Ambiguous Learning from Retrieval: Towards Zero-shot Semantic Parsing
Year: 2023

Abstract:
Current neural semantic parsers mostly take supervised approaches, which require a considerable amount of expensive training data. As a result, minimizing supervision requirements has been one of the key challenges in semantic parsing. In this paper, we propose a Retrieval as Ambiguous Supervision framework, which can effectively collect high-coverage ambiguous supervisions (i.e., the parse candidates of an utterance) via a pre-trained language modelsbased retrieval system. Then, by assuming candidates will contain the correct ones, the zeroshot task can be converted into an ambiguously supervised task. To improve the precision and coverage of such ambiguous supervision, we propose a confidence-driven self-training algorithm, in which a semantic parser is learned and exploited to disambiguate candidates iteratively. Experimental results show that our approach significantly outperforms the state-of-the-art zero-shot semantic parsing methods.

heading: 1 Introduction
text: Semantic parsing aims to map natural language sentences into computer-understandable meaning representations(MRs), which has attracted substantial attention for many years (Wong and Mooney, 2007; Kate et al., 2005; Lu et al., 2008; Dong and Lapata, 2016). Nowadays, neural network methods have become the mainstream for semantic parsing. Since neural semantic parsers are limited to the patterns observed in the training data, a large number of annotated data is required. However, annotating utterances with detailed, correct meaning representations is a difficult and time-consuming task, which relies on expert knowledge about MRs.
Recent studies in semantic parsing try to employ pre-trained language models (PLMs) to alleviate the problem of data insufficiency. Shin et al. (2021);
*Equally Contribution. †Corresponding Authors.
Wu et al. (2021); Schucher et al. (2022) reformulate semantic parsing as constrained paraphrasing generation, where paraphrasing generation is modeled by PLMs. To eliminate the need for humanannotated data, Xu et al. (2020) employ PLMs to paraphrase repeatedly and obtain millions of data. However, these methods still rely on lots of detailed annotated data or heavy data synthesis.
In this paper, we propose a Retrieval as Ambiguous Supervision (RaAS) framework for zero-shot semantic parsing, which is simple and effective. In the RaAS framework, we make full use of a PLMsbased retriever to return high-coverage candidates, and then convert zero-shot semantic parsing into ambiguously supervised semantic parsing1. As previous work found, sentence similarity and PLMs can provide effective candidates: Herzig and Berant (2019) use sentence similarity scores and Belyy et al. (2022) use PLMs to provide candidates for manual annotation, and PLMs-based paraphrasing models can provide parsing results with consider-
1In ambiguous supervision (Kate and Mooney, 2007; Kim and Mooney, 2010), where each sentence is annotated with multiple potential meaning representations and the correct ones are within them. Strictly speaking, our setting is approximate ambiguous supervision or noisy ambiguous supervision.
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able top-20 accuracy (Wu et al., 2021). Thus, we propose an effective PLMs-based retrieval system to retrieve MRs from the collected MRs datastore, and select the top-k MRs as ambiguous supervision signals, in which we suppose there is at least one true meaning representation. Then, we employ a self-training protocol that exploits the sequences modeling ability of semantic parsers to improve the coverage and precision of candidates. In our approach, semantic parsers are learned and exploited to supplement candidates and disambiguate the MRs iteratively.
Without any supervision, our PLMs-based retrieval system can provide discriminative supervision signals. In our retrieval system, the MRs datastore is built by sampling MRs under a limited depth and preserving the valid ones. Following previous work (Berant and Liang, 2014; Cao et al., 2020), we canonicalize the MRs for scoring. The sentence similarity scores between the query and canonical utterances are calculated by PLMs to retrieve MR candidates. As shown in Fig 1, the retrieval results of PLMs have high top-k accuracy. In all domains of OVERNIGHT, the average top-20 accuracy can reach 95.3% but the average top-1 accuracy is only 59.5%. We assume that the retrieval results can provide sufficient ambiguous supervision, of which the precision and coverage can be further improved by SEQ2SEQ models.
To further improve the precision and coverage of the above ambiguous supervision, we propose a confidence-driven self-training algorithm. Our learning method iterates between two stages: 1) Train the semantic parser from the high confidence instances; 2) Expand candidate sets and update the confidence weights of candidates based on the current parser.
In summary, our main contributions are:
• We propose the Retrieval as Ambiguous Supervision framework, which can exploit the prior knowledge of PLMs and the sequences modeling ability of semantic parsers simultaneously.
• We design a confidence-driven self-training algorithm on retrieval, which can improve the precision and coverage of ambiguous supervision.
• Experiments on three standard datasets show that our approach significantly outperforms previous zero-shot semantic parsing methods.

heading: 2 Retrieval as Ambiguous Supervision Framework
text: We propose Retrieval as Ambiguous Supervision framework, which treats the retrieval results as ambiguous supervision signals (Fig. 2). First, for each sentence, we use a pre-trained model to provide reliable meaning representation candidates, in which we assume that at least one is correct. So the zero-shot semantic parsing is converted into an ambiguous supervision task. Then we propose a confidence-driven self-training algorithm, in which high-confidence instances from the candidates are used to train the semantic parser and in turn the semantic parser is exploited to supplement and disambiguate the candidates. This process is iterative.

heading: 2.1 PLMs-based MRs Retrieval System
text: In order to make better use of the PLMs to retrieve semantic parsing candidates, we first use the production rules of meaning representations and the constraints of knowledge base to build the retrieval datastore D. Then, given a query sentence x, the pre-trained language models are used to calculate the retrieval score for each MR y in D. The top-k retrieval results form the candidate sets Ux, which are viewed as ambiguous supervision signals.

heading: 2.1.1 MRs Collecting
text: For each domain, we use the context free grammar (CFG) of the corresponding semantic formalism. We randomly expand the production rules of CFG to sample a large number of meaning representations Y ′. To make full use of the knowledge constraints of the knowledge base, we only preserve the executable meaning representations Y .
Following previous work (Jia and Liang, 2016; Xu et al., 2020), through synchronous grammar, we also produce canonical utterances, which are the pseudo-language representations of MRs. Finally, we collect accessible meaning representation and canonical utterance pairs ⟨y, z⟩ to build retrieval datastore D = {⟨y1, z1⟩ , ⟨y2, z2⟩ , ..., ⟨yn, zn⟩}.

heading: 2.1.2 PLMs-based Retriever
text: Following previous studies (Su and Yan, 2017; Cao et al., 2020; Wu et al., 2021), we first use canonical utterances to calculate retrieval scores. Canonical utterances can be viewed as sub-language representations of MRs. There is a one-to-one mapping between them. Formally, each MR y can be mapped to its cannonical utterance z by synchronous gr-
mmar. We use z to compute the retrieval score rx,y.
Given a query sentence x, we can calculate the cos similarity of x and each canonical utterance z in D by cos(h(x),h(z)) with the PLM encoder h. The encoder has been pre-trained on large-scale public datasets in advance and has not touched any canonical utterances. We normalize the cos similarities to calculate the scores:
scoreh(x, z) = ecos(h(x),h(z))/τ∑
⟨y′,z′⟩∈D e cos(h(x),h(z′))/τ
(1)
, in which τ is the temperature parameter. The initial confidence scores are obtained from the similarities: rx,y = scoreh(x, z). We keep the top-k retrieval results Ux = [⟨y1, z1⟩ , ⟨y2, z2⟩ , ..., ⟨yk, zk⟩] and their corresponding scores for later ambiguous learning. In our practice, k is set to 20.
Although the retrieval system can provide discriminative supervision signals, the coverage and
precision of MR candidates should be further refined. As shown in the example of Fig 3, the retrieval system pays more attention to the relevance and confuses the highly relevant utterances. In this example, the related words ‘player’, ‘amount’, ‘assist’ and ‘Kobe’ all appear in the first and second candidates, but the meanings of the correct MR #2 and #1 are very different. This demonstrates that the retrieval model does not have enough understanding of their accurate semantics. However, it still provides a good initialization of candidates and confidence scores, which can be further refined by more accurate SEQ2SEQ modeling.

heading: 2.2 Self-training on Retrieval
text: As mentioned above, after obtaining the ambiguous supervision signals Ux for each given input x and their corresponding initial confidence scores r, we propose a confidence-driven self-training protocol to improve the coverage and precision of candidates with SEQ2SEQ modeling. Our self-training algorithm operates in an EM-like manner, iterating between two stages: 1) Train a semantic parser from the candidates based on their confidence scores. 2) Exploit the current parser to expand the candidates and re-estimate their confidence scores;
In our self-training protocol, the Seq2Seq parser with semantic mapping ability is fed with reliable guidance from high-confidence instances, to denoise the supervision of relevant instances iteratively. As shown in Fig 4, after self-training iterations, the parser learns that ‘Which player’ maps to ‘player’ rather than ‘number’ and re-estimates the confidence scores to raise the ranking of the correct MR consequently. Thus the quality of supervision signals can be improved in such iterative
re-estimation, which continually produces better parsers.

heading: 2.2.1 Prompt-based Semantic Parsers
text: As shown in previous work (Lester et al., 2021; Schucher et al., 2022), the prompt tuning is suitable for solving the overfitting problem in low resource settings. Following them, we use T5(Raffel et al., 2020) as the base model, and set the prompt length to 150.
Given a tokenized utterance x = [x1, x2, ..., xn], T5 encodes x into Ex ∈ Rn×e, where e is the dimension of the embedding space. The soft prompt is represented as a parameter θp = [P1;P2; ...;Pv] ∈ Rv×e, in which v is the length of the prompt. The soft prompt is prepended to the input embeddings as [θp;Ex], which is provided to the language model. During prompt tuning, we only optimize θp, and fix the model parameters and the pre-trained vocabulary embeddings of T5.
Before self-training iterations (in Iter0), we use the top-1 of the retrieval results Ux as supervision signals to initialize the semantic parsing model.

heading: 2.2.2 Candidate Expansion and Confidence Re-estimation
text: In order to improve the precision and coverage of retrieval results, we add the top-m parsing results to the candidate set and disambiguate meaning rep-
resentation annotations in a moving-average style after each model update.
Candidate Expansion As mentioned above, the ambiguous supervision can only be retrieved from the collected data. To make up for the generation label space, the m-best beam search results of the current semantic parser in t-th iteration Y tx = [⟨y1, z1⟩ , ⟨y2, z2⟩ , ..., ⟨ym, zm⟩] are employed to update the candidate set: U tx = Ux ∪ Y tx (t ≥ 1).
Confidence Re-estimation To improve the supervision precision, and especially to resolve the problem that the retrieval system focuses more on relevance than on precise semantics, we use the generation model to refine and re-estimate the confidence stx,y of MR labels.
We first use a pre-trained paraphrase generation model g to refine the confidence scores:
s0x,y = rx,y + pg(x|z)∑
⟨y′,z′⟩∈Ux pg(x|z′) (2)
After each model update, we use the new parser p(y|x) to re-evaluate the confidence scores of the meaning representation candidates in a movingaverage style:
stx,y = (1− α) p(y|x)∑
y′∈Utx p(y ′|x) + αs
t−1 x,y (3)
For the meaning representations newly added to the candidate set, we re-estimate their confidence scores as: stx,y = (1−αt) p(y|x)∑
y′∈Utx p(y ′|x)+α
t(rx,y+
pg(x|z)∑ ⟨y′,z′⟩∈Utx pg(x|z ′)).
Finally, we get the normalized confidence scores St(y|x) as:
St(y|x) = stx,y∑
y′∈Utx s t x,y
(4)

heading: 2.2.3 Self-training Update on Retrieval
text: Our learning framework operates in an EM-like manner, iterating between two stages: 1) Add candidates and update the confidence weights of the candidates based on current model parameters; 2) Train the parser from the soft pseudo instances. In the iterations, candidate samples are weighted to train the parser.
We use the continuous self-training method proposed by Zou et al. (2019). First, according to the
normalized confidence St(y|x), we resolve the soft pseudo-labels as:
ŷtx = argmin ŷx
− ∑
y∈Utx
ŷx,y logSt(y|x) + βr(ŷx)
(5) , in which ŷtx ∈ ∆|U t x|−1. We use a negative entropy
label regularizer r(ŷx) = ∑
y∈Utx ŷx,y log ŷx,y. The distribution of labels can be solved as:
ŷtx,y = St(y|x)1/β∑
y′∈Utx St(y ′|x)1/β (6)
According to the weights of the candidate annotations, we train the parser by the following loss function:
J (x, U tx) = − ∑
y∈Utx
ŷtx,y log p(y|x; θp) (7)

heading: 2.2.4 Inference
text: When inferring, we follow the same way as confidence re-estimation. Given a query x, the candidate set consists of retrieval results and beam search results: U = Ux ∪ Yx. Then, we use the similar confidence re-estimation algorithm as in self-training: score(x, y) = p(y|x)∑
y′∈Ux p(y ′|x) + s
0 x,y
to rerank candidates. Following previous studies (Wu et al., 2021; Shin et al., 2021), we employ constrained decoding and generate canonical representations over meaning representations.

heading: 3 Experiments
text: Datasets We conduct experiments on three datasets: OVERNIGHT(λ-DCS), GEOGRANNO, and GEO(FunQL), which use different meaning representations and are on different domains. Note that we do not use any MR annotations in training set.
OVERNIGHT This is a dataset across eight domains, which contains natural language paraphrases paired with lambda DCS logical forms. We use the same train/test splits as Wang et al. (2015).
GEOGRANNO This is a semantic parsing benchmark about U.S. geography (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.
GEO(FunQL) This is another version of GEO (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. Different from the previous datasets, the construction method of this dataset does not dependent on paraphrasing, which can better verify the effectiveness of our methods. We follow the standard 600/280 train/test splits.
Pretrained Language Models We use the pretrained sentences similarity model MPNet2 (Song et al., 2020) as the retrieve model. The paraphrase generation model is the PEGASUS model (Zhang et al., 2020) fine-tuned for paraphrasing3. The PLMs have been trained on the public paraphrase datasets, which have not touched any canonical utterances. In our experiments, they are fixed and only used for retrieval and reranking.
System Settings We train all our models with 3 self-training iterations. In each iteration, the neural semantic parser is trained 1000 epochs, with the initial prompt learning rate of 0.1. We use Adam algorithm to update parameters, with batch size as 80 ~250. The temperature parameter τ is set to 0.1. We initialize soft prompt parameters by uniformly sampling within [-0.1, 0.1]. The beam size m during decoding and candidates expanding is 8. The hyper-parameters α is set to 0.5, β is set to 0.1.
Datastore Collecting We use synchronous context free grammars (SCFGs) to generate ⟨MR, CU⟩ pairs in each dataset. We generate roughly 800K, 250K, 20K pairs in OVERNIGHT, GEOGRANNO, GEO(FunQL) respectively. We only preserve the valid ones (are executable or meet type checking), and remove the redundant MRs. We collect roughly 10K, 20K, 3K valid pairs for our datastore in these datasets.
Few-shot Settings Following the previous fewshot settings in OVERNIGHT (Shin et al., 2021; Schucher et al., 2022), we randomly subsample 200 training examples for each domain as supervise data, and 20% of the remaining data is used for validation. All other data in training sets are treated as unannotated data, whose ambiguous supervision signals also come from the retrieval results.
2https://huggingface.co/sentence-transformers/all-mpnetbase-v2
3https://huggingface.co/tuner007/pegasus_paraphrase
Baselines We compare our method with the following zero-shot/unsupervised baselines: 1) Crossdomain Zero Shot (Herzig and Berant, 2018), which is trained on other source domains and generalizes to target domains in OVERNIGHT and 2) GENOVERNIGHT (Wang et al., 2015), in which models are trained on synthesized ⟨CU, MR⟩ pairs; 3) SYNTH-SEQ2SEQ, in which the neural semantic parser is trained on the synthesized ⟨CU, MR⟩ pairs; 4) SSD (Wu et al., 2021), which use a paraphrase generation model to decode meaning rep-
resentations. 5) AUTOQA (Xu et al., 2020), in which high-quality synthetic training data is generated by template-based data synthesizers and autoparaphrasers.
Zero-shot Settings Any manual MR annotations are not required in our zero-shot settings. And, except for AutoQA, all of these zero-shot methods employ unannotated sentences as we do. We follow the hypothesis in GEOGRANNO: It is easy to access unlabeled utterances, which can typically be found in query logs, or generated by users experimenting with a prototype. Instead of unannotated sentences, AutoQA uses millions of generated sentences, which are not introduced in our method. AutoQA and our approach are two different strategies. The two methods are complementary, which means that our approach can be combined with AutoQA to eliminate the need for unannotated sentences.

heading: 3.1 Experimental Results

heading: 3.1.1 Overall Results
text: The overall results of different baselines and our method are shown in Table 1 and Table 2. We can see that:

heading: 1. By exploiting the prior knowledge of PLMs
text: and the sequences modeling ability of semantic parsers simultaneously, our RaAS framework
achieves the best zero-shot semantic parsing performance. In all datasets, our method outperforms other baselines in the zero-shot settings, and further narrows the gap between zero-shot and supervised settings. These results demonstrate that zero-shot semantic parsers can be effectively constructed from the RaAS framework.
2. The retrieval system can provide a good start without any annotated data. Using pretrained language models to retrieve meaning representations, the retrieval system can obtain an average accuracy rate close to 60% even without any supervision from manually labeled data. Considering the high recall rate of retrieval results, RaAS has the potential for later continuous improvement by ambiguous learning methods.
3. Self-training can significantly improve the performances in all datasets. In OVERNIGHT the average accuracy raises from 62.4% to 71.4%. As we mentioned before, the retrieval results have high recall rates but contain lots of noise. We think that the improvement of self-training comes mainly from candidate expansion and confidence re-estimation, which can establish global consistency gradually and reduce data noise iteratively.

heading: 3.1.2 Detailed Analysis
text: Self-training iterations In Table 3, Lines (7)- (10) show the accuracies on the test dataset as the number of iterations increases. We can see that: 1) The self-training protocol is effective. When we conduct more iterations, the performance gradually increases and stabilizes at a reasonable level – from 62.4% accuracy in Iter 0 to 71.4% in Iter 3 on OVERNIGHT. 2) The self-training process can reach its equilibrium within a few iterations, and the performance of RaAS can be stabilized around the third round.
Composition of candidate set Line (2) in Table 3 shows the results of removing candidate expansion, where we only rerank retrieval candidates. Line (3) shows the results of removing retrieval candidates, where we only use beam search results of the current semantic parser.
1. The effect of candidate expansion If the candidate expansion is removed, the performances of RaAS decrease slightly. More importantly, during inferring, candidate expansion ensures the generation capability to produce various valid meaning representations, rather than only providing MRs in
the collected retrieval datastore. 2. The effect of retrieval candidates Without retrieval candidates, the performances drop slightly on average. We believe that this is because the beam search results are too similar, and the retrieval results can be a good supplement to them.
Reranking Line (4) in Table 3 shows the results of removing reranking, where we directly use beam search results of the semantic parser as output. The results of removing parser scores are shown in Line (5). We can see that without reranking, the average performance drops, but it still outperforms previous methods that exploit heavy data augmentations. However, without semantic parser scores, the performances will drop significantly.
The effect of prompt tuning Line (6) in Table 3 shows that, after changing the learning method to fine-tuning, the performances decrease slightly, which also proves the robustness and high generalization of prompt tuning.
The quality of confidence re-estimation In the Fig 5, we can see the accuracies on the validation set grow with the number of iterations. As the number of iterations increases, the performances gradually increase and stabilizes at a high level. This verifies that our self-training method can improve the quality of supervision signals iteratively by confidence re-estimation.
Few-shot settings The few-shot results are shown in Table 1. With the same few-shot settings as in previous studies, we employ T5-base to achieve comparable performances to T5-large and even T5-xl in previous work.
Training epochs Fig 6 shows the change of validation accuracies as the number of epochs increases. We can see that the performances of RaAS are stable, which verifies that our method is insensitive to the hyper-parameters of the number of training epochs in each iteration.

heading: 4 Related Work
text: Retrieval in Seq2Seq Tasks In semantic parsing, many previous studies (Su and Yan, 2017) have propose to employ paraphrase scores to retrieve or rerank MRs, which all follow the order of generating first and then scoring. Berant and Liang (2014) first generate a set of candidate MRs and choose the realization that best paraphrases the input. Yin and Neubig (2019) propose a set of reranking scorer
for neural semantic parsers. Guo et al. (2019) combine a retrieval model and a meta-learner to employ the similar datapoints from the training data. Ren et al. (2020) construct parallel sentence pairs through retrieval, and conduct unsupervised machine translation models. Lu et al. (2021); Khandelwal et al. (2021); Parvez et al. (2021) enhance the representations of instances or the robustness of decoder by retrieval. Different from the common generate-then-score framework, the order of our RaAS framework is the reverse of them. We are the first to use retrieval results to obtain supervision for zero-shot semantic parsing.
Low Resource Semantic Parsing Many low resource semantic parsing methods have been proposed to reduce the demand for annotations(Artzi and Zettlemoyer, 2013; Sun et al., 2020; Sherborne and Lapata, 2022). Many weakly supervised learning are proposed (Berant et al., 2013; Reddy et al., 2014; Agrawal et al., 2019), such as denotationbased learning (Pasupat and Liang, 2016; Goldman et al., 2018), iterative searching (Dasigi et al., 2019). Semi-supervised semantic parsing is also proposed (Yin et al., 2018; Cao et al., 2019; Ye et al., 2019). One other strategy is to augment data. 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. Shin et al. (2021); Wu et al. (2021); Schucher et al. (2022) explore the training / decoding methods of PLMs for low-resource semantic parsing. Different from previous work, our framework focuses on obtaining and facilitating supervision signals rather than model design or data synthesization.

heading: 5 Conclusions
text: In this paper, we propose a novel method for zeroshot semantic parsing with a Retrieval as Ambiguous Supervision framework. We first retrieve the top-k similar meaning representations from the collected MR datastore. Then in self-training iterations, the candidates are employed to train parsers and refined by the candidate expansion and confidence re-estimation. We leverage the ambiguous supervision signal to train a prompt-based semantic parser and propose a confidence-driven selftraining algorithm to refine the parser iteratively. The experiments show that the final semantic parser is greatly improved after iterative training.
Limitations
Firstly, due to the huge cost of large-scale PLMs, this paper only employs the T5-base as the backbone PLM in our experiments, therefore only limited analysis on the effect of model scale is presented. However, we believe a larger model will benefit our method by providing better language understanding and generation abilities.
Secondly, the synthesized canonical utterances need manually designed synchronous grammars, which are used to guide RaAS with knowledge about semantic representation language. Although most few-shot/zero-shot semantic parsing studies also rely on synchronous grammars, we leave how to model semantic representations without grammars as an open problem for future work.
Acknowledgments
We sincerely thank the reviewers for their insightful comments and valuable suggestions. This research work is supported by the National Natural Science Foundation of China under Grants no. U1936207, 62122077 and 62106251. Furthermore, this research was supported by Meituan.
Ethics Consideration
This work presents RaAS, an effective framework for zero-shot semantic parsing. All of the involved datasets come from publicly available sources. The MRs and NLs are derived from several common public datasets (Kate et al., 2005; Wang et al., 2015; Herzig and Berant, 2019). The SCFGs are used for canonicalizing MRs, which are from OVERNIGHT and GEOGRANNO(Wang et al., 2015; Herzig and Berant, 2019). Pre-trained models and evaluation codes are all publicly accessible. The hyperparameter settings are given in this paper. Our code and specification of dependencies will be released in the future.

heading: A For every submission:
text: 3 A1. Did you describe the limitations of your work?
6
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heading: 3 B3. Did you discuss if your use of existing artifact(s) was consistent with their intended use, provided
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heading: 3 C1. Did you report the number of parameters in the models used, the total computational budget
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The Responsible NLP Checklist used at ACL 2023 is adopted from NAACL 2022, with the addition of a question on AI writing assistance.

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heading: Future Work
text: Although most few-shot/zero-shot semantic parsing studies also rely on synchronous grammars, we leave how to model semantic representations without grammars as an open problem for future work. Acknowledgments
We sincerely thank the reviewers for their insightful comments and valuable suggestions. This research work is supported by the National Natural Science Foundation of China under Grants no. U1936207, 62122077 and 62106251. Furthermore, this research was supported by Meituan