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Learning Sparse Prototypes for Text Generation
Junxian He†, Taylor Berg-Kirkpatrick‡, Graham Neubig††Carnegie
Mellon University; ‡University of California San
Diego{junxianh,gneubig}@cs.cmu.edu, [email protected]
Abstract
Prototype-driven text generation uses non-parametric models that
first choose froma library of sentence “prototypes” and then modify
the prototype to generate theoutput text. While effective, these
methods are inefficient at test time as a resultof needing to store
and index the entire training corpus. Further, existing
methodsoften require heuristics to identify which prototypes to
reference at training time.In this paper, we propose a novel
generative model that automatically learns asparse prototype
support set that, nonetheless, achieves strong language
modelingperformance. This is achieved by (1) imposing a
sparsity-inducing prior on theprototype selection distribution, and
(2) utilizing amortized variational inferenceto learn a prototype
retrieval function. In experiments, our model outperformsprevious
prototype-driven language models while achieving up to a 1000x
memoryreduction, as well as a 1000x speed-up at test time. More
interestingly, we showthat the learned prototypes are able to
capture semantics and syntax at differentgranularity as we vary the
sparsity of prototype selection, and that certain
sentenceattributes can be controlled by specifying the prototype
for generation.1
1 Introduction
Language models (LMs) predict a probability distribution over
text, and are a fundamental technologywidely studied in the natural
language processing (NLP) community (Bengio et al., 2003; Merityet
al., 2018; Dai et al., 2019). Modern LMs are almost exclusively
based on parametric recurrent(Mikolov et al., 2010; Sundermeyer et
al., 2012) or self-attentional (Vaswani et al., 2017; Al-Rfouet
al., 2019) neural networks. These models are of interest
scientifically as one of the purest tests ofour ability to capture
the intricacies of human language mathematically (Linzen et al.,
2016; Kuncoroet al., 2017; Petroni et al., 2019). They also have
broad downstream applications in generating text insystems such as
machine translation (Bahdanau et al., 2015), summarization (Rush et
al., 2015), ordialog generation (Sordoni et al., 2015), as well as
in the unsupervised representation learners thatnow power many
applications in NLP (Devlin et al., 2018; Liu et al., 2019; Yang et
al., 2019).
However, there has been a recent move towards non-parametric
neural LMs (Guu et al., 2018;Khandelwal et al., 2020b) that
generate sentences by first selecting examples from an
externaldatastore. For instance, Khandelwal et al. (2020b) model
the token-level probability at test timeby interpolating the
language model with a kNN distribution from the nearest
context-token pairsin the datastore, while Guu et al. (2018) store
external memories on sentence level and feature
aprototype-then-edit process of (1) selecting a prototype sentence
from a the prototype datastore, and(2) editing this prototype to
the final desired output. In this paper, we focus on the
prototype-then-editmodel family which is a lot lighter relatively
in terms of memory and time cost at test time.
Intuitively, these non-parametric LMs are attractive because
they help remove some of the pressureon the parametric model to
memorize the entirety of the language it must model. These
intuitiveadvantages are also borne out in superior performance on
language modeling tasks (Guu et al.,
1Code is available at
https://github.com/jxhe/sparse-text-prototype.
34th Conference on Neural Information Processing Systems
(NeurIPS 2020), Vancouver, Canada.
https://github.com/jxhe/sparse-text-prototype
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I ordered a pizza with sauce
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X3i4mQNzyqfo1x/0OiXrlTXlj0yiLVu+bZtNQ50xtlSMJm7p5kXmjDFRzT9FDlMMo8rcaL1lnRRKrJ/3LRffnd8sWMktBcdttnHzS9d63cbli8hZGa6H78yBKx3Le3Dq5X6hHxnhs+GqzXAGetcIPwYtSL80qmy9htuXtTTKhpidTBjCYePv4iTiFPwhvmGUPW+vOQ57zXJ3OWfEvqPEi1B3Av4NNdfW9QHVOmkC8am9SqxXD9O8XIvooqL56HTAGOfCHuM/i7GlYgP+wbrBMHYK5nOOxPrAXhqnh0i9w/BM8/NfXv/6wsd38n0qrFzfvt7bfbW1f/LTxp93qfzH9du0f1/5p7c3a9tof1/60drTWW7teC9bytf9a+++1//mw+eHyw/2Hzyb017+q6vzDmvPzYfR/rPTO/w==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
Prototype distribution
Prototype sentence Edit vector
0 1 2 3 N
NObserved sentence
xn
tn
θ
znvMF prior
αDirichlet
hyperparam
θ
xn
tn zn
N
Inference Diagram
q(zn | tn, xn)q(tn |xn)
Figure 1: Left: the proposed generative model to generate data
by editing prototypes. Shaded circles denote theobserved variables
and unshaded denote the latents. Prototypes are sampled from a
sparse prototype distributionwhich itself is a random variable
sampled from a Dirichlet prior distribution. Right: the inference
diagram ofthe model, with q(tn|xn) being the prototype retriever
and q(zn|tn,xn) being the inverse editor.
2018; Khandelwal et al., 2020b), as well as down-stream
applications such as dialogue responsegeneration (Weston et al.,
2018; Wu et al., 2019), machine translation (Gu et al., 2018; Bapna
& Firat,2019; Khandelwal et al., 2020a), and code generation
(Hashimoto et al., 2018; Hayati et al., 2018).In addition, the
prototypes and continuous representations of the edits in
prototype-based modelslend an element of interpretability to the
modeling process. On the down side, however,
previousprototype-driven generation methods usually need to store
and index a large prototype candidate pool(in general the whole
training dataset), leading to significant issues with memory and
speed efficiencyat test time.
In this paper, we hypothesize that, in fact, a small set of
prototypes is sufficient to achieve the greatmajority of the gains
afforded by such non-parametric models. Intuitively, in a large
corpus manysentences look very similar and may be represented by
minor transformations of a single prototypesentence. For example,
the sentence “I ordered a burger with fries” can serve as the
prototype for datasamples with the form “I ordered [NOUN PHRASE]
with [NOUN PHRASE]”. This is evidencedby Guu et al. (2018)’s
observation that 70% of the test set in the Yelp restaurant review
corpus (Yelp,2017) is within word-token Jaccard distance 0.5 of one
training sentence.
To take advantage of this intuition, we propose a novel
generative model that samples prototypesfrom a latent prototype
distribution, which itself is sampled from a symmetric Dirichlet
prior, asshown in Figure 1 (Section 3.1). The Dirichlet prior with
appropriate hyperparameters is able toencourage a sparse prototype
selection distribution, allowing us to reduce the prototype support
set attest time to greatly improve efficiency. Moreover, we utilize
amortized variational inference (Kingma& Welling, 2013) to
train our model, which introduces a learnable prototype retriever
to identifyprototypes useful for generating each sentence (Section
3.2). This is different from (Guu et al., 2018)where prototypes for
each sentence are fixed before training through edit distance
heuristics.
We evaluate our approach on the MSCOCO (Lin et al., 2014) and
Yelp restaurant review (Yelp, 2017)corpora. Our method is able to
improve perplexity over the neural language model baseline by up
to14 points and previous neural editor model by 6 points while
achieving over 1000x memory savingsand a 1000x speedup at test time
(Section 4.2). Interestingly, we find that the learned prototypes
areable to represent different features when varying sparsity
levels – a strong sparsity prior forces themodel to share
prototypes and the induced prototypes turn out to represent more
generic features (e.g.syntactic form of the sentence). On the text
generation side, our model is able to generate sentencesthat
resemble the given prototype while allowing for smooth
interpolation on the edit space as well(Section 4.3).
2 Background
The prototype-then-edit framework defines a non-parametric way
to augment text generation models.Formally, given a corpus X =
{xn}Nn=1,2 the model generates each observed example xn by:
(1)retrieving a prototype sequence tn, (2) generating a continuous
edit representation zn, and (3)
2Below, we sometimes ignore the subscript to simplify notation
when there is no confusion.
2
-
generating xn conditioned on tn and zn. These intermediate
prototype and edit representationvariables can depend on extra
context in conditional generation tasks (Hodosh et al., 2013; Gu et
al.,2018), or are randomly sampled in unconditioned language
modeling. In this paper, we focus on thelatter, but our methods
could likely be applied to the former as well.
For unconditioned language modeling, Guu et al. (2018) define
the data likelihood as:
p(X) =Y
n
X
tn
Z
zn
p(zn)p(tn)p�(xn|tn, zn)dzn, (1)
where p(tn) is the prior distribution over prototypes and
defined as a uniform distribution overall training examples, p(zn)
is a continuous distribution over the edit vector, and p�(xn|tn,
zn)represents a sequence-to-sequence model parameterized by �. This
model is referred to as the neuraleditor. Guu et al. (2018)’s
stated goal of the neural editor is to take direct advantage of
trainingexamples to improve language modeling performance while
capturing interpretable semantic orsyntactic properties in the
latent prototype and edit vector variables. However, because the
prototypesare selected from the entire training dataset, such a
formulation sacrifices memory and speed efficiencydue to the
necessity of indexing and searching every training example at test
time. In the followingsection, we detail our approach to mitigate
this issue through the learning of sparse prototypes.
3 Method
First we present our our proposed generative model, then we
describe the learning and inferencetechniques for this model
class.
3.1 Model Structure
In the previous formulation, Eq. 1, maintaining the entire
training dataset at test time is necessary dueto assuming a uniform
prior over prototypes p(t). Motivated by the hypothesis that a much
smallerprototype set would suffice to achieve comparable
performance, however, we believe that p(t) can bea sparse
distribution where the probability mass concentrates on only a few
representative prototypes.Since which training examples are
representative as prototypes is unknown in advance, we propose
tomodel the prototype distribution p(t) as a latent variable,
endowing the model with freedom to infera sparse prototype
posterior automatically. We define ✓ ⌘ p(t) and further assume that
the latentprototype distribution ✓ is sampled from a prior
distribution p↵(✓) (detailed below) which is able toencourage a
sparse probability distribution, given appropriate hyperparameters.
The graphical modelis depicted in Figure 1, which gives the
following joint likelihood:
p({xn, tn, zn}Nn=1, ✓;↵,�) = p↵(✓)Y
n
p(tn|✓)p(zn)p�(xn|tn, zn). (2)
The log marginal likelihood of the data, which we will
approximate during training is:
log p(X;�,↵) = log
Z
✓p↵(✓)
hY
n
X
tn
Z
zn
p(tn|✓)p(zn)p�(xn|tn, zn)dznid✓. (3)
This is a general framework for learning sparse prototypes that
we refer to as the sparse neural editor,and in this work we
specifically experiment with the following parameterization to
instantiate thismodel class:
Prior over prototype distribution p↵(✓): We employ the Dirichlet
distribution as p↵(✓): p↵(✓) /QNk=1 ✓
↵k�1k . The support of Dirichlet distribution is the standard N
� 1 probability simplex. Here
we use the symmetric Dirichlet distribution which has the same ↵
value for all components sincewe have no prior knowledge favoring
one component over another. ↵ is positive and also referredto as
the concentration parameter, where smaller ↵ prefers a sparser
prototype distribution ✓, with↵ = 1 equivalent to a uniform
distribution over the probability simplex. In our experiments, we
oftenchoose ↵ < 1 to encourage sparsity.
Prior over edit vector p(z): We follow Guu et al. (2018) and
utilize a von-Mises Fisher (vMF)distribution to model p(z). The vMF
distribution places mass on the surface of the unit sphere, and
isparameterized by the mean direction vector µ and concentration
parameter as vMF(·|µ,). Thus,
3
-
information about the edit is captured through the directions of
different unit vector samples. Xu &Durrett (2018) empirically
show that the vMF distribution has the advantage of overcoming
posteriorcollapse that plagues a large amount of previous work in
latent variable models of text (Bowmanet al., 2016; He et al.,
2019). While Guu et al. (2018) add additional randomness on the
norm ofedit vectors by multiplying the vMF distribution with
another uniform distribution, we sample editvectors from a uniform
vMF distribution directly, which simplifies the model but we
nonethelessfound sufficient to obtain competitive results.
Formally, we define p(z) = vMF(z|·, 0).
The editor p�(x|t, z): Generally p�(x|t, z) can be parameterized
by any standard Seq2Seq modelwith the edit vector z incorporated.
To compare with Guu et al. (2018) directly in the experiments,
inthis work we adopt the same attentional LSTM architecture
(Hochreiter & Schmidhuber, 1997). z isutilized to predict the
initial hidden state of the decoder and concatenated to the input
for the decoder.
3.2 Learning and Inference
Ideally the log marginal likelihood in Eq. 3 should be optimized
during training. However, computa-tion is intractable due to
marginalization of latent variables, and we resort to amortized
variationalinference (Kingma & Welling, 2013), optimizing its
evidence lower bound (ELBO) instead:
log p(X;�,↵) � LELBO(X;�,↵,�t|x,�z|t,x,�)
=X
n
nEq�t|x (tn|xn)q�z|t,x (zn|tn,xn)[log p�(xn|tn, zn)]| {z }
reconstruction log likelihood Lrec
� Eq�t|x (tn|xn)[DKL(q�z|t,x(zn|tn,xn)||p(zn))]
� Eq�(✓)[DKL(q�t|x(tn|xn)||p(tn|✓))]o�DKL(q�(✓)||p↵(✓)),
(4)
where q represents the variational distribution to approximate
the model posterior distribution andadmits the following
factorization form:
q(✓, {tn, zn}Nn=1|X;�,�t|x,�z|t,x) = q�(✓)Y
n
q�t|x(tn|xn)q�z|t,x(zn|tn,xn). (5)
Note that we make conditional independence assumption between ✓
and other latent variables in q tosimplify the approximate
posterior, following common practice in traditional mean field
variationalinference. The inference diagram is depicted in Figure
1. The optimal q�(✓) to maximize Eq. 4 is aDirichlet distribution
parameterized by � 2 RN+ (proof is in Appendix A), i.e., q�(✓) =
Dir(✓;�).3And q�t|x(t|x) = Cat(t; f�t|x(x)), the prototype
retriever, is a categorical distribution over trainingexamples
parameterized by a neural network f�t|x(x). We assume
q�z|t,x(z|t,x), the inverse neuraleditor, is a vMF distribution
q�z|t,x(z|t,x) = vMF(g�z|t,x(t,x),) where the mean
directionparameter is from an encoder g that encodes t and x
parameterized by �z|t,x, and the scalarconcentration parameter is a
hyperparameter. Pre-fixing results in a constant KL divergence
termassociated with z and proves to be effective to mitigate the
posterior collapse issue (Xu & Durrett,2018) where x and z
become independent. Yet there might be still posterior collapse on
t where, forexample, the prototype retriever always predicts a
uniform distribution or a degenerate distributionconcentrated on a
certain prototype regardless of x. To overcome this issue, we
follow (Li et al.,2019) to combine annealing (Bowman et al., 2016)
and free-bits techniques (Kingma et al., 2016)and apply them to the
term Eq�(✓)[DKL(q�t|x(tn|xn)||p(tn|✓))].Notably, the variational
distribution family defined in Eq. 5 admits tractable closed-form
expressionsof all three KL divergence terms in Eq. 4 (detailed
derivations and expressions are in Appendix A). Tocompute the
reconstruction log likelihood Lrec, expectations over z can be
efficiently approximatedby the reparameterization trick for the vMF
distribution (Guu et al., 2018). However, the prototype tis
discrete and non-differentiable, and summing over all prototypes t
to compute Lrec is infeasibledue to the evaluation burden of log
p�(x|t, z). Thus, we use the REINFORCE algorithm (Williams,1992) to
compute the gradients of �t|x contributed from Lrec as:
@Lrec@�t|x
=1
L
LX
l=1
⇣Eq�z|t,x (z|t(l),x)
⇥log p�(x|t(l), z)
⇤� b
⌘@ log q�t|x(t(l)|x)@�t|x
, (6)
3q�(✓) is not symmetric and � is a vector.
4
-
where t(l) are samples from q�t|x(t|x). We use an average reward
from L samples as the baseline b.The neural parameters
�,�t|x,�z|t,x are updated with stochastic gradient descent to
maximize Eq. 4.With respect to the posterior Dirichlet parameter �,
we found in preliminary experiments that classicgradient descent
was unable to update it effectively – � was updated too slowly and
the Dirichlet priorbecame decoupled with the model. Thus, we
instead update � with stochastic variational inference(SVI, Hoffman
et al. (2013)) based on the formula of the optimal �⇤ given
q�t|x(t|x) (derivationscan be found in Appendix A):
�⇤k = ↵+XN
n=1q�t|x(tn = xk|xn). (7)
It is infeasibly expensive to keep � optimal under current
q�t|x(t|x) at each training step, as it wouldinvolve summing over
all training examples. Thus we perform SVI, which uses a batch of
examplesto approximate Eq. 7, leading to the following update
form:
�(t)k = (1� ⇢t)�(t�1)k + ⇢t
⇣↵+
N
B
XBi=1
q�t|x(ti = xk|xi)⌘, ⇢t = (t+ �)
�⌧ , (8)
where B is the batch size, ⇢t is the step-size at iteration t, ⌧
2 (0.5, 1] is the forgetting rate, and� � 0 is the delay parameter
to down-weight early iterations.We note that our training algorithm
is different from Guu et al. (2018) in that we use a
learnableprototype retriever q�t|x(t|x) to derive a lower bound as
the objective while Guu et al. (2018) directlyapproximate
marginalization over t. They use heuristics to fix the prototype
set for each x to beexamples similar to x in terms of edit
distance, which might produce suboptimal prototypes for
thegenerative model and also does not permit the learning of sparse
prototype support.
Sparsity and scalability: After training we expect to be able to
infer a sparse prototype distribution✓ with most components being
almost zero, based on which we can prune and store the entries over
aparticular probability threshold only, improving memory- and
time-efficiency at test time. Specifically,we compute mean of ✓
under the Dirichlet posterior: Eq�(✓)[✓k] = �k/
Pi �i, and then take the
largest M entries that occupy 90% of the probability mass. At
test time, we only maintain these Mprototypes and the prototype
retriever q�t|x(t|x) is re-normalized accordingly. One issue
presentduring training is that q�t|x(t|x) cannot fit into memory
when dealing with large datasets since it is acategorical
distribution over all training examples. In this work, we randomly
downsample a subset oftraining data as our prototype library before
training if memory is unable to fit all training examples,and learn
the sparse prototypes on top of this subsampled corpus. This acts
like a rough pre-filteringand in Section 4 we show that it suffices
to learn good prototypes and achieve competitive languagemodeling
performance. We leave more advanced techniques to address this
issue (e.g. dynamicallyupdating the prototype library) as future
work.
Architectures: We now describe the neural architectures we use
for the prototype retriever q(t|x)and inverse neural editor
q(z|t,x). q(t|x) is defined as:
q(t = xk|x) /⇢exp
�h(xk,x)/µ
�if xk 6= x
0 if xk = x,h(xk,x) = Embed(xk)>W Embed(x), (9)
I ordered sweet potato fries
I ordered a burger
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YAHHLp+q/Oe53SNQrb8obm0ZZtHrfNJuGOmdqqxxJ2NTNi8wbZaCae4oeohxGkb/VeMk6K5JYPelfLro/vVu2kFkKittu4+STrve+jcsVk7cwWgvdnwZROpbz5tbJ/UI9MsZjw1eb5QrwrBV+CF6UemlW2XwJsy1vb5IJNT2ZMoDBxNvHT8Qp/F54wyx72Fp3HvKc5+p0zop/Q40Xoe4A/h5sqqtvBapz0gTiVXuTWq0Ypv9/IaKPguqr1wFjkAN/iPsszp6GBfgP6wbL1CFo/i6p/gMlw9Rw6Rc4/gke/uvrX77b2G7+pdLqxc37re13W9sXP2z8ebf6K6Zfrf1u7V/X3qxtr/1x7c9rR2u9teu1YC1Z+6+1/177nw9/+HD+4ebDnQn95S+qOv+y5vx88P8PehDN2A==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
= =
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DimMXYx6QvvV1MgLjlU/XrEfc7JOqVN+WNTaMsWr1vmk1DnTO1VY4kbOrmReaNMlDNzaL7KIdR5G81XrLOiiRWT/qXi+4Pb5YtZJaC4rbbODnT9d62cbli8hZGa6H7wyBKx/KxuXVyv1CPjPHY8NVmuQI8a4UfghelXppVNl/CfMvbm2RCTU+mDGAw8fbxE3EKfxDeMMvut9adhzznuTqds+I/UONFqDuAfweb6uprgeqcNIF41d6kViuG6d/PRPRRUH31OmAMcuAPcZ/F2WxYgH+/brBMHYK5fMRjfWAvDFPDpV/g+Cd4+K+vf/5mY7v5P5VWL27ebm2/2dq++G7jT7vV/2L6xdrv1n6/9mpte+0/1/60drTWW7teC9ama39d+9va/77bfnf77od3fzahP/1JVee3a87Pu+j/AQxz0L4=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