the experiments described here we took a rather simple approach  First, we selected the pages that would provide training data based on intuition and availability, then chose different combinations according to results of a basic model run on development data, and eventually tested feature combinations, still on the development set 
For the sake of simplicity and transparency, we first trained an SVM with a simple bag-of-words model and default parameters as per the Scikit-learn implementation BIBREF13 on different combinations of pages  Based on results of the attempted combinations as well as on the distribution of emotions in the development dataset (Figure FIGREF9 ), we selected a best model (B-M), namely the combined set of Time, The Guardian and Disney, which yields the highest results on development data  Time and The Guardian perform well on most emotions but Disney helps to boost the performance for the Joy class 
Features
In selecting appropriate features, we mainly relied on previous work and intuition  We experimented with different combinations, and all tests were still done on Affective development, using the pages for the best model (B-M) described above as training data  Results are in Table TABREF20   Future work will further explore the simultaneous selection of features and page combinations 
We use a set of basic text-based features to capture the emotion class  These include a tf-idf bag-of-words feature, word (2-3) and character (2-5) ngrams, and features related to the presence of negation words, and to the usage of punctuation 
This feature is used in all unsupervised models as a source of information, and we mainly include it to assess its contribution, but eventually do not use it in our final model 
We used the NRC10 Lexicon because it performed best in the experiments by BIBREF10 , which is built around the emotions anger, anticipation, disgust, fear, joy, sadness, and surprise, and the valence values positive and negative  For each word in the lexicon, a boolean value indicating presence or absence is associated to each emotion  For a whole sentence, a global score per emotion can be obtained by summing the vectors for all content words of that sentence included in the lexicon, and used as feature 
As additional feature, we also included Word Embeddings, namely distributed representations of words in a vector space, which have been exceptionally successful in boosting performance in a plethora of NLP tasks  We use three different embeddings:
Google embeddings: pre-trained embeddings trained on Google News and obtained with the skip-gram architecture described in BIBREF14   This model contains 300-dimensional vectors for 3 million words and phrases 
Facebook embeddings: embeddings that we trained on our scraped Facebook pages for a total of 20,000 sentences  Using the gensim library BIBREF15 , we trained the embeddings with the following parameters: window size of 5, learning rate of 0 01 and dimensionality of 100  We filtered out words with frequency lower than 2 occurrences 
Retrofitted embeddings: Retrofitting BIBREF16 has been shown as a simple but efficient way of informing trained embeddings with additional information derived from some lexical resource, rather than including it directly at the training stage, as it's done for example to create sense-aware BIBREF17 or sentiment-aware BIBREF18 embeddings  In this work, we retrofit general embeddings to include information about emotions, so that emotion-similar words can get closer in space  Both the Google as well as our Facebook embeddings were retrofitted with lexical information obtained from the NRC10 Lexicon mentioned above, which provides emotion-similarity for each token  Note that differently from the previous two types of embeddings, the retrofitted ones do rely on handcrafted information in the form of a lexical resource 
Results on development set
We report precision, recall, and f-score on the development set  The average f-score is reported as micro-average, to better account for the skewed distribution of the classes as well as in accordance to what is usually reported for this task BIBREF19  
From Table TABREF20 we draw three main observations  First, a simple tf-idf bag-of-word mode works already very well, to the point that the other textual and lexicon-based features don't seem to contribute to the overall f-score (0 368), although there is a rather substantial variation of scores per class  Second, Google embeddings perform a lot better than Facebook embeddings, and this is likely due to the size of the corpus used for training  Retrofitting doesn't seem to help at all for the Google embeddings, but it does boost the Facebook embeddings, leading to think that with little data, more accurate task-related information is helping, but corpus size matters most  Third, in combination with embeddings, all features work better than just using tf-idf, but removing the Lexicon feature, which is the only one based on hand-crafted resources, yields even better results  Then our best model (B-M) on development data relies entirely on automatically obtained information, both in terms of training data as well as features 
Results
In Table TABREF26 we report the results of our model on the three datasets standardly used for the evaluation of emotion classification, which we have described in Section SECREF3  
Our B-M model relies on subsets of Facebook pages for training, which were chosen according to their performance on the development set as well as on the observation of emotions distribution on different pages and in the different datasets, as described in Section SECREF4   The feature set we use is our best on the development set, namely all the features plus Google-based embeddings, but excluding the lexicon  This makes our approach completely independent of any manual annotation or handcrafted resource  Our model's performance is compared to the following systems, for which results are reported in the referred literature  Please note that no other existing model was re-implemented, and results are those reported in the respective papers 
Discussion, conclusions and future work
We have explored the potential of using Facebook reactions in a distant supervised setting to perform emotion classification  The evaluation on standard benchmarks shows that models trained as such, especially when enhanced with continuous vector representations, can achieve competitive results without relying on any handcrafted resource  An interesting aspect of our approach is the view to domain adaptation via the selection of Facebook pages to be used as training data 
We believe that this approach has a lot of potential, and we see the following directions for improvement  Feature-wise, we want to train emotion-aware embeddings, in the vein of work by tang:14, and iacobacci2015sensembed  Retrofitting FB-embeddings trained on a larger corpus might also be successful, but would rely on an external lexicon 
The largest room for yielding not only better results but also interesting insights on extensions of this approach lies in the choice of training instances, both in terms of Facebook pages to get posts from, as well as in which posts to select from the given pages  For the latter, one could for example only select posts that have a certain length, ignore posts that are only quotes or captions to images, or expand posts by including content from linked html pages, which might provide larger and better contexts BIBREF23   Additionally, and most importantly, one could use an entropy-based measure to select only posts that have a strong emotion rather than just considering the majority emotion as training label  For the former, namely the choice of Facebook pages, which we believe deserves the most investigation, one could explore several avenues, especially in relation to stance-based issues BIBREF24   In our dataset, for example, a post about Chile beating Colombia in a football match during the Copa America had very contradictory reactions, depending on which side readers would cheer for  Similarly, the very same political event, for example, would get very different reactions from readers if it was posted on Fox News or The Late Night Show, as the target audience is likely to feel very differently about the same issue  This also brings up theoretical issues related more generally to the definition of the emotion detection task, as it's strongly dependent on personal traits of the audience  Also, in this work, pages initially selected on availability and intuition were further grouped into sets to make training data according to performance on development data, and label distribution  Another criterion to be exploited would be vocabulary overlap between the pages and the datasets 
Lastly, we could develop single models for each emotion, treating the problem as a multi-label task  This would even better reflect the ambiguity and subjectivity intrinsic to assigning emotions to text, where content could be at same time joyful or sad, depending on the reader 
Acknowledgements
In addition to the anonymous reviewers, we want to thank Lucia Passaro and Barbara Plank for insightful discussions, and for providing comments on draft versions of this paper 

ground_truth: Affective Text, Fairy Tales, ISEAR

 Affective Text dataset, Fairy Tales dataset, ISEAR dataset