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, tberg@eng.ucsd.edu

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)

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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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