Page 1

Extending Multi-Sense Word Embedding to Phrases and Sentences

for Unsupervised Semantic Applications

Haw-Shiuan Chang, Amol Agrawal, Andrew McCallum

CICS, University of Massachusetts Amherst

{hschang,amolagrawal,mccallum}@cs.umass.edu

Abstract

Most unsupervised NLP models represent each word with a

single point or single region in semantic space, while the ex-

isting multi-sense word embeddings cannot represent longer

word sequences like phrases or sentences. We propose a

novel embedding method for a text sequence (a phrase or a

sentence) where each sequence is represented by a distinct

set of multi-mode codebook embeddings to capture different

semantic facets of its meaning. The codebook embeddings

can be viewed as the cluster centers which summarize the

distribution of possibly co-occurring words in a pre-trained

word embedding space. We introduce an end-to-end train-

able neural model that directly predicts the set of cluster cen-

ters from the input text sequence during test time. Our ex-

periments show that the per-sentence codebook embeddings

significantly improve the performances in unsupervised sen-

tence similarity and extractive summarization benchmarks.

In phrase similarity experiments, we discover that the multi-

facet embeddings provide an interpretable semantic represen-

tation but do not outperform the single-facet baseline.

Introduction

Collecting manually labeled data is an expensive and tedious

process for new or low-resource NLP applications. Many of

these applications require the text similarity measurement

based on the text representation learned from the raw text

without any supervision. Examples of the representation in-

clude word embedding like Word2Vec (Mikolov et al. 2013)

or GloVe (Pennington, Socher, and Manning 2014), sentence

embeddings like skip-thoughts (Kiros et al. 2015), contextu-

alized word embedding like ELMo (Peters et al. 2018) and

BERT (Devlin et al. 2019) without fine-tuning.

The existing work often represents a word sequence (e.g.,

a sentence or a phrase) as a single embedding. However,

when squeezing all the information into a single embedding

(e.g., by averaging the word embeddings or using CLS em-

bedding in BERT), the representation might lose some im-

portant information of different facets in the sequence.

Inspired by the multi-sense word embeddings (Lau et al.

2012; Neelakantan et al. 2014; Athiwaratkun and Wilson

2017; Singh et al. 2020), we propose a multi-facet repre-

sentation that characterizes a phrase or a sentence as a fixed

Copyright c 2021, Association for the Advancement of Artificial

Intelligence (www.aaai.org). All rights reserved.

The company acquired the real property to save tax .

Input Phrase

Co-occurring words

Our Transformer Model

Classic multi-sense approach: During testing,

clustering co-occurring words into centers

necessary

violation

belief

tax

dollars

acquired

save

houses

organization

company

building

The distribution of all possible co-occurring words of real property (input phrase) 


in a pre-trained word embedding space

Our approach: During training, minimize

the distance between the predicted cluster

centers and the co-occurring words.

During testing, directly predict the centers

Backward pass: 


Update the model

using backdrop

Forward pass: 


Predict cluster centers

Figure 1: The input phrase real property is represented by

K = 5 cluster centers. The previous work discovers the

multiple senses by clustering the embedding of observed co-

occurring words. Instead, our compositional model learns to

predict the embeddings of cluster centers from the sequence

of words in the input phrase so as to reconstruct the (unseen)

co-occurring distribution well.

number of embeddings, where each embedding is a cluster-

ing center of the words co-occurring with the input word

sequence.

In this work, a facet refers to a mode of the co-occurring

word distribution, which might be multimodal. For example,

the multi-facet representation of real property is illustrated

in Figure 1. Real property can be observed in legal docu-

ments where it usually means real estate, while real property

can also mean a true characteristic in philosophic discus-

sions. The previous unsupervised multi-sense embeddings

discover those senses by clustering the observed neighbor-

ing words (e.g., acquired, save, and tax) and an important

facet, a mode with high probability, could be represented by

several close cluster centers. Notice that the approaches need

to solve a distinct local clustering problem for each phrase

in contrast with the topic modeling like LDA (Blei, Ng, and

Jordan 2003), which clusters all the words in the corpus into

a global set of topics.

The Thirty-Fifth AAAI Conference on Artificial Intelligence (AAAI-21)

6956

In addition to a phrase, we can also cluster the nearby

words of a sentence which appears frequently in the corpus.

The cluster centers usually correspond to important aspects

rather than senses (see an example in Figure 2) because a

sentence usually has multiple aspects but only one sense.

However, extending the clustering-based multi-sense word

embeddings to long sequences such as sentences is difficult

in practice due to two efficiency challenges. First, there are

usually many more unique phrases and sentences in a cor-

pus than there are words, while the number of parameters for

clustering-based approaches is O(|V |×|K|×|E|), where

|V | is the number of unique sequences, |K| is the number of

clusters, and |E| is the embedding dimensions. Estimating

and storing such a large number of parameters takes time and

space. More importantly, much more unique sequences im-

ply much fewer co-occurring words to be clustered for each

sequence, especially for sentences. An effective model needs

to overcome this sample efficiency challenge (i.e., sparse-

ness in the co-occurring statistics), but clustering approaches

often have too many parameters to learn the compositional

meaning of each sequence without overfitting.

Nevertheless, the sentences (or phrases) sharing multiple

words often lead to similar cluster centers, so we should be

able to solve these local clustering problems using much

fewer parameters to circumvent the challenges. To achieve

the goal, we develop a novel Transformer-based neural en-

coder and decoder. As shown in Figure 1, instead of clus-

tering co-occurring words beside an input sequence at test

time as in previous approaches, we learn a mapping between

the input sequence (i.e., phrases or sentences) and the corre-

sponding cluster centers during training so that we can di-

rectly predict those cluster centers using a single forward

pass of the neural network for an arbitrary unseen input se-

quence during testing.

To train the neural model that predicts the clustering cen-

ters, we match the sequence of predicted cluster centers and

the observed set of co-occurring word embeddings using a

non-negative and sparse permutation matrix. After the per-

mutation matrix is estimated for each input sequence, the

gradients are back-propagated to cluster centers (i.e., code-

book embeddings) and to the weights of our neural model,

which allows us to train the whole model end-to-end.

In the experiments, we evaluate whether the proposed

multi-facet embeddings could improve the similarity mea-

surement between two sentences, between a sentence and

a document (i.e., extractive summarization), and between

phrases. The results demonstrate multi-facet embeddings

significantly outperforms the classic single embedding base-

line when the input sequence is a sentence.

We also demonstrate several advantages of the proposed

multi-facet embeddings over the (contextualized) embed-

dings of all the words in a sequence. First, we discover that

our model tends to use more embeddings to represent an

important facet or important words. This tendency provides

an unsupervised estimation of word importance, which im-

proves various similarity measurements between a sentence

pair. Second, our model outputs a fixed number of facets

by compressing long sentences and extending short sen-

tences. In unsupervised extractive summarization, this ca-

pability prevents the scoring function from biasing toward

longer or shorter sentences. Finally, in the phrase similarity

experiments, our methods capture the compositional mean-

ing (e.g., a hot dog is a food) of a word sequence well and

the quality of our similarity estimation is not sensitive to the

choice of K, the number of our codebook embeddings.

Main Contributions

1. As shown in Figure 1, we propose a novel framework

that predicts the cluster centers of co-occurring word

embeddings to overcomes the sparsity challenges in our

self-supervised training signals. This allows us to extend

the idea of clustering-based multi-sense embeddings to

phrases or sentences.

2. We propose a deep architecture that can effectively en-

code a sequence and decode a set of embeddings. We also

propose non-negative sparse coding (NNSC) loss to train

our neural encoder and decoder end-to-end.

3. We demonstrate how the multi-facet embeddings could be

used in unsupervised ways to improve the similarity be-

tween sentences/phrases, infer word importance in a sen-

tence, extract important sentences in a document. In the

appendix, we show that our model could provide asym-

metric similarity measurement for hypernym detection.

4. We conduct comprehensive experiments in the main pa-

per and appendix to show that multi-facet embedding is

consistently better than classic single-facet embedding

for modeling the co-occurring word distribution of sen-

tences, while multi-facet phrase embeddings do not yield

a clear advantage against the single embedding baseline,

which supports the finding in Dubossarsky, Grossman,

and Weinshall (2018).

Method

In this section, we first formalize our training setup and next

describe our objective function and neural architecture. Our

approach is visually summarized in Figure 2.

Self-supervision Signal

We express tth sequence of words in the corpus as It =

wxt ...wyt <eos>, where xt and yt are the start and end po-

sition of the input sequence, respectively, and <eos> is the

end of sequence symbol.

We assume neighboring words beside each input phrase

or sentence are related to some facets of the se-

quence, so given It as input, our training signal is

to reconstruct a set of co-occurring words, Nt

=

{wxt−dt

1

, ...wxt−1,wyt+1, ...wyt+dt

2

}.1 In our experiments,

we train our multi-facet sentence embeddings by setting Nt

as the set of all words in the previous and the next sentence,

and train multi-facet phrase embeddings by setting a fixed

window size dt

1 = dt

2 = 5.

Since there are not many co-occurring words for a long

sequence (none are observed for unseen testing sequences),

the goal of our model is to predict the cluster centers of the

1The self-supervised signal is a generalization of the loss for

prediction-based word embedding like Word2Vec (Mikolov et al.

2013). They are the same when the input sequence length |It| is 1.

6957

Beautiful music starts . The girl sings into a microphone . <eos> A star is born on the stage .

……

Transformer Encoder (TE)

L1

Distinct linear layers 


for each input position

LK

Transformer Decoder (TD)

……

Sequence to Embeddings F(.)

Codebook

Embeddings F(It)

Nonnegative Sparse Coding Loss (Not Required for Testing)

Input Sentence (It)

Co-occurring Words (Nt)

≅

x

x

Co-occurring

Words W(Nt)

≆

Random

Words W(Nrt)

song

music

albums

television

girl

lady

Beautiful

microphone

describe

star

actor

starts

born

begin

A Pre-trained Word

Embedding Space

Coefficient

matrix (MOt)

Coefficient

matrix (MRt)

boy

stage

Figure 2: Our model for sentence representation. We represent each sentence as multiple codebook embeddings (i.e., cluster

centers) predicted by our sequence to embeddings model. Our loss encourages the model to generate codebook embeddings

whose linear combination can well reconstruct the embeddings of co-occurring words (e.g., music), while not able to reconstruct

the negatively sampled words (i.e., the co-occurring words from other sentences).

words that could ”possibly” occur beside the text sequence

rather than the cluster centers of the actual occurring words

in Nt (e.g., the hidden co-occurring distribution instead of

green and underlined words in Figure 2). The cluster cen-

ters of an unseen testing sequence are predictable because

the model could learn from similar sequences and their co-

occurring words in the training corpus.

To focus on the semantics rather than syntax, we view

the co-occurring words as a set rather than a sequence as

in skip-thoughts (Kiros et al. 2015). Notice that our model

considers the word order information in the input sequence

It, but ignores the order of the co-occurring words Nt.

Non-negative Sparse Coding Loss

In a pre-trained word embedding space, we predict the clus-

ter centers of the co-occurring word embeddings. The em-

beddings of co-occurring words Nt are arranged into a ma-

trix W(Nt) = [wt

j]j=1...|Nt| with size |E|×|Nt|, where

|E| is the dimension of pre-trained word embedding, and

each of its columns wt

j is a normalized word embedding

whose 2-norm is 1. The normalization makes the cosine dis-

tance between two words become half of their squared Eu-

clidean distance.

Similarly, we denote the predicted cluster centers ct

k of

the input sequence It as a |E| × K matrix F(It) =

[ct

k]k=1...K, where F is our neural network model and K is

the number of clusters. We fix the number of clusters K to

simplify the design of our prediction model and the unsuper-

vised scoring functions used in the downstream tasks. When

the number of modes in the (multimodal) co-occurring dis-

tribution is smaller than K, the model can output multiple

cluster centers to represent a mode (e.g., the music facet in

Figure 2 is represented by two close cluster centers). As a

result, the performances in our downstream applications are

not sensitive to the setting of K when K is larger than the

number of facets in most input word sequences.

The reconstruction loss of k-means clustering in the

word embedding space can be written as ||F(It)M −

W(Nt)||2 = ∑j ||(∑k Mk,jct

k) − wt

j||2, where Mk,j =

1 if the jth word belongs to the k cluster and 0 otherwise.

That is, M is a permutation matrix which matches the clus-

ter centers and co-occurring words and allow the cluster cen-

ters to be predicted in an arbitrary order.

Non-negative sparse coding (NNSC) (Hoyer 2002) re-

laxes the constraints by allowing the coefficient Mk,j to be

a positive value but encouraging it to be 0. We adopt NNSC

in this work because we observe that the neural network

trained by NNSC loss generates more diverse topics than k-

means loss does. We hypothesize that it is because the loss

is smoother and easier to be optimized for a neural network.

Using NNSC, we define our reconstruction error as

Er(F (It), W (Nt)) = ||F (It)MOt − W (Nt)||2

s.t., MOt = arg min

M

||F (It)M − W (Nt)||2 + λ||M||1,

∀k, j, 0 ≤ Mk,j ≤ 1,

(1)

6958

where λ is a hyper-parameter controlling the sparsity of M.

We force the coefficient value Mk,j ≤ 1 to avoid the neural

network learning to predict centers with small magnitudes

which makes the optimal values of Mk,j large and unstable.

We adopt an alternating optimization strategy similar to

the EM algorithm for k-means. At each iteration, our E-step

estimates the permutation coefficient MOt after fixing our

neural model, while our M-step treats MOt

as constants

to back-propagate the gradients of NNSC loss to our neu-

ral network. A pseudo-code of our training procedure could

be found in the appendix. Estimating the permutation be-

tween the prediction and ground truth words is often compu-

tationally expensive (Qin et al. 2019). Nevertheless, optimiz-

ing the proposed loss is efficient because for each training

sequence It, MOt can be efficiently estimated using con-

vex optimization (our implementation uses RMSprop (Tiele-

man and Hinton 2012)). Besides, we minimize the L2 dis-

tance, ||F (It)MOt − W(Nt)||2, in a pre-trained embed-

ding space as in Kumar and Tsvetkov (2019); Li et al. (2019)

rather than computing softmax.

To prevent the neural network from predicting the same

global topics regardless of the input, our loss function for

tth sequence is defined as

Lt(F ) = Er(F (It), W (Nt)) − Er(F (It), W (Nrt )), (2)

where Nrt is a set of co-occurring words of a randomly sam-

pled sequence Irt . In our experiment, we use SGD to solve

̂F = arg minF

∑

t Lt(F). Our method could be viewed as

a generalization of Word2Vec (Mikolov et al. 2013) that can

encode the compositional meaning of the words and decode

multiple embeddings.

Sequence to Embeddings

Our neural network architecture is similar to Transformer-

based sequence to sequence (seq2seq) model (Vaswani et al.

2017). We use the same encoder TE(It), which transforms

the input sequence into a contextualized embeddings

[ext ...eyt e<eos>] = TE(wxt ...wyt <eos>),

(3)

where the goal of the encoder is to map the similar sen-

tences, which are likely to have similar co-occurring word

distribution, to similar contextualized embeddings.

Different from the typical seq2seq model (Sutskever,

Vinyals, and Le 2014; Vaswani et al. 2017), our decoder

does not need to make discrete decisions because our out-

puts are a sequence of embeddings instead of words. This

allows us to predict all the codebook embeddings in a sin-

gle forward pass as in Lee et al. (2019) without requiring an

expensive softmax layer or auto-regressive decoding.2

To make different codebook embeddings capture differ-

ent facets, we pass the embeddings of <eos>, e<eos>, to

different linear layers Lk before becoming the input of the

decoder TD. The decoder allows the input embeddings to

attend each other to model the dependency among the facets

and attend the contextualized word embeddings from the

2The decoder can also be viewed as another Transformer en-

coder which attends the output of the first encoder and models the

dependency between predicted cluster centers.

encoder, ext ...eyt e<eos>, to copy the embeddings of some

keywords in the word sequence as our facet embeddings

more easily. Specifically, the codebook embeddings

F (It) = TD(L1(e<eos>)...LK (e<eos>), ext ...eyt e<eos>).

(4)

We find that removing the attention on the

ext ...eyt e<eos>

significantly deteriorates our valida-

tion loss for sentence representation because there are often

too many facets to be compressed into a single embed-

ding. On the other hand, the encoder-decoder attention

does not significantly change the performance of phrase

representation, so we remove the connection (i.e., encoder

and decoder have the same architecture) in models for

phrase representation. Notice that the framework is flexible.

For example, we can encode the genre of the document

containing the sentence if desired.

Experiments

Quantitatively evaluating the quality of our predicted clus-

ter centers is difficult because the existing label data and

metrics are built for global clustering. The previous multi-

sense word embedding studies often show that multiple em-

beddings could improve the single word embedding in the

unsupervised word similarity task to demonstrate its effec-

tiveness. Thus, our goal of experiments is to discover when

and how the multi-facet embeddings can improve the simi-

larity measurement in various unsupervised semantic tasks

upon the widely-used general-purpose representations, such

as single embedding and (contextualized) word embeddings.

Experiment Setup

Our models only require the raw corpus and sentence/phrase

boundaries, so we will only compare them with other un-

supervised alternatives that do not require any manual la-

bels or multi-lingual resources such as PPDB (Pavlick et al.

2015). To simplify the comparison, we also omit the com-

parison with the methods using character-level information

such as fastText (Bojanowski et al. 2017) or bigram informa-

tion such as Sent2Vec (Pagliardini, Gupta, and Jaggi 2018).

It is hard to make a fair comparison with BERT (Devlin

et al. 2019). Its masked language modeling loss is designed

for downstream supervised tasks and preserves more syntax

information which might be distractive in unsupervised se-

mantic applications. Furthermore, BERT uses word piece to-

kenization while other models use word tokenization. Never-

theless, we still present the performances of the BERT Base

model as a reference even though it is trained using more

parameters, larger embedding size, larger corpus, and more

computational resources compared with our models. Since

we focus on unsupervised setting, we directly use the final

hidden states of the BERT models without supervised fine-

tuning in most of the comparisons. One exception is that we

also report the performance of sentence-BERT (Reimers and

Gurevych 2019) in a low-resource setting.

Our model is trained on English Wikipedia 2016 while the

stop words are removed from the set of co-occurring words.

In the phrase experiments, we only consider noun phrases,

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Input Phrase: civil order <eos>

Output Embedding (K = 1):

e1 — government 0.817 civil 0.762 citizens 0.748

Output Embeddings (K = 3):

e1 — initiatives 0.736 organizations 0.725 efforts 0.725

e2 — army 0.815 troops 0.804 soldiers 0.786

e3 — court 0.758 federal 0.757 judicial 0.736

Input Sentence: SMS messages are used in some countries as re-

minders of hospital appointments . <eos>

Output Embedding (K = 1):

e1 — information 0.702, use 0.701, specific 0.700

Output Embeddings (K = 3):

e1 — can 0.769, possible 0.767, specific 0.767

e2 — hospital 0.857, medical 0.780, hospitals 0.739

e3 — SMS 0.791, Mobile 0.635, Messaging 0.631

Output Embeddings (K = 10):

e1 — can 0.854, should 0.834, either 0.821

e2 — hospital 0.886, medical 0.771, hospitals 0.745

e3 — services 0.768, service 0.749, web 0.722

e4 — SMS 0.891, sms 0.745, messaging 0.686

e5 — messages 0.891, message 0.801, emails 0.679

e6 — systems 0.728, technologies 0.725, integrated 0.723

e7 — appointments 0.791, appointment 0.735, duties 0.613

e8 — confirmation 0.590, request 0.568, receipt 0.563

e9 — countries 0.855, nations 0.737, Europe 0.732

e10 — Implementation 0.613, Application 0.610, Programs 0.603

Table 1: Examples of the codebook embeddings predicted

by our models with different K. The embedding in each row

is visualized by the three words whose GloVe embeddings

have the highest cosine similarities (also presented) with the

codebook embedding.

and their boundaries are extracted by applying simple reg-

ular expression rules to POS tags before training. We use

the cased version (840B) of GloVe embedding (Pennington,

Socher, and Manning 2014) as the pre-trained word embed-

ding space for our sentence representation and use the un-

cased version (42B) for phrase representation.3 To control

the effect of embedding size, we set the hidden state size in

our transformers as the GloVe embedding size (300).

Limited by computational resources, we train all the mod-

els using one GPU (e.g., NVIDIA 1080 Ti) within a week.

Because of the relatively small model size, we find that our

models underfit the data after a week (i.e., the training loss

is very close to the validation loss).

Qualitative Evaluation

The cluster centers predicted by our model are visualized in

Table 1 (as using girl and lady to visualize the red cluster

center in Figure 2). Some randomly chosen examples are

also visualized in the appendix.

The centers summarize the input sequence well and more

codebook embeddings capture more fine-grained semantic

facets of a phrase or a sentence. Furthermore, the embed-

dings capture the compositional meaning of words. For ex-

ample, each word in the phrase civil order does not mean ini-

tiatives, army, or court, which are facets of the whole phrase.

3nlp.stanford.edu/projects/glove/

When the input is a sentence, we can see that the output em-

beddings are sometimes close to the embeddings of words

in the input sentence, which explains why attending the con-

textualized word embeddings in our decoder could improve

the quality of the output embeddings.

Unsupervised Sentence Similarity

We propose two ways to evaluate the multi-facet embed-

dings using sentence similarity tasks.

First way: Since similar sentences should have similar

word distribution in nearby sentences and thus similar code-

book embeddings, the codebook embeddings of a query sen-

tence ̂Fu(S1

q ) should be able to well reconstruct the code-

book embeddings of its similar sentence ̂Fu(S2

q ). We com-

pute the reconstruction error of both directions and add them

as a symmetric distance SC:

SC(S1

q , S2

q ) = Er( ̂Fu(Si

q ), ̂Fu(S2

q ))

+ Er( ̂Fu(S2

q ), ̂Fu(Si

q )),

(5)

where ̂Fu(Sq) = [

cq

k

||cq

k||

]k=1...K is a matrix of normalized

codebook embeddings and Er function is defined in equa-

tion 1. We use the negative distance to represent similarity.

Second way: One of the main challenges in unsupervised

sentence similarity tasks is that we do not know which words

are more important in each sentence. Intuitively, if one word

in a query sentence is more important, the chance of observ-

ing related/similar words in the nearby sentences should be

higher. Thus, we should pay more attention to the words in

a sentence that have higher cosine similarity with its multi-

facet embeddings, a summary of the co-occurring word dis-

tribution. Specifically, our importance/attention weighting

for all the words in the query sentence Sq is defined by

aq = max(0, W (Sq)T

̂Fu(Sq)) 1,

(6)

where 1 is an all-one vector. We show that the attention vec-

tor (denoted as Our a in Table 2) could be combined with

various scoring functions and boost their performances. As

a baseline, we also report the performance of the attention

weights derived from the k-means loss rather than NNSC

loss and call it Our a (k-means).

Setup: STS benchmark (Cer et al. 2017) is a widely used

sentence similarity task. We compare the correlations be-

tween the predicted semantic similarity and the manually

labeled similarity. We report Pearson correlation coefficient,

which is strongly correlated with Spearman correlation in

all our experiments. Intuitively, when two sentences are less

similar to each other, humans tend to judge the similarity

based on how similar their facets are. Thus, we also compare

the performances on the lower half of the datasets where

their ground truth similarities are less than the median simi-

larity in the dataset, and we call this benchmark STSB Low.

A simple but effective way to measure sentence simi-

larity is to compute the cosine similarity between the av-

erage (contextualized) word embedding (Milajevs et al.

2014). The scoring function is labeled as Avg. Besides, we

test the sentence embedding from BERT and from skip-

thought (Kiros et al. 2015) (denoted as CLS and Skip-

thought Cosine, respectively).

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Sentences

A man is lifting weights in a garage .

A man is lifting weights .

e1 — can 0.872, even 0.851, should 0.850

e1 — can 0.865, either 0.843, should 0.841

e2 — front 0.762, bottom 0.742, down 0.714

e2 — front 0.758, bottom 0.758, sides 0.691

e3 — lifting 0.866, lift 0.663, Lifting 0.621

e3 — lifting 0.847, lift 0.635, Lifting 0.610

e4 — garage 0.876, garages 0.715, basement 0.707

e4 — lifting 0.837, lift 0.652, weights 0.629

Output

e5 — decreasing 0.677, decreases 0.655, negligible 0.649

e5 — decreasing 0.709, decreases 0.685, increases 0.682

Embeddings e6 — weights 0.883, Weights 0.678, weight 0.665

e6 — weights 0.864, weight 0.700, Weights 0.646

e7 — cylindrical 0.700, plurality 0.675, axial 0.674

e7 — annular 0.738, cylindrical 0.725, circumferential 0.701

e8 — configurations 0.620, incorporating 0.610, utilizing 0.605 e8 — methods 0.612, configurations 0.610, graphical 0.598

e9 — man 0.872, woman 0.682, men 0.672

e9 — sweating 0.498, cardiovascular 0.494, dehydration 0.485

e10 — man 0.825, men 0.671, woman 0.653

e10 — man 0.888, woman 0.690, men 0.676

Figure 3: Comparison of our attention weights and the output embeddings between two similar sentences from STSB. A darker

red indicates a larger attention value in equation 6 and the output embeddings are visualized using the same way in Table 1.

Method

Dev

Test

Score

Model

All

Low

All

Low

Cosine

Skip-thought

43.2

28.1

30.4

21.2

CLS

BERT

9.6

-0.4

4.1

0.2

Avg

62.3

42.1

51.2

39.1

SC

Our c K1

55.7

43.7

47.6

45.4

Our c K10

63.0

51.8

52.6

47.8

WMD

GloVe

58.8

35.3

40.9

25.4

Our a K1

63.1

43.3

47.5

34.8

Our a K10

66.7

47.4

52.6

39.8

Prob WMD

GloVe

75.1

59.6

63.1

52.5

Our a K1

74.4

60.8

62.9

54.4

Our a K10

76.2

62.6

66.1

58.1

Avg

GloVe

51.7

32.8

36.6

30.9

Our a K1

54.5

40.2

44.1

40.6

Our a K10

61.7

47.1

50.0

46.5

Prob avg

GloVe

70.7

56.6

59.2

54.8

Our a K1

68.5

56.0

58.1

55.2

Our a K10

72.0

60.5

61.4

59.3

SIF†

GloVe

75.1

65.7

63.2

58.1

Our a K1

72.5

64.0

61.7

58.5

Our a K10

75.2

67.6

64.6

62.2

Our a (k-means) K10 71.5

62.3

61.5

57.2

sentence-BERT (100 pairs)*

71.2

55.5

64.5

58.2

Table 2: Pearson correlation (%) in the development and

test sets in the STS benchmark. The performances of all

sentence pairs are indicated as All. Low means the perfor-

mances on the half of sentence pairs with lower similarity

(i.e., STSB Low). Our c means our codebook embeddings

and Our a means our attention vectors. * indicates a su-

pervised method. † indicates the methods which use train-

ing distribution to approximate testing distribution. The best

score with and without † are highlighted.

In order to deemphasize the syntax parts of the sentences,

Arora, Liang, and Ma (2017) propose to weight the word w

in each sentence according to

α

α+p(w) , where α is a constant

and p(w) is the probability of seeing the word w in the cor-

pus. Following its recommendation, we set α to be 10−4 in

this paper. After the weighting, we remove the first princi-

pal component of all the sentence embeddings in the train-

ing data as suggested by Arora, Liang, and Ma (2017) and

denote the method as SIF. The post-processing requires an

estimation of testing embedding distribution, which is not

desired in some applications, so we also report the perfor-

mance before removing the principal component, which is

called Prob avg.

We also test word mover’s distance (WMD) (Kusner et al.

2015), which explicitly matches every word in a pair of sen-

tences. As we do in Prob avg, we apply

α

α+p(w) to WMD

to down-weight the importance of functional words, and call

this scoring function as Prob WMD. When using Our a, we

multiple our attention vector with the weights of every word

(e.g.,

α

α+p(w) for Prob avg and Prob WMD).

To motivate the unsupervised setting, we present the per-

formance of sentence-BERT (Reimers and Gurevych 2019)

that are trained by 100 sentence pairs. We randomly sample

the sentence pairs from a data source that is not included in

STSB (e.g., headlines in STS 2014), and report the testing

performance averaged across all the sources from STS 2012

to 2016. More details are included in the appendix.

Results: In Figure 3, we first visualize our attention

weights in equation 6 and our output codebook embeddings

for a pair of similar sentences from STSB to intuitively ex-

plain why modeling co-occurring distribution could improve

the similarity measurement.

Many similar sentences might use different word choices

or using extra words to describe details, but their possible

nearby words are often similar. For example, appending in

the garage to A man is lifting weights does not significantly

change the facets of the sentences and thus the word garage

receives relatively a lower attention weight. This makes its

similarity measurement from our methods, Our c and Our

a, closer to the human judgment than other baselines.

In Table 2, Our c SC, which matches between two sets

of facets, outperforms WMD, which matches between two

sets of words in the sentence, and also outperforms BERT

Avg, especially in STSB Low. The significantly worse per-

formances from Skip-thought Cosine justify our choice of

ignoring the order in the co-occurring words.

All the scores in Our * K10 are significantly better than

Our * K1, which demonstrates the co-occurring word dis-

tribution is hard to be modeled well using a single embed-

ding. Multiplying the proposed attention weighting consis-

tently boosts the performance in all the scoring functions

especially in STSB Low and without relying on the gen-

eralization assumption of the training distribution. Finally,

using k-means loss, Our a (k-means) K10, significantly de-

grades the performance compared to Our a K10, which jus-

tify the proposed NNSC loss. In the appendix, our methods

are compared with more baselines using more datasets to test

the effectiveness of multi-facet embeddings and our design

6961

Setting

Method

R-1

R-2

Len

Unsup,

No

Sent

Order

Random

28.1

8.0

68.7

Textgraph (tfidf)†

33.2 11.8

-

Textgraph (BERT)†

30.8

9.6

-

W Emb (GloVe)

26.6

8.8

37.0

Sent Emb (GloVe)

32.6 10.7 78.2

W Emb (BERT)

31.3 11.2 45.0

Sent Emb (BERT)

32.3 10.6 91.2

Our c (K=3)

32.2 10.1 75.4

Our c (K=10)

34.0 11.6 81.3

Our c (K=100)

35.0 12.8

92.9

Unsup

Lead-3

40.3 17.6 87.0

PACSUM (BERT)†

40.7 17.8

-

Sup

RL*

41.7 19.5

-

Table 3: The ROUGE F1 scores of different methods on

CNN/Daily Mail dataset. The results with † are taken

from Zheng and Lapata (2019). The results with * are taken

from Celikyilmaz et al. (2018).

choices more comprehensively.

Unsupervised Extractive Summarization

The classic representation of a sentence uses either a sin-

gle embedding or the (contextualized) embeddings of all the

words in the sentence. In this section, we would like to show

that both options are not ideal for extracting a set of sen-

tences as a document summary.

Table 1 indicates that our multiple codebook embeddings

of a sentence capture its different facets well, so we rep-

resent a document summary S as the union of the multi-

facet embeddings of the sentences in the summary R(S) =

∪T

t=1{ ̂Fu(St)}, where { ̂Fu(St)} is the set of column vectors

in the matrix ̂Fu(St) of sentence St.

A good summary should cover multiple facets that well

represent all topics/concepts in the document (Kobayashi,

Noguchi, and Yatsuka 2015). The objective can be quantified

as discovering a summary S whose multiple embeddings

R(S) best reconstruct the distribution of normalized word

embedding w in the document D (Kobayashi, Noguchi, and

Yatsuka 2015). That is,

arg max

S

∑

w∈D

α

α + p(w)

max

s∈R(S)

wT s,

(7)

where

α

α+p(w) is the weights of words we used in the sen-

tence similarity experiments (Arora, Liang, and Ma 2017).

We greedily select sentences to optimize equation 7 as

in Kobayashi, Noguchi, and Yatsuka (2015).

Setup: We compare our multi-facet embeddings with

other alternative ways of modeling the facets of sentences.

A simple way is to compute the average word embedding as

a single-facet sentence embedding.4 This baseline is labeled

as Sent Emb. Another way is to use the (contextualized) em-

bedding of all the words in the sentences as different facets

of the sentences. Since longer sentences have more words,

4Although equation 7 weights each word in the document, we

find that the weighting

α

α+p(w) does not improve the sentence rep-

resentation when averaging the word embeddings.

we normalize the gain of the reconstruction similarity by the

sentence length. The method is denoted as W Emb. We also

test the baselines of selecting random sentences (Rnd) and

first 3 sentences (Lead-3) in the document.

The results on the testing set of CNN/Daily Mail (Her-

mann et al. 2015; See, Liu, and Manning 2017) are com-

pared using F1 of ROUGE (Lin and Hovy 2003) in Table 3.

R-1, R-2, and Len mean ROUGE-1, ROUGE-2, and average

summary length, respectively. All methods choose 3 sen-

tences by following the setting in Zheng and Lapata (2019).

Unsup, No Sent Order means the methods do not use the

sentence order information in CNN/Daily Mail.

In CNN/Daily Mail, the unsupervised methods which ac-

cess sentence order information such as Lead-3 have perfor-

mances similar to supervised methods such as RL (Celiky-

ilmaz et al. 2018). To evaluate the quality of unsupervised

sentence embeddings, we focus on comparing the unsuper-

vised methods which do not assume the first few sentences

form a good summary.

Results: In Table 3, predicting 100 clusters yields the best

results. Notice that our method greatly alleviates the compu-

tational and sample efficiency challenges, which allows us

to set cluster numbers K to be a relatively large number.

The results highlight the limitation of classic represen-

tations. The single sentence embedding cannot capture its

multiple facets. On the other hand, if a sentence is repre-

sented by the embeddings of its words, it is difficult to elim-

inate the bias of selecting longer or shorter sentences and a

facet might be composed by multiple words (e.g., the input

sentence in Table 1 describes a service, but there is not a

single word in the sentence that means service).

Unsupervised Phrase Similarity

Recently, Dubossarsky, Grossman, and Weinshall (2018)

discovered that the multiple embeddings of each word may

not improve the performance in word similarity benchmarks

even if they capture more senses or facets of polysemies.

Since our method can improve the sentence similarity es-

timation, we want to see whether multi-facet embeddings

could also help the phrase similarity estimation.

In addition to SC in equation 5, we also compute the

average of the contextualized word embeddings from our

transformer encoder as the phrase embedding. We find that

the cosine similarity between the two phrase embeddings is

a good similarity estimation, and the method is labeled as

Ours Emb.

Setup: We evaluate our phrase similarity using SemEval

2013 task 5(a) English (Korkontzelos et al. 2013) and Tur-

ney 2012 (Turney 2012). The task of SemEval 2013 is to

distinguish similar phrase pairs from dissimilar phrase pairs.

In Turney (5), given each query bigram, each model predicts

the most similar unigram among 5 candidates, and Turney

(10) adds 5 more negative phrase pairs by pairing the reverse

of the query bigram with the 5 unigrams.

Results: The performances are presented in Table 4. Ours

(K=1) is usually slightly better than Ours (K=10), and the

result supports the finding of Dubossarsky, Grossman, and

Weinshall (2018). We hypothesize that unlike sentences,

most of the phrases have only one facet/sense, and thus can

6962

Method

SemEval 2013 Turney (5) Turney (10)

Model

Score AUC

F1

Accuracy

Accuracy

BERT

CLS

54.7

66.7

29.2

15.5

Avg

66.5

67.1

43.4

24.3

GloVe

Avg

79.5

73.7

25.9

12.9

FCT LM†

Emb

-

67.2

42.6

27.6

Ours

SC

80.3

72.8

45.6

28.8

(K=10)

Emb

85.6

77.1

49.4

31.8

Ours

SC

81.1

72.7

45.3

28.4

(K=1)

Emb

87.8

78.6

50.3

32.5

Table 4: Performance of phrase similarity tasks. Every

model is trained on a lowercased corpus. In SemEval 2013,

AUC (%) is the area under the precision-recall curve of clas-

sifying similar phrase pairs. In Turney, we report the accu-

racy (%) of predicting the correct similar phrase pair among

5 or 10 candidate pairs. The results with † are taken from Yu

and Dredze (2015).

be modeled by a single embedding well. In the appendix, the

results on hypernym detection also support this hypothesis.

Even though being slightly worse, the performances of

Ours (K=10) remain strong compared with baselines. This

implies that the similarity performances are not sensitive to

the number of clusters as long as sufficiently large K is used

because the model is able to output multiple nearly dupli-

cated codebook embeddings to represent one facet (e.g., us-

ing two centers to represent the facet related to company in

Figure 1). The flexibility alleviates the issues of selecting K

in practice. Finally, the strong performances in Turney (10)

verify that our encoder respects the word order when com-

posing the input sequence.

Related Work

Topic modeling (Blei, Ng, and Jordan 2003) has been ex-

tensively studied and widely applied due to its interpretabil-

ity and flexibility of incorporating different forms of input

features (Mimno and McCallum 2008). Cao et al. (2015);

Srivastava and Sutton (2017) demonstrate that neural net-

works could be applied to discover semantically coherent

topics. Instead of optimizing a global topic model, our goal

is to efficiently discover different sets of topics/clusters on

the words beside each (unseen) phrase or sentence.

Sparse coding on word embedding space is used to model

the multiple facets of a word (Faruqui et al. 2015; Arora et al.

2018), and parameterizing word embeddings using neural

networks is used to test hypothesis (Han et al. 2018) and

save storage space (Shu and Nakayama 2018). Besides, to

capture asymmetric relations such as hypernyms, words are

represented as single or multiple regions in Gaussian embed-

dings (Vilnis and McCallum 2015; Athiwaratkun and Wil-

son 2017) rather than a single point. However, the challenges

of extending these methods to longer sequences are not ad-

dressed in these studies.

One of our main challenges is to design a loss for learn-

ing to predict cluster centers while modeling the dependency

among the clusters. This requires a matching step between

two sets and computing the distance loss after the match-

ing (Eiter and Mannila 1997). One popular loss is called

Chamfer distance, which is widely adopted in the auto-

encoder models for point clouds (Yang et al. 2018a; Liu

et al. 2019), while more sophisticated matching loss options

are also proposed (Stewart, Andriluka, and Ng 2016; Balles

and Fischbacher 2019). The goal of the previous studies fo-

cuses on measuring symmetric distances between the ground

truth set and predicted set (usually with an equal size), while

our loss tries to reconstruct the ground truth set using much

fewer codebook embeddings.

Other ways to achieve the permutation invariant loss

for neural networks include sequential decision mak-

ing (Welleck et al. 2018), mixture of experts (Yang et al.

2018b; Wang, Cho, and Wen 2019), beam search (Qin et al.

2019), predicting the permutation using a CNN (Rezatofighi

et al. 2018), Transformers (Stern et al. 2019; Gu, Liu,

and Cho 2019; Carion et al. 2020) or reinforcement learn-

ing (Welleck et al. 2019). In contrast, our goal is to effi-

ciently predict a set of cluster centers that can well recon-

struct the set of observed instances rather than directly pre-

dicting the observed instances.

Conclusions

In this work, we propose a framework for learning the co-

occurring distribution of the words surrounding a sentence

or a phrase. Even though there are usually only a few words

that co-occur with each sentence, we demonstrate that the

proposed models can learn to predict interpretable cluster

centers conditioned on an (unseen) sentence.

In the sentence similarity tasks, the results indicate that

the similarity between two sets of multi-facet embeddings

well correlates with human judgments, and we can use the

multi-facet embeddings to estimate the word importance

and improve various widely-used similarity measurements

in a pre-trained word embedding space such as GloVe. In a

single-document extractive summarization task, we demon-

strate multi-facet embeddings significantly outperform clas-

sic unsupervised sentence embedding or individual word

embeddings. Finally, the results of phrase similarity tasks

suggest that a single embedding might be sufficient to repre-

sent the co-occurring word distribution of a phrase.

Acknowledgements

We thank Ao Liu and Mohit Iyyer for many helpful discus-

sions and Nishant Yadav for suggesting several related work.

We also thank the anonymous reviewers for their construc-

tive feedback.

This work was supported in part by the Center for Data

Science and the Center for Intelligent Information Retrieval,

in part by the Chan Zuckerberg Initiative under the project

Scientific Knowledge Base Construction, in part using high

performance computing equipment obtained under a grant

from the Collaborative R&D Fund managed by the Mas-

sachusetts Technology Collaborative, in part by the National

Science Foundation (NSF) grant numbers DMR-1534431

and IIS-1514053.

Any opinions, findings, conclusions, or recommendations

expressed in this material are those of the authors and do not

necessarily reflect those of the sponsor.

6963

Ethics Statement

We propose a novel framework, neural architecture, and loss

to learn multi-facet embedding from the co-occurring statis-

tics in NLP. In this study, we exploit the co-occurring re-

lation between a sentence and its nearby words to improve

the sentence representation. In our follow-up studies, we dis-

cover that the multi-facet embeddings could also be used to

learn other types of co-occurring statistics. For example, we

can use the co-occurring relation between a scientific pa-

per and its citing paper to improve paper recommendation

methods in Bansal, Belanger, and McCallum (2016). Paul,

Chang, and McCallum (2021) use the co-occurring relation

between a sentence pattern and its entity pair to improve re-

lation extraction in Verga et al. (2016). Chang et al. (2021)

use the co-occurring relation between a context paragraph

and its subsequent words to control the topics of language

generation. In the future, the approach might also be used

to improve the efficiency of document similarity estima-

tion (Luan et al. 2020).

On the other hand, we improve the sentence similarity and

summarization tasks in this work using the assumption that

important words are more likely to appear in the nearby sen-

tences. The assumption might be violated in some domains

and our method might degrade the performances in such do-

mains if the practitioner applies our methods without con-

sidering the validity of the assumption.

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