Original: D YNAMIC P ROMPT L EARNING VIA P OLICY G RADIENT FOR S EMI - STRUCTURED M ATHEMATICAL R EASONING
Revised: D YNAMIC P ROMPT L EARNING VIA P OLICY G RADIENT FOR S EMI - STRUCTURED M ATHEMATICAL R EASONING

Original: Anonymous authors

Original: Paper under double-blind review

Original: A BSTRACT
Revised: A BSTRACT

Original: Mathematical reasoning, a core ability of human intelligence, presents unique challenges for machines in abstract thinking and logical reasoning.
Revised: Mathematical reasoning, a core ability of human intelligence, presents unique challenges for machines in abstract thinking and logical reasoning.

Original: Recent large pre-trained language models such as GPT-3 have achieved remarkable progress on mathematical reasoning tasks written in text form, such as math word problems (MWP).
Revised: Recent large pre-trained language models such as GPT-3 have achieved remarkable progress on mathematical reasoning tasks written in text form, such as math word problems (MWP).

Original: However, it is unknown if the models can handle more complex problems that involve math reasoning over heterogeneous information, such as tabular data.
Revised: However, it is unknown if the models can handle more complex problems that involve math reasoning over heterogeneous information, such as tabular data.

Original: To fill the gap, we present Tabular Math Word Problems (T AB MWP), a new dataset containing 38,431 open-domain grade-level problems that require mathematical reasoning on both textual and tabular data.
Revised: To fill the gap, we present Tabular Math Word Problems (T AB MWP), a new dataset containing 38,431 open-domain grade-level problems that require mathematical reasoning on both textual and tabular data.

Original: Each question in T AB MWP is aligned with a tabular context, which is presented as an image, semi-structured text, and a structured table.
Revised: Each question in T AB MWP is aligned with a tabular context, which is presented as an image, semi-structured text, and a structured table.

Original: There are two types of questions: free-text and multichoice , and each problem is annotated with gold solutions to reveal the multi-step reasoning process.
Revised: There are two types of questions: free-text and multichoice , and each problem is annotated with gold solutions to reveal the multi-step reasoning process.

Original: We evaluate different pre-trained models on T AB MWP, including the GPT-3 model in a few-shot setting.
Revised: We evaluate different pre-trained models on T AB MWP, including the GPT-3 model in a few-shot setting.

Original: As earlier studies suggest, since few-shot GPT-3 relies on the selection of in-context examples, its performance is unstable and can degrade to near chance.
Revised: As earlier studies suggest, since few-shot GPT-3 relies on the selection of in-context examples, its performance is unstable and can degrade to near chance.

Original: The unstable issue is more severe when handling complex problems like T AB MWP.
Revised: The unstable issue is more severe when handling complex problems like T AB MWP.

Original: To mitigate this, we further propose a novel approach, P ROMPT PG, which utilizes policy gradient to learn to select in-context examples from a small amount of training data and then constructs the corresponding prompt for the test example.
Revised: To mitigate this, we further propose a novel approach, P ROMPT PG, which utilizes policy gradient to learn to select in-context examples from a small amount of training data and then constructs the corresponding prompt for the test example.

Original: Experimental results show that our method outperforms the best baseline by 5.31% on the accuracy metric and reduces the prediction variance significantly compared to random selection, which verifies its effectiveness in the selection of in-context examples.
Revised: Experimental results show that our method outperforms the best baseline by 5.31% on the accuracy metric and reduces the prediction variance significantly compared to random selection, which verifies its effectiveness in the selection of in-context examples.

Original:  I NTRODUCTION
Revised:  I NTRODUCTION

Original: Developing machines equipped with mathematical reasoning capabilities is one of the long-standing goals of artificial intelligence.
Revised: Developing machines equipped with mathematical reasoning capabilities is one of the long-standing goals of artificial intelligence.

Original: Solving math word problems (MWPs) is a well-defined task to diagnose the ability of intelligent systems to perform numerical reasoning and problem-solving as humans.
Revised: Solving math word problems (MWPs) is a well-defined task to diagnose the ability of intelligent systems to perform numerical reasoning and problem-solving as humans.

Original: A surge of datasets has been proposed to facilitate the research in this domain (Upadhyay & Chang, 2017; Amini et al., 2019; Miao et al., 2020; Cobbe et al., 2021).
Revised: A surge of datasets has been proposed to facilitate the research in this domain (Upadhyay & Chang, 2017; Amini et al., 2019; Miao et al., 2020; Cobbe et al., 2021).

Original: However, most existing
Revised: However, most existing

Original: MWP datasets focus on textual math word problems only.
Revised: MWP datasets focus on textual math word problems only.

Original: Tables, widely distributed in different documents such as invoices, health records, and financial reports, contain rich structured information different from unstructured text.
Revised: Tables, widely distributed in different documents such as invoices, health records, and financial reports, contain rich structured information different from unstructured text.

Original: Solving math word problems in such a tabular context is much more challenging than existing MWP benchmarks since the system needs to make cell selections and align heterogeneous information before performing further numerical reasoning.
Revised: Solving math word problems in such a tabular context is much more challenging than existing MWP benchmarks since the system needs to make cell selections and align heterogeneous information before performing further numerical reasoning.

Original: To fill this gap, we propose Tabular Math Word Problems (T AB MWP), a new large-scale dataset that contains 38,431 math word problems with tabular context, taken from grade-level math curricula.
Revised: To fill this gap, we propose Tabular Math Word Problems (T AB MWP), a new large-scale dataset that contains 38,431 math word problems with tabular context, taken from grade-level math curricula.

Original: There are two question types: free-text questions in which the answer is an integer or decimal number, and multi-choice questions where the answer is a text span chosen from option candidates.
Revised: There are two question types: free-text questions in which the answer is an integer or decimal number, and multi-choice questions where the answer is a text span chosen from option candidates.

Original: Different from existing MWP datasets, each problem in T AB MWP is accompanied by a tabular context, which is represented in three formats: an image, a semi-structured text, and a structuredtable.
Revised: Different from existing MWP datasets, each problem in T AB MWP is accompanied by a tabular context, which is represented in three formats: an image, a semi-structured text, and a structured

Original: Each problem is also annotated with a detailed solution that reveals the multi-step reasoning steps to ensure full explainability.

Original: To solve problems in T AB MWP, a system requires multi-hop mathematical reasoning over heterogeneous information by looking up table cells given textual clues and conducting multi-step operations to predict the final answer.

Original: Take the problem above in Figure

Original: [Figure]
Revised: [Figure]

Original: Question: As part of a project for health class, Cara surveyed local delis about the kinds of sandwiches sold. Which shop sold fewer sandwiches,
Revised: part of a project for health class

Original: [Figure]
Revised: [Figure]

Original: Then,
Revised: Cara

Original: [Figure]
Revised: [Figure]

Original: the numbers in the Express
Revised: local

Original: [Figure]
Revised: [Figure]

Revised: information by looking up table cells given textual clues and conducting multi-step operations to predict the final answer.

Original: [Figure] 1 as an example.
Revised: Take the problem above in Figure 1 as an example.

Original: To answer the question “ how much will she spend (if Tracy buys three kinds of beads) ?”
Revised: To answer the question “ how much will she spend (if Tracy buys three kinds of beads) ?”

Original: , we first need to look up the corresponding three rows in the given table, calculate the individual cost for each kind of bead, and finally sum three costs up to get the answer of 31.44.
Revised: , we first need to look up the corresponding three rows in the given table, calculate the individual cost for each kind of bead, and finally sum three costs up to get the answer of 31.44.

Original: Inspired the success of the large pre-trained language model GPT-3 (Brown et al., 2020) in solving math word problems (Wei et al., 2022; Wang et al., 2022), we first build a strong baseline using few-shot GPT-3 on T AB MWP.
Revised: Inspired the success of the large pre-trained language model GPT-3 (Brown et al., 2020) in solving math word problems (Wei et al., 2022; Wang et al., 2022), we first build a strong baseline using few-shot GPT-3 on T AB MWP.

Original: A few in-context examples are randomly selected from the training set, along with the test example, and are constructed as a prompt for GPT-3 to predict the answer.
Revised: A few in-context examples are randomly selected from the training set, along with the test example, and are constructed as a prompt for GPT-3 to predict the answer.

Original: However, recent studies have shown that this type of few-shot learning can be highly unstable across different selections of in-context examples (Zhao et al., 2021; Liu et al., 2022a; Lu et al., 2022b).
Revised: However, recent studies have shown that this type of few-shot learning can be highly unstable across different selections of in-context examples (Zhao et al., 2021; Liu et al., 2022a; Lu et al., 2022b).

Original: It could be worse on T AB MWP since its problems are distributed across multiple question types and diverse table layouts.
Revised: It could be worse on T AB MWP since its problems are distributed across multiple question types and diverse table layouts.

Original: Liu et al.
Revised: Liu et al.

Original: (2022a) try to address this issue by retrieving semantically similar examples.
Revised: (2022a) try to address this issue by retrieving semantically similar examples.

Original: However, this method might not work well sometimes on T AB MWP because it is not capable of measuring the similarity of structured information, such as the number of cells in tables.
Revised: However, this method might not work well sometimes on T AB MWP because it is not capable of measuring the similarity of structured information, such as the number of cells in tables.

Original: To alleviate this challenge, we further propose a novel approach that can learn to select in-context examples from a small amount of training data via policy gradient for prompt learning, termed
Revised: To alleviate this challenge, we further propose a novel approach that can learn to select in-context examples from a small amount of training data via policy gradient for prompt learning, termed

Original: P ROMPT PG.
Revised: P ROMPT PG.

Original: As illustrated in Figure 2, an agent learns to find optimal in-context examples from a candidate pool, with the goal of maximizing the prediction rewards on given training examples when interacting with the GPT-3 environment.
Revised: As illustrated in Figure 2, an agent learns to find optimal in-context examples from a candidate pool, with the goal of maximizing the prediction rewards on given training examples when interacting with the GPT-3 environment.

Original: A policy network defines the strategy of how to select the in-context examples given the current training example.
Revised: A policy network defines the strategy of how to select the in-context examples given the current training example.

Original: The policy network is built on top of the language model BERT (Devlin et al., 2018) with fixed parameters, followed by a one-layer linear neural network with learnable parameters.
Revised: The policy network is built on top of the language model BERT (Devlin et al., 2018) with fixed parameters, followed by a one-layer linear neural network with learnable parameters.

Original: The learnable parameters are updated following the policy gradient strategy (Sutton et al., 1998).
Revised: The learnable parameters are updated following the policy gradient strategy (Sutton et al., 1998).

Original: Unlike random selection (Wei et al., 2022; Wang et al., 2022), brute-force search, or retrieval-based selection (Liu et al., 2022a), P ROMPT PG learns to construct the prompt dynamically given the candidate pool when interacting with the GPT-3 API.
Revised: Unlike random selection (Wei et al., 2022; Wang et al., 2022), brute-force search, or retrieval-based selection (Liu et al., 2022a), P ROMPT PG learns to construct the prompt dynamically given the candidate pool when interacting with the GPT-3 API.

Original: We implement two state-of-the-art methods as baselines, i.e., UnifiedQA (Khashabi et al., 2020) on general question answering and TAPEX (Liu et al., 2022b) on tabular question answering.
Revised: We implement two state-of-the-art methods as baselines, i.e., UnifiedQA (Khashabi et al., 2020) on general question answering and TAPEX (Liu et al., 2022b) on tabular question answering.

Original: Both are implemented in pre-trained and fine-tuned settings.
Revised: Both are implemented in pre-trained and fine-tuned settings.

Original: Experimental results show that our model
Revised: Experimental results show that our model

Original: P ROMPT PG can achieve an overall accuracy of 68.23% on T AB MWP, which greatly surpasses previous methods by a large margin of up to 5.31%.
Revised: P ROMPT PG can achieve an overall accuracy of 68.23% on T AB MWP, which greatly surpasses previous methods by a large margin of up to 5.31%.

Original: Further analysis demonstrates that P ROMPT PG can select better in-context examples compared with a wide range of existing selection strategies and reduce the prediction variance significantly compared to random selection.
Revised: Further analysis demonstrates that P ROMPT PG can select better in-context examples compared with a wide range of existing selection strategies and reduce the prediction variance significantly compared to random selection.

Original: The main contributions of our work are as follows: (a) We present a new large-scale dataset,
Revised: The main contributions of our work are as follows: (a) We present a new large-scale dataset,

Original: T AB MWP, the first dataset for math word problems with tabular context; (b) We propose a novelapproach, P ROMPT PG, which learns the prompt dynamically via policy gradient to select in-context examples for few-shot GPT-3. To the best of our knowledge, it is the first work that applies rein-
Revised: T AB MWP, the first dataset for math word problems with tabular context; (b) We propose a novel

Original: [Figure]
Revised: [Figure]

Revised: approach, P ROMPT PG, which learns the prompt dynamically via policy gradient to select in-context examples for few-shot GPT-3.

Revised: To the best of our knowledge, it is the first work that applies reinforcement learning to select in-context examples for the few-shot GPT-3 model; (c) Experimental results show that P ROMPT PG achieves an improvement of up to 5.31% on T AB MWP over existing methods, with reduced selection instability compared to random selection.

Original:  T HE T AB MWP D ATASET 2. T ASK F ORMULATION
Revised:  T HE T AB MWP D ATASET 2. T ASK F ORMULATION

Original: A tabular math word problem p is represented as a pair ( t , q ), where t is a table context and q is a question.
Revised: A tabular math word problem p is represented as a pair ( t , q ), where t is a table context and q is a question.

Original: The table t could be represented in a visual format as an image, semi-structured text, or a structured database.
Revised: The table t could be represented in a visual format as an image, semi-structured text, or a structured database.

Original: In this work, we focus on the semi-structured format as the table context for simplicity.
Revised: In this work, we focus on the semi-structured format as the table context for simplicity.

Original: The table t features complicated layouts and formats: it contains multiple rows and columns, and each cell can be a string of text, a string of a number, or a mix of them.
Revised: The table t features complicated layouts and formats: it contains multiple rows and columns, and each cell can be a string of text, a string of a number, or a mix of them.

Original: Depending on the question and answer types, the question q may be accompanied by multiple-choice options c = { c 1 , c 2 , . . .
Revised: Depending on the question and answer types, the question q may be accompanied by multiple-choice options c = { c 1 , c 2 , . . .

Original: , c n } or a unit u .
Revised: , c n } or a unit u .

Original: Given a semi-structured tabular context t and an unstructured question text q , the task is to generate the answer a , which is either numerical only text for a freetext question, or a text span from given options for a multiple-choice question.
Revised: Given a semi-structured tabular context t and an unstructured question text q , the task is to generate the answer a , which is either numerical only text for a freetext question, or a text span from given options for a multiple-choice question.

Original: 2. D ATASET C ONSTRUCTION
Revised: 2. D ATASET C ONSTRUCTION

Original: Data collection.
Revised: Data collection.

Original: We construct T AB MWP based on openly available content and more details are provided in Appendix A.1.
Revised: We construct T AB MWP based on openly available content and more details are provided in Appendix A.1.

Original: Only math word problems that are accompanied by a tabular context and a detailed solution are collected.
Revised: Only math word problems that are accompanied by a tabular context and a detailed solution are collected.

Original: We develop a script to extract the tabular context, the question, options that apply, the correct answer, and the solution for each problem.
Revised: We develop a script to extract the tabular context, the question, options that apply, the correct answer, and the solution for each problem.

Original: These elements can be precisely identified using HTML tags.
Revised: These elements can be precisely identified using HTML tags.

Original: For each table, we take a screenshot and store its raw text.
Revised: For each table, we take a screenshot and store its raw text.

Original: Data preprocessing.
Revised: Data preprocessing.

Original: To make T AB MWP compatible with various baselines, we represent the tabular context as three formats: an image, semi-structured text, and a structured spreadsheet.
Revised: To make T AB MWP compatible with various baselines, we represent the tabular context as three formats: an image, semi-structured text, and a structured spreadsheet.

Original: The semi-structured format is created by converting the raw table text into a flattened token sequence, with each row separated by a newline character ‘ \ n ’ and each column separated by ‘ | ’.
Revised: The semi-structured format is created by converting the raw table text into a flattened token sequence, with each row separated by a newline character ‘ \ n ’ and each column separated by ‘ | ’.

Original: The semistructured text is further transformed to the structured format, which can be easily retrieved and executed by SQL-based methods (Liu et al., 2022b) using packages like pandas .
Revised: The semistructured text is further transformed to the structured format, which can be easily retrieved and executed by SQL-based methods (Liu et al., 2022b) using packages like pandas .

Original: For clarity, the table title is separated from the raw table.
Revised: For clarity, the table title is separated from the raw table.

Original: Examples of three formats are shown in Appendix A.1.
Revised: Examples of three formats are shown in Appendix A.1.

Original: For better quantitative evaluation, we formalize the T AB MWP problems as two question types: (a) free-text questions, where the answer is numerical text only and the unit text is separately extracted; and (b) multi-choice questions, the answer of which is the text span from choice options.
Revised: For better quantitative evaluation, we formalize the T AB MWP problems as two question types: (a) free-text questions, where the answer is numerical text only and the unit text is separately extracted; and (b) multi-choice questions, the answer of which is the text span from choice options.

Original: The order of choice options is shuffled to alleviate distribution bias.
Revised: The order of choice options is shuffled to alleviate distribution bias.

Original: Redundant information in solutions is removed, and some solutions are manually rewritten to be more human-readable.
Revised: Redundant information in solutions is removed, and some solutions are manually rewritten to be more human-readable.

Original: Finally, problems with the same table, question, and answer text are regarded as redundant and thus removed.
Revised: Finally, problems with the same table, question, and answer text are regarded as redundant and thus removed.

Original: We further conduct quality control to ensure data quality, which is discussed in Appendix A.1.
Revised: We further conduct quality control to ensure data quality, which is discussed in Appendix A.1.

Original: A tool for visualizing 1,000 data examples can be found in the supplementary material.

Original: 2. D ATASET S TATISTICS
Revised: 2. D ATASET S TATISTICS

Original: [Table]
Revised: [Table]

Original: Key statistics.
Revised: Key statistics.

Original: The T AB MWP dataset contains 38, tabular math word problems, which are partitioned with 6:2:2 into the training, development, and test splits, corresponding to 23,059, 7,686, and 7,686 problems.
Revised: The T AB MWP dataset contains 38, tabular math word problems, which are partitioned with 6:2:2 into the training, development, and test splits, corresponding to 23,059, 7,686, and 7,686 problems.

Original: Their main statistics are shown in Table 1.
Revised: Their main statistics are shown in Table 1.

Original: 74.7% of the questions in T AB MWP belong to free-text questions, while 25.3% are multi-choice questions.
Revised: 74.7% of the questions in T AB MWP belong to free-text questions, while 25.3% are multi-choice questions.

Original: There are 28,876 different questions, 6,153 different answers, and 35, different solutions, indicating that T AB MWP has a rich diversity in the problem distribution.
Revised: There are 28,876 different questions, 6,153 different answers, and 35, different solutions, indicating that T AB MWP has a rich diversity in the problem distribution.

Original: The questions have an average of 22.1 words in length and solutions of 49.5, showing that they have lexical richness.
Revised: The questions have an average of 22.1 words in length and solutions of 49.5, showing that they have lexical richness.

Original: One distinct characteristic of T AB MWP is that each problem is accompanied by a tabular context, without which the problem would be unsolvable.
Revised: One distinct characteristic of T AB MWP is that each problem is accompanied by a tabular context, without which the problem would be unsolvable.

Original: There are 37,644 different tables in total, and 60.5% of the tables have a title.
Revised: There are 37,644 different tables in total, and 60.5% of the tables have a title.

Original: The table has an average of 5.9 rows and 2.2 columns, which results in an average of 12.9 cells and a maximum of 54 cells.
Revised: The table has an average of 5.9 rows and 2.2 columns, which results in an average of 12.9 cells and a maximum of 54 cells.

Original: These statistics suggest that tables in T AB MWP distribute diversely across semantics and layouts.
Revised: These statistics suggest that tables in T AB MWP distribute diversely across semantics and layouts.

Original: Comparison to existing datasets.
Revised: Comparison to existing datasets.

Original: As shown in Table 2, T AB MWP differs from related datasets in various aspects: (1) T AB MWP is the first dataset to study math word problems over tabular context on open domains and is the largest in terms of data size;
Revised: As shown in Table 2, T AB MWP differs from related datasets in various aspects: (1) T AB MWP is the first dataset to study math word problems over tabular context on open domains and is the largest in terms of data size;

Original: (2) Problems in T AB MWP are annotated with the tabular context, unlike previous MWP datasets in the first segment; (3) Different from Table
Revised: (2) Problems in T AB MWP are annotated with the tabular context, unlike previous MWP datasets in the first segment; (3) Different from Table

Original: QA datasets like FinQA, TAT-QA, and MultiHiertt, a lack of either mathematical reasoning or the tabular context renders the problems in T AB MWP unanswerable; (4) There are two question types in T AB MWP, and the answer could be a text span, an integer number, or a decimal number; (5)
Revised: QA datasets like FinQA, TAT-QA, and MultiHiertt, a lack of either mathematical reasoning or the tabular context renders the problems in T AB MWP unanswerable; (4) There are two question types in T AB MWP, and the answer could be a text span, an integer number, or a decimal number; (5)

Original: Each problem is annotated with natural language solutions to reveal multi-hop reasoning steps.
Revised: Each problem is annotated with natural language solutions to reveal multi-hop reasoning steps.

Original: [Table]
Revised: [Table]

Original: ✗ ✓✗ ✗ ✗ ✓ ✗ ✗ ✓ ✓ [Table] ✗ ✓ ✗ ✗ ✗ ✓ ✗ ✗ ✓ ✓ formula
Revised: ✓

Original: [Table]
Revised: [Table]

Original: ✗ ✓ ✗ ✗ ✗ ✓ ✗ ✗✓ ✓ formula
Revised: ✗ ✓ ✗ ✗ ✗ ✓ ✗ ✗

Original: [Table]
Revised: [Table]

Original: ✗✓ ✗ ✗ ✗ ✗ ✓✗ ✓ ✓ formula
Revised: ✗ ✗ ✓

Original: [Table]
Revised: [Table]

Original: ✗ ✓ ✗ ✗ ✗✓ ✗ ✓  ✓ ✓formula
Revised: ✗ ✓ ✗ ✗ ✗ ✗ ✓ ✗ ✓ ✓

Original: [Table]

Original: [Table]

Original: ✗ ✓ ✗ ✗ ✗ ✓ ✗ ✗ ✓ ✗ formula

Original: [Table]
Revised: [Table]

Original: ✗ ✓ ✗ ✗ ✗ ✓ ✗✗ ✓ ✗
Revised: ✓ ✗ ✗ ✗ ✓ ✗ ✓ ✓ ✓

Original: [Table]
Revised: [Table]

Original: ✗✓ ✗ ✗ ✗ ✓ ✓ ✓ ✓ ✗ ✗
Revised: ✗ ✗

Original: [Table]
Revised: [Table]

Original:  M ETHODS 3. F EW - SHOT GPT-3 FOR T AB MWP
Revised:  M ETHODS 3. F EW - SHOT GPT-3 FOR T AB MWP

Original: Provided with a few in-context examples of math word problems as the context, GPT-3 can generate the answer for a test problem, and shows impressive performance across different MWP datasets (Wei et al., 2022; Wang et al., 2022).
Revised: Provided with a few in-context examples of math word problems as the context, GPT-3 can generate the answer for a test problem, and shows impressive performance across different MWP datasets (Wei et al., 2022; Wang et al., 2022).

Original: Inspired by its success, we first build a strong baseline using few-shot GPT-3 on our T AB MWP dataset.
Revised: Inspired by its success, we first build a strong baseline using few-shot GPT-3 on our T AB MWP dataset.

Original: Specifically, a few training examples, along with the test example p i , are provided to GPT-3 for the answer prediction.
Revised: Specifically, a few training examples, along with the test example p i , are provided to GPT-3 for the answer prediction.

Original: Each training example consists of a table context t , a question q , options c that apply, and an answer a .
Revised: Each training example consists of a table context t , a question q , options c that apply, and an answer a .

Original: To make the few-shot
Revised: To make the few-shot

Original: GPT-3 model workable on T AB MWP, we utilize the semi-structured format as the tabular context.
Revised: GPT-3 model workable on T AB MWP, we utilize the semi-structured format as the tabular context.

Original: Following Wei et al.
Revised: Following Wei et al.

Original: (2022), a solution s can be augmented in front of the answer a to reveal the multi-step reasoning process, which is able to boost the prediction performance.
Revised: (2022), a solution s can be augmented in front of the answer a to reveal the multi-step reasoning process, which is able to boost the prediction performance.

Original: 3. D YNAMIC P ROMPTING VIA P OLICY G RADIENT
Revised: 3. D YNAMIC P ROMPTING VIA P OLICY G RADIENT

Original: The in-context examples can be randomly (Wei et al., 2022; Wang et al., 2022) or retrieval-based selected (Liu et al., 2022a) from the training set.
Revised: The in-context examples can be randomly (Wei et al., 2022; Wang et al., 2022) or retrieval-based selected (Liu et al., 2022a) from the training set.

Original: Recent research, however, has shown that few-shot
Revised: Recent research, however, has shown that few-shot

Original: GPT-3 can be highly unstable across different selections of in-context examples and permutations of those examples (Zhao et al., 2021;
Revised: GPT-3 can be highly unstable across different selections of in-context examples and permutations of those examples (Zhao et al., 2021;

Original: Liu et al., 2022a; Lu et al., 2022b).
Revised: Liu et al., 2022a; Lu et al., 2022b).

Original: This instability may be more severe on T AB MWP, where examples are more distinct because they include both unstructured questions of various types and semi-structured tables in various layouts.
Revised: This instability may be more severe on T AB MWP, where examples are more distinct because they include both unstructured questions of various types and semi-structured tables in various layouts.

Original: To alleviate this issue, we aim to propose a novel approach that can learn to select performing in-context examples using a policy gradient strategy, without brute-force searching or manually designed heuristics.
Revised: To alleviate this issue, we aim to propose a novel approach that can learn to select performing in-context examples using a policy gradient strategy, without brute-force searching or manually designed heuristics.

Original: Formally, given a T AB MWP problem p i , we want the agent to find K in-context examples e i = { e 1 i , e 2 i , ..., e K i } from a candidate pool E cand , and generate the answer ˆ a i , maximizing a reward r i
Revised: Formally, given a T AB MWP problem p i , we want the agent to find K in-context examples e i = { e 1 i , e 2 i , ..., e K i } from a candidate pool E cand , and generate the answer ˆ a i , maximizing a reward r i

Original: =
Revised: =

Original: R (ˆ a i | p i ) .
Revised: R (ˆ a i | p i ) .

Revised: The in-context examples are selected according to a policy e

Revised: [Equation]

Revised: cand

Revised: [Equation]

Original: The in-context examples are selected according to a policy e ki ∼ π θ ( e i | p i ) , e ki ∈ E cand , e ki are independent for k = { 1 , 2 , ..., K } , (1) where θ are the policy’s parameters.
Revised: ki are independent for [Equation] [Equation] ..., K } , (1) where θ are the policy’s parameters.

Original: The answer is generated through: ˆ
Revised: The answer is generated through: ˆ

Original: a i = GPT-3 ( e i , p i ) using the selected examples and the given problem as the input prompt.
Revised: a i = GPT-3 ( e i , p i ) using the selected examples and the given problem as the input prompt.

Original: The reward is then computed by evaluating the generated answer ˆ a i with respect to the ground truth answer a i :
Revised: The reward is then computed by evaluating the generated answer ˆ a i with respect to the ground truth answer a i :

Original: [Equation]
Revised: [Equation]

Original: The function E VAL () returns a reward of 1 if the generated answer aligned with the label and −otherwise.
Revised: The function E VAL () returns a reward of 1 if the generated answer aligned with the label and −otherwise.

Original: Our goal is to maximize the expected reward of the generated answer under the policy
Revised: Our goal is to maximize the expected reward of the generated answer under the policy

Original: E e i ∼ π θ ( e i | p i )
Revised: E e i ∼ π θ ( e i | p i )

Original: [ R ( GPT-3 ( e i , p i ))] .
Revised: [ R ( GPT-3 ( e i , p i ))] .

Original: We optimize the reward with respect to the parameters of the policy network using the Policy Gradient method (Sutton et al., 1998).
Revised: We optimize the reward with respect to the parameters of the policy network using the Policy Gradient method (Sutton et al., 1998).

Original: The expected reward cannot be computed in closed form, so we compute an unbiased estimation with Monte Carlo Sampling,
Revised: The expected reward cannot be computed in closed form, so we compute an unbiased estimation with Monte Carlo Sampling,

Original: [Equation]
Revised: [Equation]

Original: where N is the size of each batch yielded from our training problem set P train .
Revised: where N is the size of each batch yielded from our training problem set P train .

Original: In this work, we experiment using the REINFORCE policy gradient algorithm (Williams, 1992):
Revised: In this work, we experiment using the REINFORCE policy gradient algorithm (Williams, 1992):

Original: [Equation]
Revised: [Equation]

Original: Intuitively, if the predicted answer is correct, we update the policy so that the probability of selecting the same prompts gets higher.
Revised: Intuitively, if the predicted answer is correct, we update the policy so that the probability of selecting the same prompts gets higher.

Original: Otherwise, we update the policy to reduce the probability of selecting such less matched examples.
Revised: Otherwise, we update the policy to reduce the probability of selecting such less matched examples.

Original: The learning process is summarized in Algorithm 1 in the appendix.
Revised: The learning process is summarized in Algorithm 1 in the appendix.

Original: To get the contextualized representation of the given problem and candidate examples, we use the
Revised: To get the contextualized representation of the given problem and candidate examples, we use the

Original: BERT (Devlin et al., 2018)
Revised: BERT (Devlin et al., 2018)

Original: [CLS] token representation as the problem encoding.
Revised: [CLS] token representation as the problem encoding.

Original: We add a small linear layer on top of the BERT final pooling layer.
Revised: We add a small linear layer on top of the BERT final pooling layer.

Original: That allows our model to learn both the semantic similarity that the pre-trained BERT model provides and the hidden logical similarity shared among the math problems.
Revised: That allows our model to learn both the semantic similarity that the pre-trained BERT model provides and the hidden logical similarity shared among the math problems.

Original: During training, the parameters of BERT are fixed and only the appended linear layer is updated, i.e., θ is composed of the learnable parameters W and b :
Revised: During training, the parameters of BERT are fixed and only the appended linear layer is updated, i.e., θ is composed of the learnable parameters W and b :

Original: [Equation]
Revised: [Equation]

Original: [Equation]
Revised: [Equation]

Original:  E XPERIMENTS 4. E XPERIMENTAL S ETTINGS
Revised:  E XPERIMENTS 4. E XPERIMENTAL S ETTINGS

Original: Baselines.
Revised: Baselines.

Original: We first develop two large language models, UnifiedQA (Khashabi et al., 2020) and
Revised: We first develop two large language models, UnifiedQA (Khashabi et al., 2020) and

Original: TAPEX (Liu et al., 2022b), in both pre-trained and fine-tuned settings, as strong baselines on
Revised: TAPEX (Liu et al., 2022b), in both pre-trained and fine-tuned settings, as strong baselines on

Original: T AB MWP.
Revised: T AB MWP.

Original: Different model sizes are included to examine the performance across different model capacities.
Revised: Different model sizes are included to examine the performance across different model capacities.

Original: We further implement the zero-shot GPT-3 model, the few-shot GPT-3 model, and their chain-of-thought (CoT) reasoning variants (Wei et al., 2022).
Revised: We further implement the zero-shot GPT-3 model, the few-shot GPT-3 model, and their chain-of-thought (CoT) reasoning variants (Wei et al., 2022).

Original: We also study the heuristic guess baseline and human performance to analyze the lower and upper bounds on T AB MWP, respectively.
Revised: We also study the heuristic guess baseline and human performance to analyze the lower and upper bounds on T AB MWP, respectively.

Original: Evaluation metric.
Revised: Evaluation metric.

Original: The answer part is extracted from the GPT-3 generation using manually designed regular expressions.
Revised: The answer part is extracted from the GPT-3 generation using manually designed regular expressions.

Original: To evaluate the baselines and our method, we utilize the accuracy metric to determine if the generated answer is correct given the ground truth answer.
Revised: To evaluate the baselines and our method, we utilize the accuracy metric to determine if the generated answer is correct given the ground truth answer.

Original: For free-text problems where the answer is set as a number, we normalize the prediction and the label to decimal numbers with two-digit precision and check if their values are equivalent.
Revised: For free-text problems where the answer is set as a number, we normalize the prediction and the label to decimal numbers with two-digit precision and check if their values are equivalent.

Original: For multi-choice problems, we choose the most similar one from options to the generated answer following Khashabi et al.
Revised: For multi-choice problems, we choose the most similar one from options to the generated answer following Khashabi et al.

Original: Implementation details.
Revised: Implementation details.

Original: Fine-tuned UnifiedQA and TAPEX baselines are trained on the train split and evaluated on the test split.
Revised: Fine-tuned UnifiedQA and TAPEX baselines are trained on the train split and evaluated on the test split.

Original: Few-shot GPT-3 and few-shot-CoT GPT-3 randomly select two incontext examples from the training data to build the prompt.
Revised: Few-shot GPT-3 and few-shot-CoT GPT-3 randomly select two incontext examples from the training data to build the prompt.

Original: Our P ROMPT PG is built on top of few-shot GPT-3 with a different selection strategy: (a) in the training stage, the agent learns to select two examples from 20 candidates and is evaluated on 160 training examples to calculate the reward; (b) in the test stage, the agent with an optimal policy chooses two examples from 20 candidates for each test example.
Revised: Our P ROMPT PG is built on top of few-shot GPT-3 with a different selection strategy: (a) in the training stage, the agent learns to select two examples from 20 candidates and is evaluated on 160 training examples to calculate the reward; (b) in the test stage, the agent with an optimal policy chooses two examples from 20 candidates for each test example.

Original: The candidates are randomly selected from the training set.
Revised: The candidates are randomly selected from the training set.

Original: Experiments for two few-shot GPT-3 baselines and our P ROMPT PG are repeated three times, and the average accuracy is reported in Table 3.
Revised: Experiments for two few-shot GPT-3 baselines and our P ROMPT PG are repeated three times, and the average accuracy is reported in Table 3.

Original: More implementation details can be found in Appendix A.4.
Revised: More implementation details can be found in Appendix A.4.

Original: 4. E XPERIMENTAL R ESULTS
Revised: 4. E XPERIMENTAL R ESULTS

Original: Table 3 demonstrates the results of different baselines and our method on the T AB MWP dataset.
Revised: Table 3 demonstrates the results of different baselines and our method on the T AB MWP dataset.

Original: Benefiting from pre-training on the tabular corpus, the TAPEX baseline performs better on average than UnifiedQA with a similar model size, which is only pre-trained on unstructured textual data.
Revised: Benefiting from pre-training on the tabular corpus, the TAPEX baseline performs better on average than UnifiedQA with a similar model size, which is only pre-trained on unstructured textual data.

Original: Increasing the model size can improve the prediction accuracy for both UnifiedQA and TAPEX.
Revised: Increasing the model size can improve the prediction accuracy for both UnifiedQA and TAPEX.

Original: Fine-tuned on T AB MWP, the baseline models can significantly improve the prediction performance on the average and all aggregated accuracy metrics.
Revised: Fine-tuned on T AB MWP, the baseline models can significantly improve the prediction performance on the average and all aggregated accuracy metrics.

Original: Without any examples provided to GPT-3, zero-shot GPT-3 achieves a comparable accuracy to the best fine-tuned baselines, UnifiedQA L ARGE and TAPEX L ARGE , showing its surprisingly good generalization ability on T AB MWP.
Revised: Without any examples provided to GPT-3, zero-shot GPT-3 achieves a comparable accuracy to the best fine-tuned baselines, UnifiedQA L ARGE and TAPEX L ARGE , showing its surprisingly good generalization ability on T AB MWP.

Original: Provided with two randomly sampled in-context examples as the prompt, few-shot GPT-3 gets an improvement of 0.17%.
Revised: Provided with two randomly sampled in-context examples as the prompt, few-shot GPT-3 gets an improvement of 0.17%.

Original: Generating the multi-step solution before the answer, the few-shot-CoT GPT-3 model reports the best performance among all of these baseline models, with an accuracy of 62.92%.
Revised: Generating the multi-step solution before the answer, the few-shot-CoT GPT-3 model reports the best performance among all of these baseline models, with an accuracy of 62.92%.

Original: Unlike few-shot-CoT GPT-3 randomly selecting the in-context examples, our proposed P ROMPT PG learns to select performing examples with the help of policy gradient.
Revised: Unlike few-shot-CoT GPT-3 randomly selecting the in-context examples, our proposed P ROMPT PG learns to select performing examples with the help of policy gradient.

Original: P ROMPT
Revised: P ROMPT

Original: PG establishes a state-of-the-art performance on the T AB MWP dataset: it surpasses the best baseline few-shot-CoT GPT-3 by 5.31% on average.
Revised: PG establishes a state-of-the-art performance on the T AB MWP dataset: it surpasses the best baseline few-shot-CoT GPT-3 by 5.31% on average.

Original: P ROMPT
Revised: P ROMPT

Original: PG shows its consistent advantages on two question types, two grade groups, and most of the answer types.
Revised: PG shows its consistent advantages on two question types, two grade groups, and most of the answer types.

Original: Heuristic guess and human performance.
Revised: Heuristic guess and human performance.

Original: The accuracy of multi-choice questions by heuristic guess is 39.81%, which aligns with the fact that there are 2.88 options on average.
Revised: The accuracy of multi-choice questions by heuristic guess is 39.81%, which aligns with the fact that there are 2.88 options on average.

Original: The accuracy for free-text questions is considerably low since the inputs of T AB MWP problems do not have direct clues for the answers.
Revised: The accuracy for free-text questions is considerably low since the inputs of T AB MWP problems do not have direct clues for the answers.

Original: Humans outperform all benchmarks consistently across question types, answer types, and grade groups, with a 21.99% average accuracy advantage over our best performing
Revised: Humans outperform all benchmarks consistently across question types, answer types, and grade groups, with a 21.99% average accuracy advantage over our best performing

Original: P ROMPT PG.
Revised: P ROMPT PG.

Original: This gap is to be filled by future research on semi-structured mathematical reasoning.
Revised: This gap is to be filled by future research on semi-structured mathematical reasoning.

Original: Problem types and difficulty.
Revised: Problem types and difficulty.

Original: Among all the baselines, we find it is easier for models to answer multi-choice questions than free-text questions.
Revised: Among all the baselines, we find it is easier for models to answer multi-choice questions than free-text questions.

Original: Questions with the boolean (BOOL) and other (OTH) answer types tend to have lower accuracy scores than the extractive (EXTR) answer type, because the former ones need the abilities of fact verification and language understanding on diverse options, respectively.
Revised: Questions with the boolean (BOOL) and other (OTH) answer types tend to have lower accuracy scores than the extractive (EXTR) answer type, because the former ones need the abilities of fact verification and language understanding on diverse options, respectively.

Original: It is also not surprising for us to find that all the models perform worse on problems in grades 7-8 than in a lower-level group of 1-6.
Revised: It is also not surprising for us to find that all the models perform worse on problems in grades 7-8 than in a lower-level group of 1-6.

Original: [Table]
Revised: [Table]

Original: 4. A BLATION S TUDY
Revised: A BLATION S TUDY

Original: Here, we will study how different factors have an effect on the performances of baselines and our method on T AB MWP.
Revised: Here, we will study how different factors have an effect on the performances of baselines and our method on T AB MWP.

Original: Experiments are conducted on 1,000 development examples.
Revised: Experiments are conducted on 1,000 development examples.

Original: Blind study of the dataset.
Revised: Blind study of the dataset.

Original: We evaluate the information gain of each component of the T AB MWP problems by removing it from model inputs.
Revised: We evaluate the information gain of each component of the T AB MWP problems by removing it from model inputs.

Original: To eliminate the impact and variance caused by example selection, the study is conducted using the zero-shot GPT-3 model.
Revised: To eliminate the impact and variance caused by example selection, the study is conducted using the zero-shot GPT-3 model.

Original: As shown in Table 4, there is a dramatic decline when either the tabular context (T) or the question text (Q) is missing from the inputs.
Revised: As shown in Table 4, there is a dramatic decline when either the tabular context (T) or the question text (Q) is missing from the inputs.

Original: For example, T → A and Q
Revised: For example, T → A and Q

Original: → A only attain an average accuracy of 6.10% and 7.00%, respectively
Revised: → A only attain an average accuracy of 6.10% and 7.00%, respectively

Original: [Table]
Revised: [Table]

Original: and their accuracies are near to zero on the multi-choice questions.
Revised: and their accuracies are near to zero on the multi-choice questions.

Original: Taking both tabular and textual data as inputs (TQ → A), the model significantly beats the heuristic guess.
Revised: Taking both tabular and textual data as inputs (TQ → A), the model significantly beats the heuristic guess.

Original: With the complete input information (TQ(C) → A), the full model achieves the best performance.
Revised: With the complete input information (TQ(C) → A), the full model achieves the best performance.

Original: The blind study shows that our T AB MWP is robust and reliable in distribution
Revised: The blind study shows that our T AB MWP is robust and reliable in distribution

Original: [Table]
Revised: [Table]

Original: and all input components are indispensable parts that provide necessary information for answering the questions
Revised: and all input components are indispensable parts that provide necessary information for answering the questions

Original: [Table]
Revised: [Table]

Original: Number of training examples.
Revised: Number of training examples.

Original: We study the effect of different numbers of training examples on our dynamic prompt learning in Figure 3 (a).
Revised: We study the effect of different numbers of training examples on our dynamic prompt learning in Figure 3 (a).

Original: With more training examples, the prediction accuracy first gradually increases to a peak of around 160 training examples.
Revised: With more training examples, the prediction accuracy first gradually increases to a peak of around 160 training examples.

Original: After that, the accuracy goes down with a growing variance.
Revised: After that, the accuracy goes down with a growing variance.

Original: We reckon it is because the policy gradient algorithm can benefit from the scaling-up training data but fails to exploit more examples efficiently.[Figure] examples
Revised: We reckon it is because the policy gradient algorithm can benefit from the scaling-up training data but fails to exploit more examples efficiently.

Original: [Figure]
Revised: [Figure]

Original: given 20 candidate examples

Original: [Figure]
Revised: [Figure]

Original: Number of candidate examples.
Revised: Number of candidate examples.

Original: In Figure 3 (b), we investigate how different numbers of candidate examples can affect policy learning performance.
Revised: In Figure 3 (b), we investigate how different numbers of candidate examples can affect policy learning performance.

Original: With the increasing candidate number, it is observed that the prediction accuracy will first go up and then go down after a threshold, given 80 or 160 training examples.
Revised: With the increasing candidate number, it is observed that the prediction accuracy will first go up and then go down after a threshold, given 80 or 160 training examples.

Original: It is probably because when the candidate pool is too small, the policy gradient algorithm has a limited action space to explore enough problem types.
Revised: It is probably because when the candidate pool is too small, the policy gradient algorithm has a limited action space to explore enough problem types.

Original: In contrast, too many candidates could make the algorithm hard to learn an optimal policy in a large search space.[Table] [Figure] [Table]
Revised: In contrast, too many candidates could make the algorithm hard to learn an optimal policy in a large search space.

Original: [Figure]

Original: [Table]
Revised: [Table]

Original: Different selection strategies.
Revised: Different selection strategies.

Original: In Table 5, we compare the proposed P ROMPT PG with random selection and other heuristic-based example selection strategies for the few-shot-CoT GPT-3 model.
Revised: In Table 5, we compare the proposed P ROMPT PG with random selection and other heuristic-based example selection strategies for the few-shot-CoT GPT-3 model.

Original: Compared to random selection, selecting the same question or answer type of examples helps the model to take the task-relevant examples as the prompt, thus improving the accuracy and reducing the variance.
Revised: Compared to random selection, selecting the same question or answer type of examples helps the model to take the task-relevant examples as the prompt, thus improving the accuracy and reducing the variance.

Original: Choosing the most complex examples does not boost the prediction performance consistently.
Revised: Choosing the most complex examples does not boost the prediction performance consistently.

Original: Manual selection selects the two examples from 20 with the highest evaluation accuracy on oneshot-CoT GPT-3 as the fixed set of in-context examples.
Revised: Manual selection selects the two examples from 20 with the highest evaluation accuracy on oneshot-CoT GPT-3 as the fixed set of in-context examples.

Original: Although it achieves the lowest prediction variance of 0, it only improves by 1.7% over random selection.
Revised: Although it achieves the lowest prediction variance of 0, it only improves by 1.7% over random selection.

Original: The most semantically similar examples, as a kind of nearest neighbor search of the test example, help construct the performing and stable prompt for GPT-3.
Revised: The most semantically similar examples, as a kind of nearest neighbor search of the test example, help construct the performing and stable prompt for GPT-3.

Original: P ROMPT
Revised: P ROMPT

Original: PG shows its effectiveness in selecting optimal in-context examples over other strategies and largely reduces the instability.
Revised: PG shows its effectiveness in selecting optimal in-context examples over other strategies and largely reduces the instability.

Original: 4. C ASE S TUDY
Revised: 4. C ASE S TUDY

Original: We conduct the case study in Appendix A.7.
Revised: We conduct the case study in Appendix A.7.

Original: We visualize the two in-context examples selected by strategies of our P ROMPT
Revised: We visualize the two in-context examples selected by strategies of our P ROMPT

Original: PG, nearest neighbor search, and random selection, in Figure 5, 6, and 7, respectively.
Revised: PG, nearest neighbor search, and random selection, in Figure 5, 6, and 7, respectively.

Original: The nearest neighbor search strategy selects the “superficially” similar examples to the test example.
Revised: The nearest neighbor search strategy selects the “superficially” similar examples to the test example.

Original: Instead, P ROMPT PG tends to select examples that have multiple reasoning steps in the solution and similar abilities in mathematical reasoning, which results in higher prediction accuracy.
Revised: Instead, P ROMPT PG tends to select examples that have multiple reasoning steps in the solution and similar abilities in mathematical reasoning, which results in higher prediction accuracy.

Original: Successful examples in Figure 8 - 12 show that P ROMPT PG is able to generate reasonable reasoning steps to predict correct answers for a wide range of T AB MWP problems.
Revised: Successful examples in Figure 8 - 12 show that P ROMPT PG is able to generate reasonable reasoning steps to predict correct answers for a wide range of T AB MWP problems.

Original: Failure examples in Figure 13 - 18 suggest that P ROMPT PG has limitations when solving problems provided with complex tabular contexts or requiring a high-level ability of mathematical reasoning.
Revised: Failure examples in Figure 13 - 18 suggest that P ROMPT PG has limitations when solving problems provided with complex tabular contexts or requiring a high-level ability of mathematical reasoning.

Original:  R ELATED W ORK 5. M ATH W ORD P ROBLEMS
Revised:  R ELATED W ORK 5. M ATH W ORD P ROBLEMS

Original: The task of solving Math Word Problems (MWPs) is to predict the answer given a natural language description of a math problem.
Revised: The task of solving Math Word Problems (MWPs) is to predict the answer given a natural language description of a math problem.

Original: There have been great efforts in developing datasets for MWPs, in- cluding Dolphin18K (Huang et al., 2016), DRAW-1K (Upadhyay & Chang, 2017), Math23K (Wang et al., 2017), MathQA (Amini et al., 2019),
Revised: There have been great efforts in developing datasets for MWPs, in- cluding Dolphin18K (Huang et al., 2016), DRAW-1K (Upadhyay & Chang, 2017), Math23K (Wang et al., 2017), MathQA (Amini et al., 2019),

Original: ASDiv (Miao et al., 2020), and SVAMP (Patel et al., 2021).
Revised: ASDiv (Miao et al., 2020), and SVAMP (Patel et al., 2021).

Original: However, these datasets only involve the textual modality, and most are limited to a small data scale.
Revised: However, these datasets only involve the textual modality, and most are limited to a small data scale.

Original: Some recent datasets like DVQA (Kafle et al., 2018), Geometry3K (Lu et al., 2021a) and
Revised: Some recent datasets like DVQA (Kafle et al., 2018), Geometry3K (Lu et al., 2021a) and

Original: IconQA (Lu et al., 2021b) introduce math problems with diagrams as the visual context, where the system needs to perform mathematical reasoning over multi-modal information.
Revised: IconQA (Lu et al., 2021b) introduce math problems with diagrams as the visual context, where the system needs to perform mathematical reasoning over multi-modal information.

Original: To the best of our knowledge, our dataset T AB MWP is the first dataset that requires mathematical reasoning over heterogeneous information from both the textual question and the tabular context.
Revised: To the best of our knowledge, our dataset T AB MWP is the first dataset that requires mathematical reasoning over heterogeneous information from both the textual question and the tabular context.

Original: To solve MWPs, one popular line of previous methods is to generate the intermediate expressions and execute them to get the final answers (Huang et al., 2017; Roy & Roth, 2017; Amini et al., 2019).
Revised: To solve MWPs, one popular line of previous methods is to generate the intermediate expressions and execute them to get the final answers (Huang et al., 2017; Roy & Roth, 2017; Amini et al., 2019).

Original: Inspired by the recent progress achieved by GPT-3 in solving MWPs (Wei et al., 2022; Wang et al., 2022; Kojima et al., 2022), we evaluate T AB MWP using GPT-3 models in zero-shot and few-shot learning manners.
Revised: Inspired by the recent progress achieved by GPT-3 in solving MWPs (Wei et al., 2022; Wang et al., 2022; Kojima et al., 2022), we evaluate T AB MWP using GPT-3 models in zero-shot and few-shot learning manners.

Original: T ABLE QA D ATASETS
Revised: T ABLE QA D ATASETS

Original: Table Question Answering (Table QA) refers to the task of answering questions about tabular data.
Revised: Table Question Answering (Table QA) refers to the task of answering questions about tabular data.

Original: Numerous datasets have been developed for Table QA.
Revised: Numerous datasets have been developed for Table QA.

Original: For example, TabMCQ (Jauhar et al., 2016) is an early dataset collected from grade exams.
Revised: For example, TabMCQ (Jauhar et al., 2016) is an early dataset collected from grade exams.

Original: Datasets like WTQ (Pasupat & Liang, 2015), WikiSQL (Zhong et al., 2017), and SQA (Iyyer et al., 2017) contain semi-structured tables from Wikipedia, while Spider (Yu et al., 2018) collects structured tables sourced from databases.
Revised: Datasets like WTQ (Pasupat & Liang, 2015), WikiSQL (Zhong et al., 2017), and SQA (Iyyer et al., 2017) contain semi-structured tables from Wikipedia, while Spider (Yu et al., 2018) collects structured tables sourced from databases.

Original: Recent work aims at introducing datasets that require multi-hop reasoning between the textual and  because they need numerical reasoning on financial reports with tabular data.
Revised: Recent work aims at introducing datasets that require multi-hop reasoning between the textual and tabular data: HybridQA (Chen et al., 2020b), OTTQA (Chen et al., 2020a), MultiModalQA (Talmor et al., 2020), AIT-QA (Katsis et al., 2021), and FeTaQA (Nan et al., 2022). Datasets most related to our T AB MWP dataset are FinQA (Chen et al., 2021), TAT-QA (Zhu et al., 2021), and MultiHiertt (Zhao et al., 2022) because they need numerical reasoning on financial reports with tabular data.

Original: Note that 77.6% of questions in TAT-QA can be solvable without mathematical reasoning and 50.0% of questions in
Revised: Note that 77.6% of questions in TAT-QA can be solvable without mathematical reasoning and 50.0% of questions in

Original: FinQA are not table-must to be answered.
Revised: FinQA are not table-must to be answered.

Original: In contrast, our proposed T AB MWP collects questions where both mathematical reasoning and tabular context are necessary.
Revised: In contrast, our proposed T AB MWP collects questions where both mathematical reasoning and tabular context are necessary.

Original: 5. P ROMPT L EARNING FOR L ANGUAGE M ODELS
Revised: 5. P ROMPT L EARNING FOR L ANGUAGE M ODELS

Original: Large pre-trained language models, such as GPT-3 (Brown et al., 2020), have shown their remarkable ability of few-shot learning on a wide range of downstream tasks (Houlsby et al., 2019;
Revised: Large pre-trained language models, such as GPT-3 (Brown et al., 2020), have shown their remarkable ability of few-shot learning on a wide range of downstream tasks (Houlsby et al., 2019;

Original: Brown et al., 2020;
Revised: Brown et al., 2020;

Original: Lu et al., 2022a).
Revised: Lu et al., 2022a).

Original: Given a few in-context examples as demonstrations, GPT-3 can generalize to unseen test examples without parameter updating.
Revised: Given a few in-context examples as demonstrations, GPT-3 can generalize to unseen test examples without parameter updating.

Original: For example, Wei et al.
Revised: For example, Wei et al.

Original: (2022) randomly select different in-context examples from the training set and formulate their corresponding prompt with a test sample.
Revised: (2022) randomly select different in-context examples from the training set and formulate their corresponding prompt with a test sample.

Original: However, recent studies show that few-shot GPT-3 highly depends on the selection of in-context examples and could be unstable, varying from the near chance to near stateof-the-art performance (Zhao et al., 2021;
Revised: However, recent studies show that few-shot GPT-3 highly depends on the selection of in-context examples and could be unstable, varying from the near chance to near stateof-the-art performance (Zhao et al., 2021;

Original: Liu et al., 2022a).
Revised: Liu et al., 2022a).

Original: To mitigate the volatility of selecting in-context examples, Lu et al.
Revised: To mitigate the volatility of selecting in-context examples, Lu et al.

Original: (2022b)
Revised: (2022b)

Original: propose retrieving relevant examples that are semantically similar to the test sample.
Revised: propose retrieving relevant examples that are semantically similar to the test sample.

Original: Other possible strategies could be using brute-force permutation search or relying on manually designed heuristics like choosing the most complex examples.
Revised: Other possible strategies could be using brute-force permutation search or relying on manually designed heuristics like choosing the most complex examples.

Original: Inspired by reinforcement learning’s ability to search for an optimal action policy, we propose applying the policy gradient strategy (Sutton et al., 1998) to learn to select in-context examples more efficiently and stably without designing human-designed heuristics.
Revised: Inspired by reinforcement learning’s ability to search for an optimal action policy, we propose applying the policy gradient strategy (Sutton et al., 1998) to learn to select in-context examples more efficiently and stably without designing human-designed heuristics.

Original:  C ONCLUSION
Revised:  C ONCLUSION

Original: In this paper, we propose T AB MWP, the first large-scale dataset for math word problems in tabular contexts.
Revised: In this paper, we propose T AB MWP, the first large-scale dataset for math word problems in tabular contexts.

Original: T AB MWP contains 38,431 open-domain problems with two question types and three answer types, and each problem is annotated with a multi-step solution.
Revised: T AB MWP contains 38,431 open-domain problems with two question types and three answer types, and each problem is annotated with a multi-step solution.

Original: We evaluate T AB MWP using state-of-the-art QA and TableQA methods in both pre-trained and fine-tuned settings, as well as the large pre-trained language model GPT-3.
Revised: We evaluate T AB MWP using state-of-the-art QA and TableQA methods in both pre-trained and fine-tuned settings, as well as the large pre-trained language model GPT-3.

Original: We further propose a novel approach, P ROMPT PG, for few-shot GPT-3, which utilizes policy gradient to learn to select in-context examples from the training data and construct the performing prompt for the test example.
Revised: We further propose a novel approach, P ROMPT PG, for few-shot GPT-3, which utilizes policy gradient to learn to select in-context examples from the training data and construct the performing prompt for the test example.

Original: Experimental results show that P ROMPT PG outperforms existing strong baselines by a large margin of 5.31% and reduces the accuracy volatility compared to random selection.
Revised: Experimental results show that P ROMPT PG outperforms existing strong baselines by a large margin of 5.31% and reduces the accuracy volatility compared to random selection.

Original: To the best of our knowledge, it is the first work that applies reinforcement learning to select in-context examples for the few-shot GPT-3 model.
Revised: To the best of our knowledge, it is the first work that applies reinforcement learning to select in-context examples for the few-shot GPT-3 model.

Revised:  A CKNOWLEDGMENT

Revised: We would like to thank Zhou Yu and Jiuxiang Gu for insightful discussions on dataset collection.

Revised: We thank Muhao Chen and Yao Fu for constructive suggestions in developing baselines and experiments.

Revised: The work does not relate to Liang Qiu’s position at Amazon Alexa.

Original: A A PPENDIX A. D ATASET COLLECTION
Revised: A A PPENDIX A. D ATASET COLLECTION

Original: The raw problems are collected from an online learning website, IXL 1 , which hosts a large number of high-quality math problems curated by educational experts.
Revised: The raw problems are collected from an online learning website, IXL 2 , which hosts a large number of high-quality math problems curated by educational experts.

Original: Quality control.
Revised: Quality control.

Original: The goal of constructing T AB MWP is to collect math word problems that necessitate multi-hop mathematical reasoning between the question and the tabular context.
Revised: The goal of constructing T AB MWP is to collect math word problems that necessitate multi-hop mathematical reasoning between the question and the tabular context.

Original: Therefore, we ask human experts to filter problems that can be solved either without the context of the table or by looking up table cells without numerical reasoning.
Revised: Therefore, we ask human experts to filter problems that can be solved either without the context of the table or by looking up table cells without numerical reasoning.

Original: To further ensure data quality, we ask human experts to perform a final review to re-check the dataset and manually revise incorrect annotations
Revised: To further ensure data quality, we ask human experts to perform a final review to re-check the dataset and manually revise incorrect annotations

Original: [Table]
Revised: [Table]

Original: Under review as a conference paper at ICLR
Revised: Under review as a conference paper at ICLR

Original: [Table]
Revised: [Table]

Original: A. H UMAN STUDY
Revised: A. H UMAN STUDY

Original: To examine how humans perform on our T AB MWP dataset, we released the human evaluation task on Amazon Mechanical Turk (AMT) to the test split.
Revised: To examine how humans perform on our T AB MWP dataset, we released the human evaluation task on Amazon Mechanical Turk (AMT) to the test split.

Original: We designed two sub-tasks for the human study: answering the free-text questions and answering the multi-choice questions.
Revised: We designed two sub-tasks for the human study: answering the free-text questions and answering the multi-choice questions.

Original: The user interfaces for the two sub-tasks are shown in Figure 4.
Revised: The user interfaces for the two sub-tasks are shown in Figure 4.

Original: Each human intelligence task (HIT) containsexam questions and 15 test questions.
Revised: Each human intelligence task (HIT) containsexam questions and 15 test questions.

Original: A worker should have a HIT Approval Rate of 98% or higher and be approved with 5,000 or more HITs.
Revised: A worker should have a HIT Approval Rate of 98% or higher and be approved with 5,000 or more HITs.

Original: The worker is provided with detailed instructions at the beginning and needs to pass at least 3 free-text exam questions or 4 multi-choice exam questions to be qualified for the human study.
Revised: The worker is provided with detailed instructions at the beginning and needs to pass at least 3 free-text exam questions or 4 multi-choice exam questions to be qualified for the human study.

Original: Each HIT is assigned to two different workers.
Revised: Each HIT is assigned to two different workers.

Original: We assign a reward of $0.80 and $0.60 for one HIT of free-text and multi-choice sub-tasks, respectively.
Revised: We assign a reward of $0.80 and $0.60 for one HIT of free-text and multi-choice sub-tasks, respectively.

Original: A. T HE P ROMPT PG A LGORITHM
Revised: A. T HE P ROMPT PG A LGORITHM

Original: The pipeline of P ROMPT PG to learn to select in-context examples is summarized in Algorithm 1.
Revised: The pipeline of P ROMPT PG to learn to select in-context examples is summarized in Algorithm 1.

Original: A. I MPLEMENTATION D ETAILS
Revised: A. I MPLEMENTATION D ETAILS

Original: Heuristics guess.
Revised: Heuristics guess.

Original: To investigate the lower bound of the accuracy on T AB MWP, we design simple heuristics to guess answers for each question type.
Revised: To investigate the lower bound of the accuracy on T AB MWP, we design simple heuristics to guess answers for each question type.

Original: For multi-choice questions, we randomly for 15: return
Revised: For multi-choice questions, we randomly ← a a

Original:  16: end function select one from the given options with even probabilities.
Revised: ∈ {− L batch ← L batch − r i ln π p for 12: Optimize wrt for 14: for 15: return θ 16: end function select one from the given options with even probabilities.

Original: For free-text questions on T AB MWP, the answers could only be integral or decimal numbers.
Revised: For free-text questions on T AB MWP, the answers could only be integral or decimal numbers.

Original: Intuitively, we take advantage of regular expressions to extract all the numbers from the tabular context and the question text as candidates, and then randomly choose one number as the prediction.
Revised: Intuitively, we take advantage of regular expressions to extract all the numbers from the tabular context and the question text as candidates, and then randomly choose one number as the prediction.

Original: UnifiedQA baselines.
Revised: UnifiedQA baselines.

Original: UnifiedQA (Khashabi et al., 2020) is a T5-based (Raffel et al., 2020) QA system that was pre-trained on 8 seed QA datasets of multiple formats but with a unified text-to-text paradigm.
Revised: UnifiedQA (Khashabi et al., 2020) is a T5-based (Raffel et al., 2020) QA system that was pre-trained on 8 seed QA datasets of multiple formats but with a unified text-to-text paradigm.

Original: We load the pre-trained checkpoint as the pre-trained baseline and train it on T AB MWP as the fine-tuned baseline.
Revised: We load the pre-trained checkpoint as the pre-trained baseline and train it on T AB MWP as the fine-tuned baseline.

Original: Three different parameter sizes are compared: SMALL (60M), BASE (220M), and LARGE (770M).
Revised: Three different parameter sizes are compared: SMALL (60M), BASE (220M), and LARGE (770M).

Original: TAPEX baselines.
Revised: TAPEX baselines.

Original: TAPEX (Liu et al., 2022b) is a BART-based (Lewis et al., 2020) language model pre-trained on structured tabular data to mimic the behavior of a SQL executor that can answer table-based questions.
Revised: TAPEX (Liu et al., 2022b) is a BART-based (Lewis et al., 2020) language model pre-trained on structured tabular data to mimic the behavior of a SQL executor that can answer table-based questions.

Original: TAPEX shows state-of-the-art performance on four table-related datasets.
Revised: TAPEX shows state-of-the-art performance on four table-related datasets.

Original: We establish the pre-trained and fine-tuned baselines on top of TAPEX with two model sizes: BASE (140M) and LARGE (400M).
Revised: We establish the pre-trained and fine-tuned baselines on top of TAPEX with two model sizes: BASE (140M) and LARGE (400M).

Original: Zero-shot GPT-3 and zero-shot-CoT GPT-3.
Revised: Zero-shot GPT-3 and zero-shot-CoT GPT-3.

Original: We establish the zero-shot baseline based on GPT- (Brown et al., 2020).
Revised: We establish the zero-shot baseline based on GPT- (Brown et al., 2020).

Original: The zero-shot setup follows the format of TQ(C)
Revised: The zero-shot setup follows the format of TQ(C)

Original: → A where the input is the concatenation of tokens of the tabular context (T), the question text (Q), and choice options (C) that apply while the output is to predict the answer (A).
Revised: → A where the input is the concatenation of tokens of the tabular context (T), the question text (Q), and choice options (C) that apply while the output is to predict the answer (A).

Original: Following Kojima et al.
Revised: Following Kojima et al.

Original: , we further build zero-shot-CoT GPT-3, which refers to the GPT-3 model with a chain-of-thought (CoT) prompt.
Revised: , we further build zero-shot-CoT GPT-3, which refers to the GPT-3 model with a chain-of-thought (CoT) prompt.

Original: Specifically, we add the prompt “ Let’s think step by step ” at the end of the input to ask the model to generate the multi-step solution (S) to mimic the reasoning process as humans.
Revised: Specifically, we add the prompt “ Let’s think step by step ” at the end of the input to ask the model to generate the multi-step solution (S) to mimic the reasoning process as humans.

Original: Then the model takes the raw input and the newly generated solution to predict the final answer.
Revised: Then the model takes the raw input and the newly generated solution to predict the final answer.

Original: Few-shot GPT-3 and few-shot-CoT GPT-3.
Revised: Few-shot GPT-3 and few-shot-CoT GPT-3.

Original: In the few-shot setting, we follow the standard prompting (Wei et al., 2022) where in-context examples are randomly selected from the training data as demonstrations for the text example.
Revised: In the few-shot setting, we follow the standard prompting (Wei et al., 2022) where in-context examples are randomly selected from the training data as demonstrations for the text example.

Original: Similarly, the few-shot-CoT GPT-3 baseline takes the prompt template of TQ(C)
Revised: Similarly, the few-shot-CoT GPT-3 baseline takes the prompt template of TQ(C)

Original: →
Revised: →

Original: SA to generate the solution before the final answer.
Revised: SA to generate the solution before the final answer.

Original: Experimental details.
Revised: Experimental details.

Original: Our experiments for UnifiedQA baselines, TAPEX baselines, and our proposed P ROMPT PG are conducted using PyTorch on two Nvidia RTX 3090 GPUs.
Revised: Our experiments for UnifiedQA baselines, TAPEX baselines, and our proposed P ROMPT PG are conducted using PyTorch on two Nvidia RTX 3090 GPUs.

Original: For fine-tuning the UnifiedQA and TAPEX baselines, we use the Adam optimizer (Kingma & Ba, 2014) with an initial learning rate of 5e − 5 .
Revised: For fine-tuning the UnifiedQA and TAPEX baselines, we use the Adam optimizer (Kingma & Ba, 2014) with an initial learning rate of 5e − 5 .

Original: The training process takes 10 epochs with a batch size of 16.
Revised: The training process takes 10 epochs with a batch size of 16.

Original: The maximum number of input tokens is set as 200 and the maximum output length is 100.
Revised: The maximum number of input tokens is set as 200 and the maximum output length is 100.

Original: In our proposed P ROMPT PG, the embedding size of the added linear neural network is 768.
Revised: In our proposed P ROMPT PG, the embedding size of the added linear neural network is 768.

Original: To learn the policy network, we use the Adam optimizer with an initial learning rate of 1e − 3 .
Revised: To learn the policy network, we use the Adam optimizer with an initial learning rate of 1e − 3 .

Original: The maximum number of training epochs is 30, with a batch size of 20.
Revised: The maximum number of training epochs is 30, with a batch size of 20.

Original: The training process is stopped early if there is any NaN value in the loss for a batch of training data.
Revised: The training process is stopped early if there is any NaN value in the loss for a batch of training data.

Original: For the GPT-3 engine, we use TEXT - DAVINCI -002, the most capable engine recommended by the official documentation.
Revised: For the GPT-3 engine, we use TEXT - DAVINCI -002, the most capable engine recommended by the official documentation.

Original: The temperature is set as 0 and the top probability is set as 1.0 to get the most deterministic prediction.
Revised: The temperature is set as 0 and the top probability is set as 1.0 to get the most deterministic prediction.

Original: The maximum number of tokens allowed for generating text is 512.
Revised: The maximum number of tokens allowed for generating text is 512.

Original: Both the frequency penalty and the presence penalty are set as the default value, i [Table] e., 0.
Revised: Both the frequency penalty and the presence penalty are set as the default value, i.e., 0.

Original: A. M ORE E XPERIMENTAL R ESULTS
Revised: A. M ORE E XPERIMENTAL R ESULTS

Original: [Table] [Table]
Revised: [Table] [Table]

Original: Number of few-shot examples.
Revised: Number of few-shot examples.

Original: We study the few-shot-CoT GPT-3 model with random selection in terms of the different numbers of in-context shots.
Revised: We study the few-shot-CoT GPT-3 model with random selection in terms of the different numbers of in-context shots.

Original: For each number of in-context shots, the experiment was conducted on 1,000 development examples and repeated three times.
Revised: For each number of in-context shots, the experiment was conducted on 1,000 development examples and repeated three times.

Original: The results are shown in Table 9.
Revised: The results are shown in Table 9.

Original: When increasing the number of in-context shots from the current 2 to 4, the few-shot-CoT GPT-3 model reduces the prediction variance from the random selection of incontext shots and achieves an accuracy improvement of 2.5%.
Revised: When increasing the number of in-context shots from the current 2 to 4, the few-shot-CoT GPT-3 model reduces the prediction variance from the random selection of incontext shots and achieves an accuracy improvement of 2.5%.

Original: When the number of in-context shots is increased to 5, the model with random selection does not gain further benefits.
Revised: When the number of in-context shots is increased to 5, the model with random selection does not gain further benefits.

Original: Our PromptPG displays impressive advantages over random selection in terms of data efficiency and prediction accuracy.
Revised: Our PromptPG displays impressive advantages over random selection in terms of data efficiency and prediction accuracy.

Original: With only two in-context shots, PromptPG achieves the highest accuracy of 70.9% and a comparable low deviation compared to random selection with more shots.
Revised: With only two in-context shots, PromptPG achieves the highest accuracy of 70.9% and a comparable low deviation compared to random selection with more shots.

Original: A. R ELATED WORK OF P OLICY G RADIENT
Revised: A. R ELATED WORK OF P OLICY G RADIENT

Original: Policy gradient is an approach to solving reinforcement learning problems that targets modeling and optimizing the policy directly.
Revised: Policy gradient is an approach to solving reinforcement learning problems that targets modeling and optimizing the policy directly.

Original: Many policy gradient algorithms have been proposed in the past decade (Silver et al., 2014; Lillicrap et al., 2015; Mnih et al., 2016; Schulman et al., 2017; BarthMaron et al., 2018).
Revised: Many policy gradient algorithms have been proposed in the past decade (Silver et al., 2014; Lillicrap et al., 2015; Mnih et al., 2016; Schulman et al., 2017; BarthMaron et al., 2018).

Original: They have been proven effective in areas like robotics (Peters & Schaal, 2006) and chatbots (Kandasamy et al., 2017).
Revised: They have been proven effective in areas like robotics (Peters & Schaal, 2006) and chatbots (Kandasamy et al., 2017).

Original: In recent work that focuses on aligning language models with human values (Ouyang et al., 2022; Qiu et al., 2022; Glaese et al., 2022), policy gradient has been used to optimize language models with rewards learned from human feedback and preference.
Revised: In recent work that focuses on aligning language models with human values (Ouyang et al., 2022; Qiu et al., 2022; Glaese et al., 2022), policy gradient has been used to optimize language models with rewards learned from human feedback and preference.

Original: To the best of our knowledge, our PromptPG is the first work that proposes to select prompts dynamically for large pre-trained language models in the mathematical reasoning field.
Revised: To the best of our knowledge, our PromptPG is the first work that proposes to select prompts dynamically for large pre-trained language models in the mathematical reasoning field.

Original: A. C ASE STUDY EXAMPLES
Revised: A. C ASE STUDY EXAMPLES

Original: [Table]
Revised: [Table]

Original: [Table] [Table]
Revised: [Table] [Table]

Original: looking price online favorite company has Luna can add upgrade to phone an additional or can
Revised: [Table]

Original: to
Revised: [Table]

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Table] [Table]
Revised: [Table] [Table]

Original: Question: Rebecca bought 2.5 kilograms of oval beads.
Revised: Question: Rebecca bought 2.5 kilograms of oval beads.

Original: How much did she spend?
Revised: How much did she spend?

Original: (Unit: $)
Revised: (Unit: $)

Original: Answer: (Step 1)
Revised: Answer: (Step 1)

Original: Find the cost of the oval
Revised: Find the cost of the oval

Original: beads.
Revised: beads.

Original: Multiply the price per kilogram by the number of kilograms.
Revised: Multiply the price per kilogram by the number of kilograms.

Original: (Step 2) $ 2 × 
Revised: (Step 2) $2 × 2.

Original: =
Revised: =

Original: $
Revised: $

Original: (Step 3)
Revised: (Step 3)

Original: She spent $5.
Revised: She spent $5.

Original: The answer is
Revised: The answer is

Original: ▷ Test example (ID: 17417)
Revised: ▷ Test example (ID: 17417)

Original: [Table]
Revised: [Table]

Original: cake | 5 |
Revised: [Table] 5 |

Original: [Table]
Revised: [Table]

Original: rope | 16 |
Revised: | 16 |

Original: [Table]
Revised: [Table]

Original: [Figure]

Original: [Table]

Original: [Figure]
Revised: [Figure]

Original: Question:
Revised: Question:

Original: At Josie’s birthday party, children and parents celebrated by participating in some activities.
Revised: At Josie’s birthday party, children and parents celebrated by participating in some activities.

Original: How many more children than parents are playing tag?
Revised: How many more children than parents are playing tag?

Original: (Unit: children)
Revised: (Unit: children)

Original: Answer: (Step 1) To find the difference between the number of children and parents playing tag, subtract the number of parents from the number of children.
Revised: Answer: (Step 1) To find the difference between the number of children and parents playing tag, subtract the number of parents from the number of children.

Original: (Step 2) 9 -
Revised: [Figure]

Original: [Figure]
Revised: [Figure]

Original: =
Revised: There [Figure] [Figure] children

Original: [Figure]
Revised: [Figure]

Original: (Step 3) There are 5 more children than parents
Revised: parents

Original: [Figure]
Revised: [Figure]

Original: tag. Theanswer is 5.
Revised: The

Original: [Figure]
Revised: [Figure]

Revised: Output:

Original: The selected examples require similar abilities of mathematical reasoning to the test example.
Revised: The selected examples require similar abilities of mathematical reasoning to the test example.

Original: [Table]
Revised: [Table]

Original: [Table]

Original: [Table]
Revised: [Table]

Original: Question: Dr. Thornton, a pediatrician, weighed all the children who recently visited her office.
Revised: Question: Dr. Thornton, a pediatrician, weighed all the children who recently visited her office.

Original: How many children weighed exactly 52 pounds?
Revised: How many children weighed exactly 52 pounds?

Original: (Unit: children)
Revised: (Unit: children)

Original: [Table]
Revised: [Table]

Original: (Step 1)
Revised: (Step 1)

Original: For the number 52, the stem is 5, and the leaf is 2.
Revised: For the number 52, the stem is 5, and the leaf is 2.

Original: Find the row where the stem is 5.
Revised: Find the row where the stem is 5.

Original: In that row, count all the leaves equal to 2.
Revised: In that row, count all the leaves equal to 2.

Original: [Table] [Table]
Revised: (Step 2)

Original: You counted 2 leaves, which are blue in the stem-and-leaf plot above.
Revised: You counted 2 leaves, which are blue in the stem-and-leaf plot above.

Original: [Table] [Table] children weighed exactly 52 pounds.
Revised: (Step 3) 2 children weighed exactly 52 pounds.

Original: The answer is 2.
Revised: The answer is 2.

Original: [Table]
Revised: [Table]

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Table] [Table]
Revised: [Table] [Table]

Original: | $2/lb
Revised: | $2/lb

Original: Question: If Vince buys 3.4 pounds of buttermilk pancake mix, how much will he spend?
Revised: Question: If Vince buys 3.4 pounds of buttermilk pancake mix, how much will he spend?

Original: (Unit: $)
Revised: (Unit: $)

Original: Answer:
Revised: Answer:

Original: (Step 1) Find the cost of the buttermilk pancake mix.
Revised: (Step 1) Find the cost of the buttermilk pancake mix.

Original: Multiply the price per pound by the number of pounds.
Revised: Multiply the price per pound by the number of pounds.

Original: (Step 2) $2 × 3.4 = $6.
Revised: (Step 2) $2 × 3.4 = $6.

Original: (Step 3)
Revised: (Step 3)

Original: He will spend $6.80.
Revised: He will spend $6.80.

Original: The answer is 6.80.
Revised: The answer is 6.80.

Original: [Table] [Table]
Revised: [Table] [Table]

Original: Singing | 14 |
Revised: Singing | 14 |

Original: Eating cake | 5 |
Revised: Eating cake | 5 |

Original: Jumping rope | 16 |
Revised: Jumping rope | 16 |

Original: Swimming | 16 |
Revised: Swimming | 16 |

Original: Playing tag | 4 |
Revised: Playing tag | 4 |

Revised: [Figure]

Revised: [Table]

Revised: [Figure]

Revised: [Table]

Revised: [Figure]

Original: [Table]
Revised: [Table]

Revised: [Figure]

Revised: [Table]

Original: Question:
Revised: Question:

Original: At Josie’s birthday party, children and parents celebrated by participating in some activities.
Revised: At Josie’s birthday party, children and parents celebrated by participating in some activities.

Original: How many more children than parents are playing tag?
Revised: How many more children than parents are playing tag?

Original: (Unit: children)
Revised: (Unit: children)

Original: Answer:
Revised: Answer:

Revised: “Playing tag”

Revised: the

Revised: is 4,

Revised: the

Revised: all

Original: Output:
Revised: Output:

Original: Ground truth:
Revised: Ground truth:

Original: [Table]
Revised: [Table]

Original: [Table]

Original: [Table]
Revised: [Table]

Original: Question:
Revised: Question:

Original: A farmer recalled how many watermelons were harvested in the past 4 days.
Revised: A farmer recalled how many watermelons were harvested in the past 4 days.

Original: On which day were the mostharvested?
Revised: On which day were the most

Original: [Table]
Revised: [Table]

Original: Answer:
Revised: Answer:

Revised: [Table]

Original: [Table]
Revised: [Table]

Original: 1) Find the greatest number in the table.
Revised: Find the greatest number in the table.

Original: Remember to compare the numbers starting with the highest place value.
Revised: Remember to compare the numbers starting with the highest place value.

Original: The greatest number 
Revised: The greatest number is

Original: [Table]

Original: [Table]
Revised: [Table]

Original: find the corresponding day.
Revised: find the corresponding day.

Original: Wednesday corresponds to 59.
Revised: Wednesday corresponds to 59.

Original: The answer is Wednesday.
Revised: The answer is Wednesday.

Revised: [Table]

Revised: [Table]

Revised: Linden

Original: [Table]
Revised: [Table]

Revised: Mooreland

Original: [Table]
Revised: [Table]

Revised: Crestview

Revised: [Table]

Original: Question:
Revised: Question:

Original: The parks department compared how many basketball hoops there are at each park.
Revised: The parks department compared how many basketball hoops there are at each park.

Original: What is the mode of the numbers?
Revised: What is the mode of the numbers?

Original: Answer:
Revised: Answer:

Original: (Step 1) Read the numbers from the table.
Revised: (Step 1) Read the numbers from the table.

Original: (Step 2)
Revised: (Step 2)

Original: First, arrange the numbers from least to greatest: 2, 2, 3, 4, 4, 4, 7, 7.
Revised: First, arrange the numbers from least to greatest: 2, 2, 3, 4, 4, 4, 7, 7.

Original: (Step 3)
Revised: (Step 3)

Original: Now count how many times each number appears.
Revised: Now count how many times each number appears.

Original: (Step 4) 2 appears 2 times.
Revised: (Step 4) 2 appears 2 times.

Original: 3 appears 1 time.
Revised: 3 appears 1 time.

Original: 4 appears 3 times.
Revised: 4 appears 3 times.

Original: 7 appears 2 times.
Revised: 7 appears 2 times.

Original: (Step 5)
Revised: (Step 5)

Original: The number that appears most often is 4.
Revised: The number that appears most often is 4.

Original: (Step 6)
Revised: (Step 6)

Original: The mode is 4.
Revised: The mode is 4.

Original: The answer is 4.
Revised: The answer is 4.

Original: [Table] [Table]
Revised: [Table] [Table]

Original: Swimming | 16 |
Revised: Swimming | 16 |

Original: Playing tag | 4 |
Revised: Playing tag | 4 |

Original: Birthday party
Revised: Birthday party

Original: Activity
Revised: Activity

Original: Parents
Revised: Parents

Original: Children
Revised: Children

Original: Singing
Revised: Singing

Original: Eating cake
Revised: Eating cake

Original: Jumpingrope
Revised: Jumping

Revised: [Figure]

Original: Swimming
Revised: Swimming

Original: Playing tag
Revised: [Figure]

Original: Birthday party
Revised: Birthday party

Original: Activity | Parents | Children
Revised: Activity | Parents | Children

Original: Singing | 14 | 20 Eating cake | 5 | 
Revised: Singing | 14 | [Figure] | [Figure]

Original: Jumping rope | 16 | 20 Swimming | 16 | 
Revised: | [Figure] | [Figure]

Original: Playing tag | 4 |
Revised: | Playing [Figure] |

Revised: [Figure]

Revised: |

Original: Question:
Revised: Question:

Original: At Josie’s birthday party, children and parents celebrated by participating in some activities.
Revised: At Josie’s birthday party, children and parents celebrated by participating in some activities.

Original: How many more children than parents are playing tag?
Revised: How many more children than parents are playing tag?

Original: (Unit: children)
Revised: (Unit: children)

Original: Answer:
Revised: Answer:

Original: (Step 1) Find the difference between the number of children and the number of parents for each activity.
Revised: (Step 1) Find the difference between the number of children and the number of parents for each activity.

Original: (Step 2) For singing, the difference is 6.
Revised: (Step 2) For singing, the difference is 6.

Original: (Step 3)
Revised: (Step 3)

Original: For eating cake, the difference is 5.
Revised: For eating cake, the difference is 5.

Original: (Step 4) For jumping rope, the difference is 4.
Revised: (Step 4) For jumping rope, the difference is 4.

Original: (Step 5)
Revised: (Step 5)

Original: For swimming, the difference is 3.
Revised: For swimming, the difference is 3.

Original: (Step 6) For playing tag, the difference is 5.
Revised: (Step 6) For playing tag, the difference is 5.

Original: (Step 7)
Revised: (Step 7)

Original: The greatest difference is 6.
Revised: The greatest difference is 6.

Original: The answer is 6.
Revised: The answer is 6.

Original: Output:
Revised: Output:

Original: Ground truth:
Revised: Ground truth:

Original: [Table]

Original: $

Original: [Table]
Revised: [Table]

Original: Question: The school district compared how many math teachers each high school has.
Revised: Question: The school district compared how many math teachers each high school has.

Original: What is the mean of the numbers?
Revised: What is the mean of the numbers?

Original: Answer:
Revised: Answer:

Original: (Step 1)
Revised: (Step 1)

Original: The mean is the average of the numbers.
Revised: The mean is the average of the numbers.

Original: (Step 2)
Revised: (Step 2)

Original: To find the mean, add all the numbers and divide by the number of items.
Revised: To find the mean, add all the numbers and divide by the number of items.

Original: (Step 3) 9 + 10 + 4 + 2 + 6 + 4 + 8 + 5 =(Step 4)
Revised: (Step 3) 9 + 10 + 4 + 2 + 6 + 4 + 8 + 5 =(Step 4)

Original: There are 8 items, so the mean is 

Revised: There are 8 items, so the mean is

Original: ÷ 8 = 6.
Revised: ÷ 8 = 6.

Original: (Step 5)
Revised: [Figure]

Original: The
Revised: The

Original: [Figure]
Revised: [Figure]

Original: the numbers is 6.

Original: Output:
Revised: Output:

Original: [Table]
Revised: [Table]

Original:  [Table]
Revised: [Figure] [Table] [Figure] [Table]

Original:  [Table]
Revised: [Figure] [Table] [Figure] [Table]

Original:  [Table]
Revised: [Figure] [Table] [Figure] [Table]

Revised: [Figure]

Original: [Table] 
Revised: [Table] [Figure] [Table] [Figure]

Revised: [Table]

Original: [Figure]
Revised: [Figure]

Original: \(|\
Revised: [Table] [Figure] [Table] [Figure]

Revised: [Table]

Revised: [Figure]

Revised: [Table]

Revised: [Figure]

Revised: [Table]

Original: [Figure]
Revised: [Figure]

Original: Question: Austin went to the store and bought 3 pounds of fool’s gold, 1 pound of topaz, and 2 pounds of tiger’s eye.
Revised: Question: Austin went to the store and bought 3 pounds of fool’s gold, 1 pound of topaz, and 2 pounds of tiger’s eye.

Original: How much did he spend?
Revised: How much did he spend?

Original: (unit: $)
Revised: (unit: $)

Original: Answer: (Step 1) To find the total amount Austin spent, multiply the price per pound of each type of stone by the number of pounds of that stone that he bought, and then add all of the products together.
Revised: Answer: (Step 1) To find the total amount Austin spent, multiply the price per pound of each type of stone by the number of pounds of that stone that he bought, and then add all of the products together.

Original: [Figure]
Revised: [Figure]

Original: Output: 87.
Revised: Output: 87.

Original: [Table]
Revised: [Table]

Original: [Table] [Table] 
Revised: [Table] [Table] [Table]

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Table]
Revised: [Table]

Original: | 1:45 P.M. | 2:45 P.M. \\ the playground | 12:45 P.M. | 2:00 P.M. | 2:15 P.M. | 2:45 P.M. | 3:45 P.M. \\ the doctor's office | 1:15 P.M. | 2:30 P.M. | 2:45 P.M.| 3:15 P.M. | 4:15 P.M. \\
Revised: | 1:45 P.M. | 2:45 P.M. \\ the playground | 12:45 P.M. | 2:00 P.M. | 2:15 P.M. | 2:45 P.M. | 3:45 P.M. \\ the doctor's office | 1:15 P.M. | 2:30 P.M. | 2:45 P.M.

Revised: | 3:15 P.M. | 4:15 P.M. \\

Original: Question: Look at the following schedule.
Revised: Question: Look at the following schedule.

Original: Lena is at the mall.
Revised: Lena is at the mall.

Original: If she wants to arrive at the library at 1.
Revised: If she wants to arrive at the library at 1.

Original: P.M., what time should she get on the bus?
Revised: P.M., what time should she get on the bus?

Original: Options: ( A) A.M. (B)
Revised: Options: (A) 11:15 A.M. ( B

Original: 30 A.M. (C)  P.M. (D
Revised: ) 10:30 A.M. (C) 12:30 P.M. (D

Original: :15 P
Revised: 12:15 P.M.

Original: Answer:
Revised: Answer:

Original: Output: (A) 11:15 A.M.
Revised: Output: (A) 11:15 A.M.

Original: [Table]
Revised: [Table]

Original: [Table]

Original: [Table]
Revised: [Table]

Original: Question: Ariana has $16.50.
Revised: Question: Ariana has $16.50.

Original: Does she have enough to buy a paperback book and a mystery novel?
Revised: Does she have enough to buy a paperback book and a mystery novel?

Original: Options: (A) yes (B) no
Revised: Options: (A) yes (B) no

Original: Answer: (Step 1) To answer this question, look at the table to find the price of a paperback book and the price of a mystery novel.
Revised: Answer: (Step 1) To answer this question, look at the table to find the price of a paperback book and the price of a mystery novel.

Original: (Step 2)
Revised: (Step 2)

Original: A paperback book costs $8.45 and a mystery novel costs $8.26.
Revised: A paperback book costs $8.45 and a mystery novel costs $8.26.

Original: (Step 3) $8.45 + $8.26 = $16.
Revised: (Step 3) $8.45 + $8.26 = $16.

Original: (Step 4) Since $16.71 is greater than $16.50, Ariana does not have enough money to buy a paperback book and a mystery novel.
Revised: (Step 4) Since $16.71 is greater than $16.50, Ariana does not have enough money to buy a paperback book and a mystery novel.

Original: The answer is no.
Revised: The answer is no.

Original: Output: (B) no
Revised: Output: (B) no

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Table]
Revised: [Table]

Original: yellow tiger's eye \(|\) $0.85 \\ piece of green slate \(|\) $0.59 \\ piece of red sandstone \(|\) $0.19 \\ piece of rose quartz \(|\) $0.61 \\ smooth piece of marble \(|\) $0.45 \\
Revised: yellow tiger's eye \(|\) $0.85 \\ piece of green slate \(|\) $0.59 \\ piece of red sandstone \(|\) $0.19 \\ piece of rose quartz \(|\) $0.61 \\ smooth piece of marble \(|\) $0.45 \\

Original: Question: How much money does Connor need to buy a piece of rose quartz, a piece of green slate, and a piece of red sandstone?
Revised: Question: How much money does Connor need to buy a piece of rose quartz, a piece of green slate, and a piece of red sandstone?

Original: (unit: $)
Revised: (unit: $)

Original: Answer: (Step 1) Connor needs to buy a piece of rose quartz, a piece of green slate, and a piece of red sandstone.
Revised: Answer: ( needs to buy a piece of rose quartz

Original: To find the total amount of money Connor needs, add the prices of the three items.
Revised: a piece of green slate piece To

Original: (Step 2) $0.85 + $0.59 + $0.19 =$1.
Revised: $ 19 =

Original: (Step3)
Revised: (Step

Original: Connor needs $1.63 tobuy a piece of rose quartz, a piece of green slate, and a piece ofred sandstone.
Revised: Connor needs $ .63 to a piece of

Original: The answer is 1.63.
Revised: The answer is 1.63.

Original: Output: 1.
Revised: Output: 1.

Original: Ground truth: 1.
Revised: Ground truth: 1.

Original: [Table]
Revised: [Table]

Original: |
Revised: |

Original: [Table]
Revised: [Table]

Original: |
Revised: |

Original: [Table]
Revised: [Table]

Original: |
Revised: |

Original: [Table]
Revised: [Table]

Original: |
Revised: |

Original: [Table]

Original: |

Original: [Table]
Revised: [Table]

Original: |

Original: [Table]

Original: [Table]

Original: Question:
Revised: Question:

Original: A farmer counted the number of apples on each tree in her orchard.
Revised: A farmer counted the number of apples on each tree in her orchard.

Original: How many trees have at least 51 apples but fewer than 83 apples?
Revised: How many trees have at least 51 apples but fewer than 83 apples?

Original: (unit: trees)
Revised: (unit: trees)

Original: Answer: (Step 1) To solve this problem, look at the table and find all the trees that have at least 51 apples but fewer than 83 apples.
Revised: Answer: (Step 1) To solve this problem, look at the table and find all the trees that have at least 51 apples but fewer than 83 apples.

Original: (Step 2)
Revised: (Step 2)

Original: There are three trees that have at least 51 apples but fewer than 83 apples.
Revised: There are three trees that have at least 51 apples but fewer than 83 apples.

Original: The answer is 3.
Revised: The answer is 3.

Original: Output:
Revised: Output:

Original: Ground truth:
Revised: Ground truth:

Original: [Figure]
Revised: Day | Number of lawn mowers

Original: Tuesday | Wednesday |
Revised: Tuesday | Wednesday |

Original: Thursday | Friday |
Revised: Thursday | Friday |

Original: Saturday | Sunday |
Revised: Saturday | Sunday |

Original: Monday |
Revised: Monday |

Original: [Figure]
Revised: [Figure]

Original: [Table]
Revised: [Table]

Original: Tuesday
Revised: Tuesday

Original: [Figure]

Original: Wednesday
Revised: Wednesday

Original: [Figure]

Original: Thursday Friday
Revised: Thursday Friday

Original: Saturday Sunday
Revised: Saturday Sunday

Original: [Table]
Revised: [Table]

Original: Monday
Revised: Monday

Original: [Table] [Table]
Revised: [Table] [Table]

Original: |
Revised: |\

Original: [Table]
Revised: [Table]

Original: Question: A garden supply store kept track of how many lawn mowers it sold in the past 7 days.
Revised: Question: A garden supply store kept track of how many lawn mowers it sold in the past 7 days.

Original: What is the median of the numbers?
Revised: What is the median of the numbers?

Original: Answer:
Revised: Answer:

Original: (Step 1)
Revised: (Step 1)

Original: The median is the ”middle” value.
Revised: The median is the ”middle” value.

Original: To find the median, put the numbers in order from least to greatest and find the number in the middle.
Revised: To find the median, put the numbers in order from least to greatest and find the number in the middle.

Original: (Step 2) 8, 7, 5, 7, 9, 8,(Step 3)
Revised: (Step 2) 8, 7, 5, 7, 9, 8,(Step 3)

Original: The median is 7.
Revised: The median is 7.

Original: The answer is 7.
Revised: The answer is 7.

Original: Output:
Revised: Output:

Original: Ground truth:
Revised: Ground truth:

Original: [Table]
Revised: [Table]

Original: Question: Look at the following schedule.
Revised: Question: Look at the following schedule.

Original: Haley is at Ocean City at 9.45 A.M. How soon can she get to
Revised: Haley is at Ocean City at 9.45 A.M. How soon can she get to

Original: Surfing Beach?
Revised: Surfing Beach?

Original: [Table] : (A) 1:45 P.M. (B) 12: [Table] P.M. (C)
Revised: Options: (A) 1:45 P.M. (B) 12:00 P.M. (C)

Original: [Table] [Table]
Revised: [Table] [Table]

Original: .M.
Revised: .M.

Original: (D)
Revised: (D)

Original: [Table]

Original: [Table]
Revised: [Table]

Original: .M.
Revised: 15 P.M.

Original: Answer: (Step 1) Find 9:45 A.M. on the schedule.
Revised: Answer: (Step 1) Find 9:45 A.M. on the schedule.

Original: (Step 2)
Revised: (Step 2)

Original: The next stop is Whale Watch Harbor at 10:15 A.M.
Revised: The next stop is Whale Watch Harbor at 10:15 A.M.

Original: (Step 3)
Revised: (Step 3)

Original: The earliest she can get to Surfing Beach is 12:00 P.M.
Revised: The earliest she can get to Surfing Beach is 12:00 P.M.

Original: The answer is 12:00 P.M.
Revised: The answer is 12:00 P.M.

Original: Output: (B) 12:00 P.M.
Revised: Output: (B) 12:00 P.M.

Original: Ground truth: (A) 1:45 P.M.
Revised: Ground truth: (A) 1:45 P.M.

Original: [Table]
Revised: [Table]

Original: Carson |
Revised: Carson |

Original: Zach |
Revised: Zach |

Original: Lila |
Revised: Lila |

Original: Nicole
Revised: Nicole

Original: |
Revised: |

Original: Shane |
Revised: Shane |

Original: Henry |
Revised: Henry |

Revised: Devin |

Original: [Table]
Revised: [Table]

Original: Question: Some students compared how many blocks they live from school.
Revised: Question: Some students compared how many blocks they live from school.

Original: What is the mean of the numbers?
Revised: What is the mean of the numbers?

Original: Answer:
Revised: Answer:

Original: (Step 1)
Revised: (Step 1)

Original: The mean is the average of the numbers.
Revised: The mean is the average of the numbers.

Original: (Step 2)
Revised: (Step 2)

Original: To find the mean, add the numbers and divide by the number of students.
Revised: To find the mean, add the numbers and divide by the number of students.

Original: (Step 3) 14 + 8 + 17 + 17 + 3 + 7 + 5 + 17 =(
Revised: (Step 3) 14 + 8 + 17 + 17 + 3 + 7 + 5 + 17 =(

Original: Step 4)
Revised: Step 4)

Original: There are 8 students, so divide 86 by 8.
Revised: There are 8 students, so divide 86 by 8.

Original: (Step 5) 

Revised: (Step 5)

Original: ÷ 8 = 10.
Revised: ÷ 8 = 10.

Original: (Step 6)
Revised: (Step 6)

Original: The mean is 10.75.
Revised: The mean is 10.75.

Original: The answer is 10.75.
Revised: The answer is 10.75.

Original: Output: 10.
Revised: Output: 10.

Original: Ground truth:
Revised: Ground truth:

Original: [Table]
Revised: [Table]

Original: Question: Some friends played miniature golf and wrote down their scores.
Revised: : Some friends played miniature golf and wrote down their scores.

Original: How many more strokes did
Revised: How many more strokes did

Original: Hugo take than Anita?
Revised: Hugo take than Anita?

Original: (unit: strokes)

Original: Answer: [Table]
Revised: [Table] [Table]