Authors: Y. Cao

## Introduction

People communicate in natural language, which is flexible but often vague, whereas computer languages have no room for ambiguity. For a computer to respond to users' questions or commands in natural language, it needs to extract meaning, resolve ambiguity, and translate to executable programs. This is the task of semantic parsing (SP), whose applications include voice assistants, code generation, natural language interfaces to databases (NLDB), and many more. Our Turing by Borealis AI system is an NLDB, a software system enabling users to interact with databases in natural language, as illustrated in Figure 1.

Figure 1. A natural language database interface (NLDB), like our turing system ($B$), translates a natural language question ($A$) to its corresponding SQL query ($C$), executes the query against the database ($D$), and finally returns the answer back to the user ($E$).

The semantic parsing model powering an NLDB needs to be trained with questions and their corresponding SQL queries. If the model only generalizes to new questions on the training domain, the NLDB cannot be quickly adapted to new databases, so it would not be very useful in practice. Hence, the model somehow needs to generalize to new databases with unseen schema and unseen questions. This is cross-domain or cross-database text-to-SQL semantic parsing.

The goal of this blog post is to glimpse into how models (like our Turing by Borealis AI system) for this task work without popping the hood. It is suitable for any reader with basic knowledge of machine learning and natural language processing.

We will first give a brief review of SQL that readers can skip if already familiar, then introduce two running examples of text-to-SQL prediction. The examples will illustrate some challenges involved in cross-domain semantic parsing and illustrate why simple methods would not succeed. Afterwards, we will describe a high-level framework that treats cross-database text-to-SQL as a graph-to-tree mapping. We will use the two running examples, to show how the framework tackles the challenges that we identified. Finally, we will provide some pointers for interested readers to learn more, including our recent ACL papers (Xu et al., 2021a,b; Norouzi et al., 2021) that respectively set the new state-of-the-art accuracy on the Spider text-to-SQL benchmark and some code generation problems.

## SQL primer

Before showing the examples, let us review some SQL basics. SQL stands for Structured Query Language and is used for storing, manipulating and retrieving data in relational databases. We will just focus on the retrieval here.

## Schema

Relational databases store information records in tables. The schema of a database describes the structure of the domain: what are the tables, what columns does each table contain, the data type of each column, as well as special roles that some columns play. The first type of special role is a primary key. This is a column or a combination of columns that has to be unique for each data record. The second type of special role is a foreign key, which is a column or combination of columns whose values match the primary key records of another table. Foreign key relations link tables together.

## Basic SELECT Query

A basic SQL query looks like the following SELECT * FROM my_table, where * is a reserved token meaning "all columns". This query will return all rows of the table my_table. The star can be replaced by one or more column names, in which case, the query would only return the mentioned attributes in each row. Slightly more advanced queries will involve filtering condition, expressed using a WHERE clause: SELECT * FROM my_table WHERE condition. This query will only return records for which the condition holds true. The SQL syntax for the actual condition is generally self-explanatory.

## GROUP BY and HAVING

Sometimes columns could correspond to categorical attributes like "sector". Here, an interesting class of questions involves aggregating some properties associated with each categorical value of the column. For this purpose, we would need the GROUP BY clause: SELECT MAX(salary), sector FROM my_table GROUP BY sector, which would find the highest salary per each sector. If we want to filter the categories,  we can use the HAVING clause. For example, we might want to filter out sectors based on their associated statistics, HAVING is similar to WHERE but operates on grouped categories instead. For example, SELECT MAX(income), sector FROM my_table GROUP BY sector HAVING AVG(salary) < 50000.

## JOIN

Last but not least, the concept of JOIN needs some explanation. As SQL databases store records in tables, sometimes we need to "merge" corresponding rows of two or more tables. We might need the merged records as the final result or as an intermediate step to compute something else. This requires joining one or more tables with the syntax: SELECT * FROM table1 JOIN table2 ON table1.col_fkey = table2.col_pkey. The ON part introduces a condition that is usually an equality relation between the foreign key and primary key columns like in this example but can also be on other columns. This query returns the combination of rows in table1 and rows in table2 whose value in the column col_fkey of table1 equals to the value of col_pkey of table2

## Two text-to-SQL examples

To predict the correct SQL from a natural language question, the model needs to correctly interpret each input word in the context of both the sentence and the schema. Furthermore, it needs to generate a syntactically correct SQL query as the output otherwise the database cannot execute it. To illustrate the challenges more concretely, let's consider two examples for the "Employee_hire_evaluation" database of the Spider benchmark. This database is a development set domain that models would not have seen during training.

## Schema of the domain

The database has the following tables: employee, shop, hiring, evaluation. Each table has a number of columns:

• employee: employee_id, name, age, city, with employee_id being the primary key.
• shop: shop_id, name, location, district, number_products, manager_name, with shop_ID being the primary key.
• hiring: shop_id, employee_ID, start_from, is_full_time, with employee_id being the primary key, and also a foreign key to Employee table's employee_id, and shop_id being a foreign key to shop table's shop_id.
• evaluation: employee_id, year_awarded, bonus, with employee_id and year_awarded together as the primary key, and employee_id as a foreign key referencing Employee table's employee_id.

## Example One

Question: Which cities have more than one employee under 30?

Correct SQL:
SELECT employee.city FROM employee WHERE employee.age < 30 GROUP BY employee.city HAVING COUNT (*) > 1

Analysis: Besides the general logic of the SQL query, a model needs to infer two conditions from the question, employee.age < 30 and COUNT (*) > 1. The entities involved in the conditions (tables, columns or the star) are not explicitly mentioned in the text and have to be inferred. The model needs to deduce that "employee under 30" requires column age, by leveraging two pieces of information. First, it can have some prior common sense knowledge that the expression "employee under [NUMBER]" refers to employee age rather than some other attribute. Second, it could exclude other columns because the value "$30$" is too different from other columns' values based on type or range. For the second condition, the model needs to infer from the entire phrase "Which cities have more than one employee ..." that the condition is on the number of employees in each city, hence requiring GROUP BY [$\ldots$] HAVING [$\ldots$]. Finally, it needs to piece the two conditions together as well as the rest of the query using the correct syntax.

## Example Two

Question: What's the average age in each shop?

Correct SQL:
SELECT AVG (employee.age) , shop.shop_id FROM employee JOIN hiring JOIN shop ON employee.employee_id = hiring.employee_id AND hiring.shop_id = shop.shop_id GROUP BY shop.shop_id

Analysis: To correctly predict this SQL, not only does the SP model needs to infer correctly from "in each shop" that the output contains GROUP BY shop.shop_id , it also needs to infer the involvement of tables employee, hiring which are not explicitly mentioned like shop. The table employee can be inferred based on the need for its age column. On the other hand, the hiring table can only be inferred from the need to link between employee.age and shop.shop_id.

## Would a simple approach work?

You might wonder whether some generic or simple approach can already solve this cross-database text-to-SQL problem. For example, let's consider the sequence-to-sequence model often used in machine translation. Text-to-SQL semantic parsing bears some similarity to machine translation if we view SQL as a foreign language to translate into. However, some crucial differences exist. First, typical training datasets for machine translation larger than those for SQL semantic parsing by two orders of magnitude or even more. Second, in machine translation, partially correct results can still provide partial utility, but for an NLDB, any small mistake in the predicted SQL query could invalidate the result. Third, as we have seen from the examples, the database schema is crucial for correct translation to SQL, which sequence-to-sequence machine translation models do not consider. For these reasons, typical neural sequence-to-sequence models do not work well.

Another baseline is shallow semantic parsing in which we simplify the problem and assume that there are a fixed number of user intentions. An intent classifier could then select the template that best corresponds to the user question from a pre-defined list. Then a model extracts the relevant information from the user question to fill in the template slots. For instance, we can turn the first example into a template whose SQL would have some slots to be filled:

SELECT employee.city FROM employee WHERE employee.age [COMP_A] [A] GROUP BY employee.city HAVING COUNT (*) [COMP_C] [C]

Given enough training examples of question tagged with its corresponding template ID and slot values, then a model could potentially answer questions like "show me the cities with less than 5 employees over twenty five.", by identifying this template out of many, then predicting that COMP_A $:=$ <, A $:=$ 5, COMP_C $:=$ >, C $:=$ 25. This approach is commonly used in voice-assistant and task-oriented dialogue systems. The main drawback is that the templates need to be pre-defined, so the system cannot generalize to new queries on the fly. Hence this approach is also unsuitable for cross-database NLDB in general.

## Cross-database semantic parsing as graph-to-tree mapping

As shown by the two running examples, successful cross-database SQL semantic parsing really requires the model to reason using at least three sets of knowledge:

• Explicit knowledge about the domain expressed in the schema;
• Implicit background or common sense knowledge;
• Knowledge of SQL.

We now describe a general framework for cross-database text-to-SQL that leverages all of this knowledge. The backbone of the overall system is a neural network with encoder-decoder architecture, which is adapted in various ways to leverage explicit symbolic knowledge.

Figure 2. Overview of the graph-to-tree framework processing Example One. On the input side, the question and schema are modelled jointly as a graph. Between every pair of tokens within and across the question and schema, there is an implicit edge, which is not drawn for visual simplicity. Additionally, some edges carry special meanings, which are drawn with different colours. Some correspond to foreign key relations in the schema (in green) , while others correspond to lexicon evidence linking a question token to a schema element (red for exact word match; yellow for partial word match). On the output side, we model the SQL as its abstract syntax tree rather than a linear string. The tree structure embodies our prior knowledge of SQL grammar and its compositionality.

Motivated by the examples, we see that the model needs to jointly encode the question and schema, considering how words relate to each other within and across the question and the schema. So the input for cross-database semantic parsing has an inherent graph structure; the nodes are the tokens in the questions and schema and are linked by different edges. On the output side, to produce grammatically correct SQLs and leverage programming-language-specific inductive prior, we treat the prediction problem as generation of the abstract syntax tree (AST) of the program. Hence, we can characterize this task a graph-to-tree mapping.

Figure 2 illustrates the overall framework for Example One: an encoder consumes the input graph, and a decoder produces the output AST. Joint modelling of question and schema as a graph was popularized by the relation-aware transformer (RAT) work (Wang et al., 2019) while TranX (Yin and Neubig, 2018) provides a unified framework for modelling output programs as ASTs. Our Turing by Borealis AI system also follows this overall approach, with many additional innovations that we will not cover here.

## Question-Schema joint encoding

As mentioned above, we view each token in the question and schema as a node in a graph. The most basic edge type among the nodes is a generic link between any pair of tokens, reflecting the assumption that a-priori any token could provide relevant context to any other token, so a link cannot be ruled out. This essentially yields a fully connected graph. For visual simplicity, we omit these edges from Figure 2.

However, other types of relations carry special meanings and are sparse. These include (i) foreign key relations that link a column in one table to the primary key of another table, (ii) exact string match and partial string match between words in the questions and words in column or table names and (iii) implicit links between a table and its columns. Some of these edges are illustrated in different colours on the input side in Figure 2. Because there can be more than one type of edge between two tokens to be modelled, this input is technically a multi-graph.

How do these edges help predict the correct SQL? Let's return to the examples.

## Example one

In Example One (Figure 2), the word "employee" in the question exactly matches the table name employee, so a special edge for an exact match is created in this input graph during preprocessing. For a graph neural network or relation-aware transformer that can encode a graph by propagating information along edges, this link creates a potential pathway for information from the representation of the columns (employee_ID, name, age, city) of table employee to contextualize the representation of the question token "employee", and vice versa. This makes it more likely for employee_ID, name, age, city to be selected compared to columns in the other tables when predicting a column corresponding to the condition "employee under 30".

## Example two

The second example is more interesting. The question mentions the table name shop explicitly, while the table employee can be easily inferred based on the column mention age. However, for hiring there is no textual evidence from the question, direct or indirect, that the SQL query should involve hiring. The only way to infer is through the foreign key links and the fact that otherwise shop and employee are disconnected and cannot be joined. This potential reasoning process is illustrated in Figure 3.

Figure 3. Foreign key relations among tables help infer the missing information not present in the question. a) if the foreign key relationships of the schema are not modelled (hence in grey), there is no way to infer that table hiring is needed in this case. b) with the foreign key links modelled (in green), the structure of schema shows that hiring is the needed the missing link between employee and shop, even though there are no direct textual cues from the question.

Now that we understand how the (multi-)graph structure would help the semantic parsing model, let's formalize what the encoder does at a high level. Let $\mathcal{S}=\{s_1,\dots, s_{\lvert \mathcal{S} \rvert}\}$ denote the schema elements, consisting of tables and their columns, and use $Q=q_1\dots q_{\lvert Q \rvert}$ to denote the sequence of words in the question. Let $\mathcal{G}=\langle\mathcal{V}, \mathcal{E}\rangle$ denote the multi-graph with edge sets $\mathcal{E}$. The encoder, $f_{\text{enc}}$, maps $\mathcal{G}$ to a joint representation $\mathcal{H} =$ $\{\phi^q_1, \ldots,\phi^q_{\lvert Q \rvert} \} \cup \{\phi^s_1, \ldots,\phi^s_{\lvert \mathcal{S} \rvert} \}$. The fully connected portion of the multi-graph can be well modelled by a transformer (see [link] for our blog series on Transformers). Indeed, one can flatten the schema into a linear string, with the tokens belonging to different column or table names separated by a special token like "[SEP]" and concatenate this string with the question string before feeding into a pre-trained model such as BERT. The use of pre-trained BERT (or other variants) here is how implicit common sense knowledge is embodied in the semantic parser. To model information propagation along the special sparse edges of the multi-graph, we can then feed the BERT output embeddings into a relation-aware transformer (Wang et al., 2019). There are a few subtle details omitted here, which we will give some pointers for at the end of this article.

## Grammar-based decoding

If we model SQL queries as linear sequences of text tokens on the output side, it is not easy to leverage the SQL grammar knowledge. During inference, one could use a grammar validator program to check if a generated sequence is legal; however, the neural network is still not using this information during training for better generalization. Furthermore, the grammar not only captures what is illegal but also how SQL expressions can be composed. Leveraging this prior knowledge will significantly improve the learning efficiency from a small number of examples. Therefore, we want to cast the problem as generating the abstract syntax tree of SQL queries.

Figure 4. How the TranX framework makes symbolic grammar knowledge accessible to a neural decoder: instead of directly predicting tokens of surface SQL code, the model would predict the sequence of AST-constructing action sequences. Before training, we preprocess the SQL code string by transforming it into its AST ($B$ $\leftarrow$ $C$). Then the TranX transition system builds the action sequences ($A$ $\leftarrow$ $B$) guided by the SQL grammar, expressed in the abstract syntax description language of TranX ($G$). Training can be done via maximum likelihood sequence learning with teacher-forcing. During inference, the model predicts action sequences guided by the grammar and the transition system, which defines the set of legal generation at each step. The generated action sequences are then post-processed deterministically to form the surface SQL code strings ($A \rightarrow B\rightarrow C$).

A common approach to predict an abstract syntax tree (AST) is to use a grammar-based transition system like TranX (Yin and Neubig, 2018), which decomposes the generation process of an abstract syntax tree (AST) into a sequence of actions. The neural model learns to predict the action sequence, and the transition system then constructs the AST using the predicted action sequence. Finally, another deterministic routine maps the AST into a linear string format of SQL, aka the surface code (Figure 4).

## Grammar

Figure 5 shows a snippet of the SQL grammar for TranX used by our Turing by Borealis AI system. It is specified in an abstract syntax description language (ASDL). It is similar to a context-free grammar, but more powerful, with each production rule's right-hand side being a function call signature with strongly-typed arguments. The type names are non-terminal symbols in the grammar, for which there are further production rules. This grammar is specific to the programming language of interest, or a subset of features in a programming language, and needs to be developed by a human expert.

 stmt = Intersect(query_expr lbody, query_expr rbody)      | Union(query_expr lbody, query_expr rbody)      | Except(query_expr lbody, query_expr rbody)      | SingleQuery(query_expr body) query_expr = Query(sel_expr sel_val, from_expr? from_val,                 where_expr? where_val, having_expr? having_val,                 orderBy_expr? orderBy_val, groupBy_expr? groupBy_val) sel_expr = Select(sel_col* sel_col_val) sel_col = SelectCol(agg_op agg_op_val, val_unit val_unit_val) from_expr = From(from_cond_expr* from_cond_val) ...

Figure 5. Example of SQL grammar expressed in the abstract syntax description language (ASDL) of TranX.

## Transition system

The transition system converts between an AST and its AST-constructing action sequence, leveraging a grammar like the one in Figure 5. The transition system starts at the root of the AST and derives the action sequence by a top-down, left-to-right depth-first traversal of the tree. At each step, it generates one of the possible parametrized action types.

For cross-domain text-to-SQL parsing, the action types can include: (1) ApplyRule[$r$] which applies a production rule $r$ of the grammar to the latest generated node in the AST; (2) Reduce which marks the complete generation of a subtree corresponding to a function call (in the ASDL grammar); (3-4) SelectTable[$t$] and SelectColumn[$c$] which, respectively, choose a table $t$ and a column $c$ from the database schema $\mathcal{S}$; (5) CopyToken[$k$] which copies a token $q_k$ from the user question $Q$; (6) GenToken[$l$] which generates a token $w_l$ from a vocabulary. In practice, with careful design, it is possible to simplify and avoid SelectTable and GenToken, which is part of the technical novelties in our Turing by Borealis AI system.

## Training

Before training, the TranX system first converts the surface SQL code to the AST representation using a deterministic domain-specific routine. Then, leveraging the grammar, it converts the AST into the action sequence (Figure 4). The actual training is then standard maximum likelihood with teacher-forcing, which you can read about in this tutorial. At each step, the model predicts the correct action conditioned on the ground-truth partial action sequence up to that point, as well as the encoder representation $\mathcal{H}$ of the question and schema. Most of the action types are parameterized by some argument, for example, production rule $r$ for ApplyRule, column $c$ for SelectColumn. The model first predicts the action type, then conditioned on the ground-truth action type (regardless of the predicted one), predicts the argument.

## Inference

The inference process builds upon beam-search, which you can learn more about in this tutorial. The difference here is that the beam-search is guided by the grammar and the transition system. This grammar-guided beam-search decoding sounds complex and indeed has many tedious implementation details, but it is conceptually simple: at each step of decoding, for each partial sequence in the beam, the transition system tracks all action types and arguments that are legal according to the grammar; the neural net can only select from those options. Once beam-search produces multiple action sequences, the transition system converts them to ASTs, then converts them to surface SQL code strings using the domain-specific post-processing routine as illustrated in Figure 5.

Besides the neural attention over the encoder representation, some other weak reasoning using the grammar happens here during beam-search inference. By tracking multiple partial trees (implicitly, via partial action sequences), a hypothesis scored high at the beginning could drop sharply because its high-probability continuation could violate the grammar. As a result, another partial tree that is less likely at first, could become more plausible and eventually be the top prediction.

## Further reading

Inferring and encoding special edges in the multi-graph: we saw some examples of special edges between a question token and schema word, but there could be other types of links. For example, suppose a question word happens to match a database value in some column. In that case, this is evidence that this question word has an implicit relationship to the corresponding column. More generally, these edges are inferred using heuristic pre-processing rules, in a process known as schema linking. The relation-aware transformer layers can learn to deal with some degree of noise in the links. For more details, please see the original RAT paper (Wang et al,. 2019).

We also discussed using a pre-trained transformer to encode the implicit fully-connected part of the multi-graph, in conjunction with RAT-based modelling of the sparse special edges. But the pre-trained transformer builds contextualized representation for subword tokens, whereas table and column names are usually phrases. The Appendix section of Xu et al. (2021a) contains more information about how these models can be pieced together.

Modelling tables implicitly through columns: as mentioned previously, it is possible to drop the SelectTable action altogether. The idea is to globally uniquely identify the columns rather than using the column names only. We can add the table representation to all of its column representations on the input encoding side before feeding into the RAT layers. On the output side, we can give each column a globally unique ID for SelectColumn. Then the table can be inferred deterministically from the predicted columns during post-processing. This design choice simplifies the relation learning for encoding and makes the output action sequences shorter. On some rare occasions, this becomes an over-simplification causing failures for some complex queries, for instance, when there are multiple self-joins. Please see XU et al., (2021b) for more details.

TranX transition system and leveraging tree structures in the neural decoder: so far, we only showed how TranX works on the high level, but readers interested in using the framework for semantic parsing should consult (Yin and Neubig, 2018) for more details. In particular, the TranX transition system exposes the topology of the AST to the linear action sequence decoding process via something called parent frontier field. The parent does not always correspond to the immediate preceding step in the action sequence. Yet, it is important to directly condition on its representation during decoding, which is known as parent feeding.

Handling values in the question: in Example One, the value $30$ from the question is exactly the token needed in the condition part of the SQL statement, so it can be just copied over. However, in general, this might not always be the case. Most models use a combination of generation and copy attention. But as mentioned earlier, Turing (Xu et al., 2021b) simplifies away the generation and only performs the copy action. The idea is that during training, the model learns to identify the question text span providing evidence for the value, which significantly simplifies the learning problem and reduces overfitting. A heuristic search-based post-processor is responsible for producing the actual value to be used in the SQL at inference time.

Training and generalization when the model is deep and the dataset small: using relation-aware transformer layers on top of pre-trained transformers like BERT or RoBERTa can quickly make the overall model very deep and hard to train. The usual rules-of-thumb for optimizing transformers are to use a large batch size, make the model shallower, or both. However, our recent work finds a way to train ultra-deep transformers ($48$ layers) using a small batch size and this improves the model generalization, especially for hard cases. This technique allowed us to place No. $1$ on the Spider Leaderboard (Exact Set Match without Values) 1.

Beyond teacher-forcing maximum likelihood: other sequence learning methods could also be used in theory, such as scheduled sampling or beam-search optimization (BSO). See our work on training a globally normalized semantic parsing model using a method similar to BSO (Huang et al., 2021), which works on some simple dataset, but not yet on complex ones like Spider.

Other approaches for semantic parsing: there are other promising approaches that do not follow the framework presented in this blog. For cross-database semantic parsing, Rubin and Berant (2021) abandons autoregressive decoding, but instead performs semi-autoregressive bottom-up semantic parsing. The advantage is that at each step of decoding, the model both conditions on and predicts semantically meaningful sub-programs, instead of semantically-vacuous partial trees. The method performs competitively on Spider, which is impressive; moreover, it potentially has better compositional or out-of-distribution generalization. On the other end of the spectrum, if our goal is not cross-domain text-to-SQL, but generic code generation, then our recent ACL work (Norouzi et al., 2021) shows that leveraging a large monolingual corpus of programming language source code enables simple transformer-based seq-to-seq baseline to perform competitively. Note that this does not contradict our discussion about simple seq-to-seq baseline unable to perform well in cross-database semantic parsing.

Explaining the queries: an essential feature of Turing by Borealis AI is the ability to explain the predicted queries to non-technical users. This allows people to use their own judgment to pick out which of the top hypotheses is more likely to be correct. Please check out our paper (Xu et al., 2021b) for more information about the explanation system.

1 As of June-02-2021, the time of publication of this blog. Our entry is "DT-Fixup SQL-SP + RoBERTa (DB content used) Borealis AI".

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