#  From Paraphrasing to Semantic Parsing: Unsupervised Semantic Parsing via
Synchronous Semantic Decoding

Shan Wu1,3, Bo Chen1, Chunlei Xin1,3, Xianpei Han1,2,11footnotemark: 1
${}^{\,}$, Le Sun1,2, ${}^{\,}$,
Weipeng Zhang4, Jiansong Chen4, Fan Yang4, Xunliang Cai4
1Chinese Information Processing Laboratory 2State Key Laboratory of Computer
Science
Institute of Software, Chinese Academy of Sciences, Beijing, China
3University of Chinese Academy of Sciences, Beijing, China 4Meituan
<EMAIL_ADDRESS>
<EMAIL_ADDRESS>
<EMAIL_ADDRESS>Corresponding
Author

(2021-5-26 14:08:30)

###### Abstract

Semantic parsing is challenging due to the structure gap and the semantic gap
between utterances and logical forms. In this paper, we propose an
unsupervised semantic parsing method – Synchronous Semantic Decoding (SSD),
which can simultaneously resolve the semantic gap and the structure gap by
jointly leveraging paraphrasing and grammar-constrained decoding.
Specifically, we reformulate semantic parsing as a constrained paraphrasing
problem: given an utterance, our model synchronously generates its canonical
utterance111Canonical utterances are pseudo-language representations of
logical forms, which have the synchronous structure of logical forms.(Berant
and Liang, 2014; Xiao et al., 2016; Su and Yan, 2017; Cao et al., 2020) and
meaning representation. During synchronous decoding: the utterance
paraphrasing is constrained by the structure of the logical form, therefore
the canonical utterance can be paraphrased controlledly; the semantic decoding
is guided by the semantics of the canonical utterance, therefore its logical
form can be generated unsupervisedly. Experimental results show that SSD is a
promising approach and can achieve competitive unsupervised semantic parsing
performance on multiple datasets.

##  1 Introduction

Semantic parsing aims to translate natural language utterances to their formal
meaning representations, such as lambda calculus (Zettlemoyer and Collins,
2005; Wong and Mooney, 2007), FunQL (Kate et al., 2005; Lu et al., 2008), and
SQL queries. Currently, most neural semantic parsers (Dong and Lapata, 2016;
Chen et al., 2018b; Zhao et al., 2020; Shao et al., 2020) model semantic
parsing as a sequence to sequence translation task via encoder-decoder
framework.

Figure 1:  Different from previous staged methods (indicated by gray lines),
our method generates canonical utterance and logical form synchronously. The
semantic gap and the structure gap are simultaneously resolved by jointly
leveraging paraphrasing and grammar-constrained decoding. Thus, our
synchronous decoding employs both the semantic and the structure constraints
to solve unsupervised semantic parsing.

Semantic parsing is a challenging task due to the structure gap and the
semantic gap between natural language utterances and logical forms. For
structure gap, because utterances are usually word sequences and logical forms
are usually trees/graphs constrained by specific grammars, a semantic parser
needs to learn the complex structure transformation rules between them. For
semantic gap, because the flexibility of natural languages, the same meaning
can be expressed using very different utterances, a semantic parser needs be
able to map various expressions to their semantic form. To address the
structure gap and the semantic gap, current semantic parsers usually rely on a
large amount of labeled data, often resulting in data bottleneck problem.

Previous studies have found that the structure gap and the semantic gap can be
alleviated by leveraging external resources, therefore the reliance on data
can be reduced. For structure gap, previous studies found that constrained
decoding can effectively constrain the output structure by injecting grammars
of logical forms and facts in knowledge bases during inference. For example,
the grammar-based neural semantic parsers (Xiao et al., 2016; Yin and Neubig,
2017) and the constrained decoding algorithm (Krishnamurthy et al., 2017). For
semantic gap, previous studies have found that paraphrasing is an effective
technique for resolving the diversity of natural expressions. Using
paraphrasing, semantic parsers can handle the different expressions of the
same meaning, therefore can reduce the requirement of labeled data. For
example, supervised methods (Berant and Liang, 2014; Su and Yan, 2017) use the
paraphrasing scores between canonical utterances and sentences to re-rank
logical forms; Two-stage (Cao et al., 2020) rewrites utterances to canonical
utterances which can be easily parsed. The main drawback of these studies is
that they use constrained decoding and paraphrasing independently and
separately, therefore they can only alleviate either semantic gap or structure
gap.

In this paper, we propose an unsupervised semantic parsing method –
Synchronous Semantic Decoding (SSD), which can simultaneously resolve the
structure gap and the semantic gap by jointly leveraging paraphrasing and
grammar-constrained decoding. Specifically, we model semantic parsing as a
constrained paraphrasing task: given an utterance, we synchronously decode its
canonical utterance and its logical form using a general paraphrase model,
where the canonical utterance and the logical form share the same underlying
structure. Based on the synchronous decoding, the canonical utterance
generation can be constrained by the structure of logical form, and the
logical form generation can be guided by the semantics of canonical form. By
modeling the interdependency between canonical utterance and logical form, and
exploiting them through synchronous decoding, our method can perform effective
unsupervised semantic parsing using only pretrained general paraphrasing model
– no annotated data for semantic parsing is needed.

We conduct experiments on Geo and Overnight. Experimental results show that
our method is promising, which can achieve competitive unsupervised semantic
parsing performance, and can be further improved with external resources. The
main contributions of this paper are:

  * •

We propose an unsupervised semantic parsing method – Synchronous Semantic
Decoding , which can simultaneously resolve the semantic gap and the structure
gap by jointly leveraging paraphrasing and grammar-constrained semantic
decoding.

  * •

We design two effective synchronous semantic decoding algorithms – rule-level
inference and word-level inference, which can generate paraphrases under the
grammar constraints and synchronously decode meaning representations.

  * •

Our model achieves competitive unsupervised semantic parsing performance on
Geo and Overnight datasets.

Figure 2:  Overview of our approach.  The sentence is paraphrased to
canonical utterance and parsed to  logical form synchronously. When decoding
“traverse”, the paraphrase model tends to generate the words such as “run”,
“flow”, “traverse” to preserve semantics. And synchronous grammar limits the
next words of the canonical utterance to follow the candidate production
rules. Then it is easy to discard “run” and “flow”, and select the most likely
word “traverse” with its production rule from the candidates. In this parper,
we propose rule-level and word-level inference methods to decode words and
production rules synchronously.

##  2 Model Overview

We now present overview of our synchronous semantic decoding algorithm, which
can jointly leverage paraphrasing and grammar-constrained decoding for
unsupervised semantic parsing. Given an utterance, SSD reformulates semantic
parsing as a constrained paraphrasing problem, and synchronously generates its
canonical utterance and logical form. For example in Fig. 1, given “How many
rivers run through Texas”, SSD generates “What is the number of river traverse
State0” as its canonical form and Answer(Count(River(Traverse_2(
State0)))) as its logical form. During synchronous decoding: the utterance
paraphrase generation is constrained by the grammar of logical forms,
therefore the canonical utterance can be generated controlledly; the logical
form is generated synchronously with the canonical utterance via synchronous
grammar. Logical form generation is controlled by the semantic constraints
from paraphrasing and structure constraints from grammars and database
schemas. Therefore the logical form can be generated unsupervisedly.

To this end, SSD needs to address two challenges. Firstly, we need to design
paraphrasing-based decoding algorithms which can effectively impose grammar
constraints on inference. Secondly, current paraphrasing models are trained on
natural language sentences, which are different from the unnatural canonical
utterances. Therefore SSD needs to resolve this style bias for effective
canonical utterance generation.

Specifically, we first propose two inference algorithms for constrained
paraphrasing based synchronous semantic decoding: rule-level inference and
word-level inference. Then we resolve the style bias of paraphrase model via
adaptive fine-tuning and utterance reranking, where adaptive fine-tuning can
adjust the paraphrase model to generate canonical utterances, and utterance
reranking resolves the style bias by focusing more on semantic coherence. In
Sections 3-5, we provide the details of our implementation.

##  3 Synchronous Semantic Decoding

Given an utterance $x$, we turn semantic parsing into a constrained
paraphrasing task. Concretely, we use synchronous context-free grammar as our
synchronous grammar, which provides a one-to-one mapping from a logical form
$y$ to its canonical utterance $c^{y}$. The parsing task
$\hat{y}=\arg\max\limits_{y\in\mathcal{Y}}p_{\text{{parse}}}(y|x)$ is then
transferred to
$\hat{y}=\arg\max\limits_{y\in\mathcal{Y}}p_{\text{{paraphrase}}}(c^{y}|x)$.
Instead of directly parsing utterance into its logical form, SSD generates its
canonical utterance and obtains its logical form based on the one-to-one
mapping relation. In following we first introduce the grammar constraints in
decoding, and then present two inference algorithms for generating paraphrases
under the grammar constraints.

###  3.1 Grammar Constraints in Decoding

Synchronous context-free grammar(SCFG) is employed as our synchronous grammar,
which is widely used to convert a meaning representation into an unique
canonical utterance (Wang et al., 2015; Jia and Liang, 2016). An SCFG consists
of a set of production rules: $N\rightarrow\left<\alpha,\beta\right>$, where
$N$ is a non-terminal, and $\alpha$ and $\beta$ are sequence of terminal and
non-terminal symbols. Each non-terminal symbol in $\alpha$ is aligned to the
same non-terminal symbol in $\beta$, and vice versa. Therefore, an SCFG
defines a set of joint derivations of aligned pairs of utterances and logical
forms.

SCFGs can provide useful constraints for semantic decoding by restricting the
decoding space and exploiting the semantic knowledge:

##### Grammar Constraints

The grammars ensure the generated utterances/logical forms are grammar-legal.
In this way the search space can be greatly reduced. For example, when
expanding the non-terminal $r in Fig 1 we don’t need to consider the words
“run” and “flow”, because they are not in the candidate grammar rules.

##### Semantic Constraints

Like the type checking in Wang et al. (2015), the constraints of knowledge
base schema can be integrated to further refine the grammar. The semantic
constraints ensure the generated utterances/logical forms will be semantically
valid.

###  3.2 Decoding

####  3.2.1 Rule-Level Inference

(a) Rule-Level Inference

(b) Word-Level Inference

Figure 3: From the utterance “which state is city0 in”, two inference methods
generate its canonical utterance “what is state that city0 located in” and its
logical form Answer(State(Loc_1(City0))). The ways they handle non-terminal $c
which is not at the end of utterance-side production rule are represented by
purple lines.

1

Input : input utterance $x$, paraphrasing model $Para$, beam size $B$, maximum
output length $L$, SCFG rules $R$, maximum search depth $K$;

2

3$beam_{0}\leftarrow\\{\left<s\right>\\}$

4$outputs\leftarrow\\{\\}$

5for  _$t=1$ to $L$_ do

6 for  _${\rm hypothesis}$ $c$ in $beam_{t-1}$ _ do

7 for  _$r$ in expand rules for $c$ _ do

8 if  _all non-terminals in $r_{\beta}$ are on the right_ then

9 $c^{\prime}\leftarrow\text{Expand}(c,r)$

10 $beam_{t}\leftarrow beam_{t}\cup\\{c^{\prime}\\}$

11 else

12 $c^{\prime}\leftarrow\text{expand}(c,r)$

13 $beam_{t}^{c^{\prime}}\leftarrow\\{c^{\prime}\\}$

14 for  _$k=1$ to $K$_ do

15 for  _${\rm hypothesis}$ $h$ in $beam_{t+k-1}^{c^{\prime}}$_ do

16 $r_{h}$ $\leftarrow$ expand rules for $h$’s first non-terminal

17
$beam_{{}_{t\\!+\\!k\\!}}^{c^{\prime}}\leftarrow\\!beam_{{}_{t\\!+\\!k}}^{c^{\prime}}\\!\\!\cup\text{Expand}(h,r_{h})$

18
$beam_{{}_{t\\!+\\!k\\!}}^{c^{\prime}}\leftarrow\text{NBest}(beam_{{}_{t\\!+\\!k\\!}}^{c^{\prime}},B)$

19 Move utterances from $beam_{{}_{t\\!+\\!k\\!}}^{c^{\prime}}$ to
$beam_{{}_{t\\!+\\!k\\!}}$, if non-terminals are on the right of the
utterances.

20 $beam_{t}\leftarrow$ NBest($beam_{t}$,$B-|outputs|$)

21 Move full utterances from $beam_{t}$ to $outputs$

22 if  _$beam_{t}$ is empty_ then

23 return _$outputs$_

return _$outputs$_

Algorithm 1 Rule-level inference

One strategy to generate paraphrase under the grammar constraint is taking the
grammar rule as the decoding unit. Grammar-based decoders have been proposed
to output sequences of grammar rules instead of words(Yin and Neubig, 2017).
Like them, our rule-level inference method takes the grammar rule as the
decoding unit. Figure 3 (a) shows an example of our rule level inference
method.

When the non-terminal in the utterance-side production rule is at the end of
the rule (e.g., $\text{\$e}\rightarrow\left<\text{state
\$s},\texttt{State(}\text{\$s}\texttt{)}\right>$), denoting the utterance-side
production rule as $r_{\beta}=[w_{1},w_{2},...,w_{L_{r}},N]$, we can simply
expand non-terminals in canonical utterances by this rule, and generate the
canonical utterances from left to right with probabilities computed by:

$\displaystyle P(c^{y_{\leq
t}}|x)=P(c^{y_{<t}}|x)\prod_{i=1}^{L_{r}}P_{{\text{paraphrase}}}(w_{i}|x,c^{y_{<t}},w_{<i})$
(1)

Otherwise, we generate the next production rules to expand this rule (i.e.,
rule with purple line), until there is no non-terminal on the left of words,
or the generating step reaches the depth of $K$. We use beam search during the
inference. The inference details are described in Algorithm 1.

####  3.2.2 Word-Level Inference

Except for rule-level inference, we also propose a word-level inference
algorithm, which generates paraphrases word by word under the SCFG
constraints.

Firstly, we construct a deterministic automaton using LR(1) parser (Knuth,
1965) from the CFG in utterance side. The automaton can transit from one state
to another in response to an input. The inputs of the automaton are words and
the states of it are utterance/logical form segments. LR(1) parser peeks ahead
one lookahead input symbol, and the state transition table describes the
acceptable inputs and the next states.

Then, in each decoding step we generate a word with a new state which is
transited from previous state. An example is shown in Figure 3 (b). Only the
acceptable words in the current state can be generated, and the end-of-
sentence symbol can only be generated when reaching the final state. Beam
search is also used in this inference.

##  4 Adaptive Fine-tuning

The above decoding algorithms only rely on a paraphrase generation model ,
which generates canonical utterance and logical form synchronously for
semantic parsing. We can directly use general paraphrase generation models
such as GPT-2(Radford et al., 2019), T5(Raffel et al., 2020) for SSD. However,
as described in above, there exists a style bias between natural language
sentences and canonical utterances, which hurts the performance of
unsupervised semantic paring. In this section, we describe how to alleviate
this bias via adaptive fine-tuning. Given a text generation model, after
pretraining it using paraphrase corpus, we fine-tune it using synthesized
$\left<\right.$sentence, canonical utterance$\left.\right>$ pairs.

Previous studies have shown that the pre-training on synthesized data can
significantly improve the performance of semantic parsing (Xu et al., 2020a;
Marzoev et al., 2020; Yu et al., 2020; Xu et al., 2020b). Specifically, we
design three data synthesis algorithms:
1) CUs We sample CUs from SCFGs, and preserve executable ones. As we do not
have the paired sentences, we only fine-tune the language model of the PLMs on
CUs.
2) Self Paras We use the trained paraphrase model to get the natural language
paraphrases of the sampled canonical utterances to form
$\left<\right.$sentence, canonical utterance$\left.\right>$ pairs.
3) External Paras We also use external paraphrase methods such as back
translation to get the pairs.

##  5 Utterance Reranking

Adaptive fine-tuning resolves the style bias problem by fitting a better
paraphrase model. In this section, we propose an utterance reranking algorithm
to further alleviate the style bias by reranking and selecting the best
canonical form.

Given the utterance $x$ and top-$N$ parsing results
$(y_{n},c_{n}),n=1,2,...,N$, we rerank all candidates by focusing on semantic
similarities between $x$ and $c_{n}$, so that canonical utterances can be
effectively selected. Reranking for semantic parsing has been exploited in
many previous studies (Berant and Liang, 2014; Yin and Neubig, 2019). These
works employ reranking for canonical utterances selection. Differently, our
re-ranker does not need labeled data. Formally, we measure two similarities
between $x$ and $c_{n}$ and the final reranking score is calculated by:

$\displaystyle score(x,c)=$ $\displaystyle\log p(c|x)+s_{rec}(x,c)$ (2)
$\displaystyle+s_{asso}(x,c)$

##### Reconstruction Score

The reconstruction score measures the coherence and adequacy of the canonical
utterances, using the probability of reproducing the original input sentence
$x$ from $c$ with the trained paraphrasing model: $s_{rec}(x,c)=\log
p_{pr}(x|c)$

##### Association Score

The association score measures whether $x$ and $c$ contain words that are
likely to be paraphrases. We calculate it as:

$\displaystyle s_{asso}(x,c)=$
$\displaystyle\log{\prod_{i=1}^{|c|}\sum_{j=0}^{|x|}p\left(c_{i}|x_{j}\right)a(j|i)}$
(3)
$\displaystyle+\log{\prod_{j=1}^{|x|}\sum_{i=0}^{|c|}p\left(x_{j}|c_{i}\right)a(i|j)}$

in which, $p\left(c_{i}|x_{j}\right)$ means the paraphrase probability from
$x_{j}$ to $c_{i}$, and $a(j|i)$ means the alignment probability. The
paraphrase probability and alignment are trained and inferred as the
translation model in SMT IBM model 2.

##  6 Experiments

###  6.1 Experimental Settings

##### Datasets

We conduct experiments on three datasets: Overnight($\lambda$-DCS),
Geo(FunQL), and GeoGranno, which use different meaning representations and on
different domains. Our implementations are public
available222https://github.com/lingowu/ssd.

OvernightThis is a multi-domain dataset, which contains natural language
paraphrases paired with lambda DCS logical forms across eight domains. We use
the same train/test splits as Wang et al. (2015).

Geo(FunQL)This is a semantic parsing benchmark about U.S. geography (Zelle and
Mooney, 1996) using the variable-free semantic representation FunQL (Kate et
al., 2005). We extend the FunQL grammar to SCFG for this dataset. We follow
the standard 600/280 train/test splits.

GeoGrannoThis is another version of Geo (Herzig and Berant, 2019), in which
lambda DCS logical forms paired with canonical utterances are produced from
SCFG. Instead of paraphrasing sentences, crowd workers are required to select
the correct canonical utterance from candidate list. We follow the split
(train/valid/test 487/59/278) in original paper.

| Bas. | Blo. | Cal. | Hou. | Pub. | Rec. | Res. | Soc. | Avg.
---|---|---|---|---|---|---|---|---|---
Supervised
Recombination Jia and Liang (2016) | 85.2 | 58.1 | 78.0 | 71.4 | 76.4 | 79.6 | 76.2 | 81.4 | 75.8
CrossDomain (Su and Yan, 2017) | 86.2 | 60.2 | 79.8 | 71.4 | 78.9 | 84.7 | 81.6 | 82.9 | 78.2
Seq2Action (Chen et al., 2018b) | 88.2 | 61.4 | 81.5 | 74.1 | 80.7 | 82.9 | 80.7 | 82.1 | 79.0
Dual (Cao et al., 2019) | 87.5 | 63.7 | 79.8 | 73.0 | 81.4 | 81.5 | 81.6 | 83.0 | 78.9
Two-stage (Cao et al., 2020) | 87.2 | 65.7 | 80.4 | 75.7 | 80.1 | 86.1 | 82.8 | 82.7 | 80.1
SSD (Word-Level) | 86.2 | 64.9 | 81.7 | 72.7 | 82.3 | 81.7 | 81.5 | 82.7 | 79.2
SSD (Grammar-Level) | 86.2 | 64.9 | 81.7 | 72.7 | 82.3 | 81.7 | 81.5 | 82.7 | 79.0
Unsupervised (with nonparallel data)
Two-stage (Cao et al., 2020) | 64.7 | 53.4 | 58.3 | 59.3 | 60.3 | 68.1 | 73.2 | 48.4 | 60.7
WmdSamples (Cao et al., 2020) | 31.9 | 29.0 | 36.1 | 47.9 | 34.2 | 41.0 | 53.8 | 35.8 | 38.7
SSD-Samples (Word-Level) | 71.7 | 58.7 | 60.1 | 61.7 | 57.6 | 64.3 | 70.9 | 46.0 | 61.4
SSD-Samples (Grammar-Level) | 71.3 | 58.8 | 60.6 | 62.2 | 58.8 | 65.4 | 71.1 | 49.1 | 62.2
Unsupervised
Cross-domain Zero Shot | - | 28.3 | 53.6 | 52.4 | 55.3 | 60.2 | 61.7 | - | -
GenOvernight | 15.6 | 27.7 | 17.3 | 45.9 | 46.7 | 26.3 | 61.3 | 9.7 | 31.3
Synth-Seq2Seq | 16.1 | 23.6 | 16.1 | 30.2 | 36.6 | 26.9 | 43.1 | 9.2 | 25.2
SynthPara-Seq2Seq | 28.4 | 37.3 | 33.9 | 38.1 | 39.1 | 41.7 | 62.7 | 23.3 | 38.1
SSD (Word-Level) | 68.3 | 54.9 | 51.2 | 55.0 | 54.7 | 60.2 | 65.4 | 33.6 | 55.4
SSD (Grammar-Level) | 68.8 | 58.1 | 56.5 | 56.1 | 57.8 | 59.3 | 66.9 | 37.1 | 57.6
|  |  |  |  |  |  |  |  |

Table 1: Overall results on Overnight.

##### Paraphrase Model

We obtain the paraphrase model by training T5 and GPT2.0 on WikiAnswer
Paraphrase333http://knowitall.cs.washington.edu/ paralex, we train 10 epochs
with learning rate as 1e-5. Follow Li et al. (2019), we sample 500K pairs of
sentences in WikiAnswer corpus as training set and 6K as dev set. We generate
adaptive fine-tuning datasets proportional to their labeled datasets, and
back-translation(from English to Chinese then translate back) is used to
obtain external paraphrases data. On average, we sample 423 CUs per domain,
and synthesize 847 instances per domain in Self Paras and 1252 in External
Paras.

##### Unsupervised settings

In unsupervised settings, we do not use any annotated semantic parsing data.
The paraphrase generation models are fixed after the paraphrasing pre-training
and the adaptive fine-tuning. The models are employed to generate canonical
utterances and MRs synchronously via rule-level or word-level inference. In
rule-level inference, the leftmost non-terminators are eliminated by
cyclically expanded and the maximum depth $K$ is set to 5, the beam size is
set to 20. SSD uses T5 as the pre-trained language model in all the proposed
components, including adaptive fine-tuning, reranking and the two decoding
constraints. Ablation experiments are conducted over all components with rule-
level inference.

| Bas. | Blo. | Cal. | Hou. | Pub. | Rec. | Res. | Soc. |  | Overn.
---
Avg.
| Geo
---
Granno
| Geo
---
(FunQL)
CompleteModel | 68.8 | 58.1 | 56.5 | 56.1 | 57.8 | 59.3 | 66.9 | 37.1 | 57.6 | 58.5 | 63.2
Constraints
\- Semantic | 65.5 | 54.4 | 52.4 | 51.9 | 56.5 | 57.4 | 62.0 | 35.7 | 54.5 | 56.5 | 61.1
\- Grammar | 63.9 | 52.1 | 47.6 | 50.3 | 45.3 | 52.3 | 56.3 | 29.9 | 49.7 | 50.7 | 53.9
Adaptive Fine-tuning
\- External Paras | 66.8 | 56.6 | 51.6 | 54.0 | 48.4 | 56.9 | 63.3 | 32.4 | 53.8 | 56.5 | 61.1
\- Paras (Only CUs) | 64.5 | 55.4 | 50.0 | 51.3 | 47.8 | 55.6 | 62.0 | 31.7 | 52.3 | 54.3 | 59.6
\- Fine-tuning | 63.9 | 53.6 | 48.4 | 47.6 | 44.9 | 53.2 | 62.5 | 31.4 | 50.7 | 51.8 | 55.4
Reranking
\- Reranking | 58.2 | 57.2 | 56.3 | 50.2 | 55.7 | 58.0 | 62.9 | 37.7 | 54.6 | 57.2 | 62.5
Oracle (R@20) | 71.2 | 83.2 | 86.9 | 76.9 | 82.7 | 86.9 | 88.1 | 62.8 | 79.8 | 70.9 | 81.4
Pretrained Language Models
GPT-2 | 67.0 | 54.6 | 53.7 | 55.7 | 56.1 | 58.9 | 66.4 | 32.7 | 55.6 | 58.3 | 62.1
Rand | 58.3 | 48.6 | 45.8 | 47.6 | 50.3 | 55.6 | 54.5 | 30.3 | 48.9 | 51.4 | 54.3

Table 2:  Albation results of our model with different settings on the three
datasets.

##### Unsupervised settings (with external nonparallel data)

Cao et al. (2020) have shown that external nonparallel data (including
nonparallel natural language utterances and canonical utterances) can be used
to build unsupervised semantic parsers. For fair comparison, we also conduct
unsupervised experiments with external unparallel data. Specifically, we
enhance the original SSD using the Samples methods (Cao et al., 2020): we
label each input sentences with the most possible outputs in the nonparallel
corpus and use these samples as peusdo training data – we denote this setting
as SSD-Samples.

##### Supervised settings

Our SSD method can be further enhanced using annotated training instances.
Specifically, given the annotated $\left<\text{utterance, logical
form}\right>$ instances, we first transform logical form to its canonical
form, then use them to further fine-tune our paraphrase models after
unsupervised pre-training.

##### Baselines

We compare our method with the following unsupervised baselines: 1) Cross-
domain Zero Shot(Herzig and Berant, 2018), which trains on other source
domains and then generalizes to target domains in Overnight and 2)
GenOvernight(Wang et al., 2015) in which models are trained on synthesized
$\left<\text{CU, MR}\right>$ pairs; 3) We also implement Seq2Seq baseline on
the synthesized data as Synth-Seq2Seq. 4) SynthPara-Seq2Seq is trained on the
synthesized data and $\left<\text{CU paraphrase, MR}\right>$ pairs, the
paraphrases are obtained in the same way in Section 4.

###  6.2 Experimental Results

####  6.2.1 Overall Results

|  | Geo
---
Granno
| Geo
---
(FunQL)
Supervised
DepHT (Jie and Lu, 2018) | - | 89.3
CopyNet (Herzig and Berant, 2019) | 72.0 | -
One-stage (Cao et al., 2020) | 71.9 | -
Two-stage (Cao et al., 2020) | 71.6 | -
Seq2Seq (Guo et al., 2020) | - | 87.1
SSD (Word-Level) | 72.9 | 88.3
SSD (Grammar-Level) | 72.0 | 87.9
Unsupervised (with nonparallel data)
Two-stage (Cao et al., 2020) | 63.7 | -
WmdSamples (Cao et al., 2020) | 35.3 | -
SSD-Samples (Word-Level) | 64.0 | 64.3
SSD-Samples (Grammar-Level) | 64.4 | 65.0
Unsupervised
Synth-Seq2Seq | 32.7 | 36.1
SynthPara-Seq2Seq | 41.4 | 45.4
SSD (Word-Level) | 57.2 | 62.8
SSD (Grammar-Level) | 58.5 | 63.2

Table 3: Overall results on GeoGranno and Geo(FunQL).

The overall results of different baselines and our method are shown in Table 1
and Table 3 (We also demonstrate several cases in Appendix). For our method,
we report its performances on three settings. We can see that:

1\. By synchronously decoding canonical utterances and meaning
representations, SSD achieves competitive unsupervised semantic parsing
performance. In all datasets, our method outperforms other baselines in the
unsupervised settings. These results demonstrate that unsupervised semantic
parsers can be effectively built by simultaneously exploit semantic and
structural constraints, without the need of labeled data.

2\. Our model can achieve competitive performance on different datasets with
different settings. In supervised settings, our model can achieve competitive
performance with SOTA. With nonparallel data, our model can outperform Two-
stage. On Geo(FunQL) our model also obtains a significant improvement compared
with baselines, which also verifies that our method is not limited to specific
datasets (i.e., Overnight and GeoGranno, which are constructed with SCFG and
paraphrasing.)

3\. Both rule-level inference and word-level inference can effectively
generate paraphrases under the grammar constraints. The rule-level inference
can achieve better performance, we believe this is because rule-level
inference is more compact than word-level inference, therefore the rule-level
inference can search wider space and benefit beam search more.

####  6.2.2 Detailed Analysis

##### Effect of Decoding Constraints

To analyze the effect of decoding constraints, we conduct ablation experiments
with different constraint settings and the results are shown in Table 2:
-Semantic denotes removing the semantic constraint, -Grammar denotes all
constraints are removed at the same time, the decoding is unrestricted. We can
see that the constrained decoding is critical for our paraphrasing-based
semantic parsing, and both grammar constraints and semantic constraints
contribute to the improvement.

##### Effect of Adaptive Fine-tuning

To analyze the effect of adaptive fine-tuning, we show the results with
different settings by ablating a fine-tuning corpus at a time (see Table 2).
We can see that adaptive fine-tuning can significantly improve the
performance. And the paraphrase generation model can be effectively fine-tuned
only using CUs or Self Paras, which can be easily constructed.

##### Effect of Reranking

To analyze the effect of reranking, we compare the settings with/without
reranking and its upper bound – Oracle, which can always select the correct
logical form if it is within the beam. Experimental results show that
reranking can improve the semantic parsing performance. Moreover, there is
still a large margin between our method and Oracle, i.e., the unsupervised
semantic parsing can be significantly promoted by designing better reranking
algorithms.

##### Effect of Adding Labeled Data

To investigate the effect of adding labeled data, we test our method by
varying the size of the labeled data on Overnight from 0% to 100%. In Fig. 4,
we can see that our method can outperform baselines using the same labeled
data. And a small amount of data can produce a good performance using our
method.

Figure 4: Semi-supervised results of different ratios of labeled data on
Overnight.

##### Effect of Pretrained Language Models

To analyze the effect of PLMs, we show the results with different PLM
settings: instead of T5 we use GPT-2 or randomly initialized transformers to
construct paraphrasing models. Experimental results show that powerful PLMs
can improve the performance. Powered by the language generation models to do
semantic parsing, our method can benefit from the rapid development of PLMs.

##  7 Related Work

##### Data Scarcity in Semantic Parsing.

Witnessed the labeled data bottleneck problem, many techniques have been
proposed to reduce the demand for labeled logical forms. Many weakly
supervised learning are proposed (Artzi and Zettlemoyer, 2013; Berant et al.,
2013; Reddy et al., 2014; Agrawal et al., 2019; Chen et al., 2020), such as
denotation-base learning (Pasupat and Liang, 2016; Goldman et al., 2018),
iterative searching (Dasigi et al., 2019). Semi-supervised semantic parsing is
also proposed(Chen et al., 2018a). Such as variational auto-encoding (Yin et
al., 2018), dual learning framework for semantic parsing (Cao et al., 2019),
dual information maximization method (Ye et al., 2019), and back-translation
(Sun et al., 2019). One other strategy is to generate data for semantic
parsing, e.g., Wang et al. (2015) construct a semantic parsing dataset from
grammar rules and crowdsourcing paraphrase. Guo et al. (2018) produce pseudo-
labeled data. Jia and Liang (2016) create new “recombinant” training examples
with SCFG. The domain transfer techniques are also used to reduce the cost of
data collecting for the unseen domain (Su and Yan, 2017; Herzig and Berant,
2018; Lu et al., 2019; Zhong et al., 2020). Goldwasser et al. (2011); Poon and
Domingos (2009); Schmitt et al. (2020) leverage external resources or
techniques for unsupervised learning.

##### Constrained Decoding.

After neural parsers model semantic parsing as a sentence to logical form
translation task (Yih et al., 2015; Krishnamurthy et al., 2017; Iyyer et al.,
2017; Jie and Lu, 2018; Lindemann et al., 2020), many constrained decoding
algorithms are also proposed, such as type constraint-based illegal token
filtering (Krishnamurthy et al., 2017); Lisp interpreter-based method (Liang
et al., 2017); type constraints for generating valid actions (Iyyer et al.,
2017).

##### Paraphrasing in Semantic Parsing.

Paraphrase models have been widely used in semantic parsing. ParaSempre
(Berant and Liang, 2014) use paraphrase model to rerank candidate logical
forms. Wang et al. (2015) employ SCFG grammar rules to produce MR and
canonical utterance pairs, and construct Overnight dataset by paraphrasing
utterances. Dong et al. (2017) use paraphrasing to expand the expressions of
query sentences. Compared with these methods, we combine paraphrasing with
grammar-constrained decoding, therefore SSD can further reduce the requirement
of labeled data and achieve unsupervised semantic parsing.

##  8 Conclusions

We propose an unsupervised semantic parsing method – Synchronous Semantic
Decoding, which leverages paraphrasing and grammar-constrained decoding to
simultaneously resolve the semantic gap and the structure gap. Specifically,
we design two synchronous semantic decoding algorithms for paraphrasing under
grammar constraints, and exploit adaptive fine-tuning and utterance reranking
to alleviate the style bias in semantic parsing. Experimental results show
that our approach can achieve competitive performance in unsupervised
settings.

## Acknowledgments

We sincerely thank the reviewers for their insightful comments and valuable
suggestions. Moreover, this work is supported by the National Key Research and
Development Program of China(No. 2020AAA0106400), the National Natural Science
Foundation of China under Grants no. 61906182 and 62076233, and in part by the
Youth Innovation Promotion Association CAS(2018141).

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Cases |  | $x\rightarrow c$
---
$logP(c|x)$
| $x\leftarrow c$
---
$s_{rec}(x,c)$
| $x\leftrightarrow c$
---
$s_{asso}(x,c)$
| Overall
---
Reranking
Score
Input: restaurants that accept credit cards and offer takeout |  |  |  |
Outputs: restaurant that takes credit cards and that has take-out | -54.2 | -3.1 | -20.3 | -77.6
Outputs: restaurant that has take-out and that takes credit cards | -72.0 | -8.8 | -20.3 | -101.1
Outputs: restaurant that takes credit cards | -77.2 | -22.4 | -31.9 | -131.5
Outputs: restaurant that takes credit cards and that takes credit cards | -84.2 | -26.7 | -28.1 | -139.0
Input: meetings held in the same place as the weekly standup meeting |  |  |  |
Outputs: meeting whose date is date of weekly standup | -62.2 | -40.2 | -67.1 | -169.5
Outputs: meeting whose location is location of weekly standup | -62.7 | -22.1 | -62.4 | -147.2
Outputs: meeting whose location is location that is location of weekly standup | -65.0 | -21.1 | -63.5 | 149.6
Outputs: meeting whose date is at most date of weekly standup | -67.2 | -35.8 | -73.3 | -176.3
Input: meetings held in the same place as the weekly standup meeting |  |  |  |
Outputs: meeting whose location is location of weekly standup | -2.7 | -22.1 | -62.4 | -86.2
Outputs: meeting whose location is location that is location of weekly standup | -6.0 | -21.1 | -63.5 | -90.6
Outputs: location that is location of weekly standup | -18.0 | -32.6 | -62.8 | -113.4
Outputs: meeting whose date is date of weekly standup | -31.2 | -40.2 | -67.1 | -138.5

Table 4: Output cases from SSD on Overnight. The outputs are sorted by the
generation score $logP(c|x)$. The underlined canonical utterances are correct.
Adaptive fine-tuning is employed in the third case, and not employed in the
first two cases. Accuracies on Overnight. In GenOvernight Wang et al. (2015),
all the canonical utterances are also generated without manual annotation. The
previous methods with superscript $*$ means they use different unsupervised
settings.
---

##  Appendix A A Appendix

###  A.1 Case Study

In Table 4, we present the cases generated from SSD. Cases show that SSD can
output semantics-similar and grammar-legal utterances. In case 1, “take-out”
does not appear in paraphrase dataset, we can still efficiently generate the
utterances containing it, which shows our constrained-paraphrasing based
semantic parser has the generalization ability on unseen words. We found that
the parser maintains high recall, covering the correct canonical utterances in
our n-best list of predictions. As case 2 shows the designed utterance
reranking score can select the best canonical utterances by focusing on
coherence and adequacy. With adaptive fine-tuning (case 3), our model can
generate the utterances focusing more on semantics to alleviate the style
bias.