Is a Question Decomposition Unit All We Need?

Introduction

With the advent of large LMs, we have achieved state-of-the-art performance on many NLP benchmarks (Radford et al., 2019; Brown et al., 2020; Sanh et al., 2021a). Our benchmarks are evolving and becoming harder over time. To solve new benchmarks, we have been designing more complex and bigger LMs at the cost of computational resources, time and its negative impact on the environment. Building newer LMs for solving new benchmarks may not be an ideal and sustainable option over time. Inspired by humans, who often view new tasks as a combination of existing tasks, we explore if we can mimic humans and help the model solve a new task by decomposing Mishra et al. (2021a) it as a combination of tasks that the model excels at and already knows.

As NLP applications are increasingly more and more popular among people in their daily activities, it is essential to develop methods that involve humans in NLP-powered applications in meaningful ways. Our approach attempts to fill this gap in LMs by providing a human-centric approach to modifying data. Solving complex QA tasks such as multi-hop QA, and numerical reasoning has been a challenge for models. Question Decomposition (QD) has recently been explored to empower models to solve these tasks with the added advantage of interpretability. However, previous studies on QD are limited to some specific datasets Khot et al. (2020b) such as DROP Dua et al. (2019) and HotpotQA Yang et al. (2018). We analyze a range of datasets involving various forms of reasoning to investigate if “a Question Decomposition Unit All We Need?"

Figure 1 shows the schematic representation of a QD unit. The original question is difficult for a model to answer. However, it becomes easier for the model when a human decomposes the question into a set of simpler questions.

We manually decompose randomly selected 50 samples of each dataset. The decompositions we perform are purely based on intuitions to reduce the complexity of the question, inspired by the success of task-level instruction decomposition Mishra et al. (2021a) in improving model performance. We experiment with GPT3 Brown et al. (2020) and RoBERTA Liu et al. (2019) fine-tuned on SQuAD 2.0 (Rajpurkar et al., 2018) and find that HQD significantly improves model performance (24% for GPT-3 and 29% for RoBERTa-SQuAD along with a symbolic calculator). Here, the evaluation happens on unseen tasks on which the model is not fine-tuned. Our findings indicate that Human-in-the-loop Question Decomposition (HQD) can potentially provide an alternate path to building large LMs. We hope our work will encourage the community to develop human-centric solutions that actively involve humans while leveraging NLP resources.

Related Work

A recent methodology to reason over multiple sentences in reading comprehension datasets is to decompose the question into single-hop questions (Talmor and Berant, 2018; Min et al., 2019). Min et al. (2019) decompose questions from HotpotQA using span predictions based on reasoning types and picks the best decomposition using a decomposition scorer. Khot et al. (2020b) generate decompositions by training a BART model on question generation task by providing context, answers and hints. Wolfson et al. (2020) crowd-sourced annotations for decompositions of questions. Perez et al. (2020), on the other hand, uses the unsupervised mechanism of generating decomposition by mapping a hard question to a set of candidate sub-questions from a question corpus. Iyyer et al. (2017) answer a question sequentially using a neural semantic parsing framework over crowdsourced decompositions for questions from WikiTableQuestions. Decomposition using text-to-SQL query conversion has also been studied (Guo et al., 2019). Also, knowledge graphs are combined with neural networks to generate decompositions (Gupta and Lewis, 2018). Recently, Xie et al. (2022) presented another use case where decompositions can be used to probe models to create explanations for their reasoning.

Methods

We select eight datasets covering a diverse set of reasoning skills and domains: (1) HotpotQA (Yang et al., 2018), (2) DROP (Dua et al., 2019), (3) MultiRC (Khashabi et al., 2018), (4) StrategyQA (Geva et al., 2021), (5) QASC Khot et al. (2020a), (6) MathQA Amini et al. (2019), (7) SVAMP Patel et al. (2021), and (8) Break Wolfson et al. (2020). Table 1 indicates the different task types for each dataset.

2 Decomposition Process

For each dataset, we randomly select 50 instances for manual decomposition. The question in each dataset is decomposed into two or more questions. Table 2, 3, 4 and 5 show examples of decomposition for various datasets. For each dataset, we created a set $\mathcal{D}$ for decomposed questions. Each element $\mathcal{D}_{i}\in\mathcal{D}$ can be represented as below:

where $\mathcal{C}_{i}$ is the context paragraphs, $\mathcal{Q}_{i}$ is the original question, $\mathcal{Q}_{d}$ is the set of decomposed questions, $\mathcal{A}_{i}$ is an original answer, and $\mathcal{A}_{d}$ is the set of answers for corresponding decomposed questions. For questions that require arithmetic or logical operations, we use a computational unit as suggested in Khot et al. (2020b), which takes a decomposed question as input in the following format:

where $\mathcal{O}=$ {summation, difference, division, multiplication, greater, lesser, power, concat, return, remainder}, #$m_{i}$ are answers of previous decomposed questions and $!$ separates the operands.

Experimental Setup

We use GPT-3 Brown et al. (2020) to generate answers for original and decomposed questions. To show that QD significantly improves performance even on simpler models, we use RoBERTa-base finetuned on SQuAD 2.0 dataset (i.e., RoBERTa-SQuAD). Additionally, we use RoBERTa-base finetuned on BoolQ dataset Clark et al. (2019) (i.e., RoBERTa-BoolQ) for original and decomposed questions in StrategyQA since they are True/False type questions.

Experiments

To create baselines, we evaluate all models on the original question along with the context. We evaluate all models on the manually decomposed questions in the proposed method. We carry out all experiments in GPT-3 by designing prompts for each datasetSee Appendix A for more details. For RoBERTa-based models, we use RoBERTa-SQuAD for MultiRC, Break, HotpotQA and DROP datasets, since SQuAD 2.0 is designed for a reading comprehension task. For StrategyQA, we use two RoBERTa-base models: (1) RoBERTa-BoolQ, which is used to answer the final boolean type of questions, and (2) RoBERTa-SQuAD which is used to answer the remaining decomposition questions. For SVAMP, we use the RoBERTa-SQuAD model to extract the necessary operands using decomposed questions and then we use the computational module to perform various operations. In all experiments, we use decomposition to get to the final answer sequentially.

Metrics

For all our experiments, we use Rouge-L Lin (2004), $F_{1}$-score and Exact Match (EM) as the evaluation metrics.

Results and Analysis

Here, we divide our datasets into four categories: (1) RC: HotpotQA, DROP, MultiRC, and Break in Reading Comprehension (RC), (2) MATH: MathQA and SVAMP in Mathematical reasoning , (3) MC: QASC in Multi-Choice QA (MC) , and (4) SR: StrategyQA in Strategy Reasoning (SR). All results presented in this sections are averaged over tasks for each category.

Figure 3 shows the GPT-3 performance in terms of average $F_{1}$-scores for each category. From the Figure 3, we can observe that our proposed approach outperforms baseline by $\sim 24\%$. Appendix D presents all results in terms of $F_{1}$-scores, EM and Rouge-L for all datasets and categories.

RoBERTa

Figure 2 represents the results we obtain using RoBERTa-based models in terms of $F_{1}$-scores for each category. On an average, we achieve $\sim 29\%$ of significant improvement compared to the baseline. Appendix D presents all results in terms of $F_{1}$-scores, EM and Rouge-L for all datasets and categories.

2 Analysis

There can be multiple ways to decompose a question based on the context. Multiple factors go into deciding how to break down a question. One factor is the strength of the model. For instance, if we use a model finetuned on SQuAD, it might be beneficial to ensure that the decompositions are more granular and are generated to answer from a context span. On the other hand, if we have a more sophisticated model like GPT3, we might not necessarily need to do so. The results shown in Figure 2 are obtained on RoBERTa finetuned on SQuAD by using decompositions originally designed for GPT3; note that in this case, the answers to the decompositions might not always be the span of a particular sentence in the context. However, we achieve a decent performance improvement. We believe the performance gain will be greater if decompositions are designed to match the model’s strengths. Examples of such decompositions are included in the Appendix A.

Qualitative Analysis

We conduct qualitative analysis to capture the evaluation aspects missed in the automated evaluation metrics. Here, we manually inspect and consider a generated answer to be correct if it is semantically similar to the gold annotation. Figure 4 and 5 show the contribution of QD in correcting model prediction. We observe that the decompositions correct more than 60% of the errors made on the original questions.

Error Analysis

We conduct error analysis and observe that the major source of error is the error propagated from one of the decomposed questions. Errors, in general, are of two types: (i) incorrect span selection and (ii) failure to collect all possible answers in the initial step of decomposition; this often omits the actual correct answer leaving no room for later decomposition units to generate the correct answer. Errors occur in QASC because our method of context-independent decomposition (via intuition) sometimes leads to open-ended questions which models find hard to answer. Examples of errors have been included in the Appendix B.

Effect of Decomposition on Math Datasets

We observe that Math datasets benefit the most from decomposition. This may be because of two reasons: 1) majority of math questions can be decomposed as a combination of extractive QA (where the answer is a span) and a symbolic calculation. Both of these are strengths of language models (note that we use calculators that provide accurate answers consistently). However, this is not necessarily true in case of other QA tasks. In a decomposition chain, if the answer in one step goes wrong, it propagates till the end and the final prediction becomes wrong. 2) language models by default struggle to do math tasks Patel et al. (2021); Mishra et al. (2022), so the performance improvement seems more prominent there.

Effect of Number of Decompositions on Results

We typically decompose a question based on the number of operations associated with it (e.g. mathematical calculation or single hop operation). Increase in the number of decompositions has the advantage that it simplifies the original question, but it can also have the disadvantage that if the answer to one of the questions in the chain is incorrect, the end answer becomes incorrect. This is also evident from our empirical analysis on HOTPOTQA and SVAMP datasets where we observe that there is no direct correlation between the number of labeling QA and the final performance. Figure 6 shows the variation in model performance improvement observed for questions with 2, 3, 4 and 5 decompositions.

Efforts to Automate Decomposition

For HotpotQA, DROP, and SVAMP, we attempt to automate the decomposition process using GPT3. A limitation for generating decompositions for HotpotQA is that the context length makes it difficult to provide sufficient examples in prompt. With DROP and SVAMP, we observe that GPT-3 often generates incorrect arithmetic operations for the last sub-question. It also often fails to develop coherent decompositions of the questions. We also finetune a BART-base Lewis et al. (2020) model on our handwritten decompositions. However, the model overfits and fails to produce meaningful decompositions, probably due to the limited number of training samples (see Appendix C for examples, details and results).

Conclusion

The recent trend of building large LMs may not be sustainable to solve evolving benchmarks. We believe that modifying data samples can significantly help the model improve performance. We study the effect of Question Decomposition (QD) on a diverse set of tasks. We decompose questions manually and significantly improve model performance (24% for GPT3 and 29% for RoBERTa-SQuAD along with a symbolic calculator). Our findings indicate that Human-in-the-loop Question Decomposition (HQD) can potentially provide an alternate path to building large LMs. Our approach provides a viable option to involve people in NLP research. We hope our work will encourage the community to develop human-centric solutions that actively involve humans while leveraging NLP resources.

Limitations

Our human-in-the-loop methodology shows promising results by decomposing questions, however, certain questions are still difficult to decompose for humans as well. For instance, the question "Which country is New York in?", is hard to decompose further. Determining which questions to decompose is also an important challenge and under-explored in this work. Furthermore, decomposed questions in the chain which have more than one correct answers might lead to an incorrect final answer. Automating the process of decomposition while addressing these issues is a promising area for future work.

References

Appendix A Prompts

Due to the success of large LMs, prompt-based learning is becoming popular to achieve generalization and eliminate the need of creating task-specific models and large scale datasets Liu et al. (2021). Recently, instructional prompts have been pivotal in improving the performance of LMs and achieving zero-shot generalization Mishra et al. (2021b); Wei et al. (2021); Sanh et al. (2021b); Wei et al. (2022); Ouyang et al. (2022); Parmar et al. (2022); Puri et al. (2022); Kuznia et al. (2022); Luo et al. (2022). We present the instructional prompts that we used to generate answers for various datasets.

Given a context, answer the question using information and facts present in the context. Keep the answer short. Example: Input: Mehmed built a fleet to besiege the city from the sea .Contemporary estimates of the strength of the Ottoman fleet span between about 110 ships , 145 , 160 , 200-250 to 430 . A more realistic modern estimate predicts a fleet strength of 126 ships comprising 6 large galleys, 10 ordinary galleys, 15 smaller galleys, 75 large rowing boats, and 20 horse-transports.:44 Before the siege of Constantinople, it was known that the Ottomans had the ability to cast medium-sized cannons, but the range of some pieces they were able to field far surpassed the defenders’ expectations. Instrumental to this Ottoman advancement in arms production was a somewhat mysterious figure by the name of Orban , a Hungarian .:374 One cannon designed by Orban was named "Basilica" and was 27 feet long, and able to hurl a 600lb stone ball over a mile . Question: How many ordinary galleys and large rowing boats is estimated from the fleet strength? Output: Answer: 85 Input: Context: <> Question: <> Output: Answer: <

>

A.2 MATHQA

Prompt for the original question: Given a problem and 5 options, return the correct option. In order to choose the correct option, you will have to perform some mathematical operations based on the information present in the problem. Look at the examples given below to understand how to answer. Input: Problem: the volume of water inside a swimming pool doubles every hour . if the pool is filled to its full capacity within 8 hours , in how many hours was it filled to one quarter of its capacity Options: a ) 2, b ) 4, c ) 5, d ) 6, e ) 7 Output: Answer: 6 Input: Problem: a train 200 m long can cross an electric pole in 5 sec and then find the speed of the train ? Options: a ) 114 , b ) 124 , c ) 134 , d ) 144 , e ) 154 Output: Answer: 144 Input: Problem: <> Options: <> Output: Answer: <

>

A.3 SVAMP

Prompt used for both decomposed questions and original questions. The examples contain both decomposed type questions and original type questions. Given some context, answer a given question. Use the examples given below as reference. Example 1: Input: Context: It takes 4.0 apples to make 1.0 pie. Question: How many apples does it take to make 504.0 pies? Output: Answer: 2016 Example 2: Input: Context: Mary is baking a cake.The recipe calls for 7.0 cups of flour and 3.0 cups of sugar.She already put in 2.0 cups of flour. Question: How many cups of flour did recipe called? Output: Answer: 7 Example 3: Input: Context: Each pack of dvds costs 76 dollars. If there is a discount of 25 dollars on each pack Question: How much is each pack of dvds without the discount? Output: Answer: 76 Example 4: Input: Context: Conner has 25000.0 dollars in his bank account.Every month he spends 1500.0 dollars.He does not add money to the account. Question: How many dollars Conner spends every month? Output: Answer: 1500 Input: Context: > Question: <> Output: Answer: <

>

A.4 StrategyQA

Input: Context: A melodrama is a dramatic work …The passengers’ response to the hijacking has come to be invested with great moral significance. Question: What do tearjerkers refer to? Output: Answer: a story, song, play, film, or broadcast that moves or is intended to move its audience to tears. Input: Context: The purpose of the course is learning to soldier as … The main motor symptoms are collectively called "parkinsonism", or a "parkinsonian syndrome". Question: True or False: Could someone experiencing A tremor, or shaking, Slowed movement (bradykinesia), Rigid muscles, Impaired posture and balance, Loss of automatic movements, Speech changes, Writing changes. complete Volunteer for assignment and be on active duty. Have a General Technical (GT) Score of 105 or higher Output: Answer: False Input: Context: The Scientific Revolution was a series of events that marked the emergence of modern science during the early modern period, …The first-generation iPhone was released on June 29, 2007, and multiple new hardware iterations with new iOS releases have been released since. Question: True or False: Did 1543 occur before 2007? Output: Answer: False Input: Context: <> Question: <> Output: Answer: <

>

A.5 QASC

Prompt for original question: Answer the given question. The question contains options A-H, choose and return the correct option. Look at the examples given below. Input: What are the vibrations in the ear called? (A) intensity (B) very complex (C) melanin content (D) lamphreys (E) Otoacoustic (F) weater (G) Seisometers (H) trucks and cars Output: Answer: Otoacoustic Input: <> Output: Answer: <

> Prompt for decomposed question: Given a yes or no question, return yes if the answer is yes. Otherwise return no. <> Answer: <

>

A.6 MultiRC

Given a context-question pair, answer the question using information and facts present in the context. Keep your answers as short as possible. Example: Input: Context: Should places at the same distance from the equator have the same climate? You might think they should. Unfortunately, you would not be correct to think this. Climate types vary due to other factors besides distance from the equator. So what are these factors? How can they have such a large impact on local climates? For one thing, these factors are big. You may wonder, are they as big as a car. Think bigger. Are they bigger than a house? Think bigger. Are they bigger than a football stadium? You are still not close. We are talking about mountains and oceans. They are big features and big factors. Oceans and mountains play a huge role in climates around the world. You can see this in Figure above. Only one of those factors is latitude, or distance from the equator. Question: Name at least one factor of climate Output: Answer: Oceans Example: Input: Context: Earth processes have not changed over time. The way things happen now is the same way things happened in the past. Mountains grow and mountains slowly wear away. The same process is at work the same as it was billions of years ago. As the environment changes, living creatures adapt. They change over time. Some organisms may not be able to adapt. They become extinct. Becoming extinct means they die out completely. Some geologists study the history of the Earth. They want to learn about Earths past. They use clues from rocks and fossils. They use these clues to make sense of events. The goal is to place things in the order they happened. They also want to know how long it took for those events to happen. Question: What is one example of how the earth’s processes are the same today as in the past? Output: Answer: Things develop and then wither away Input: Context:: <> Question: <> Output: Answer: >

Appendix B Error Examples

This section discusses the errors generated by using decompositions. We observe two types of errors while answering decomposed questions. The final answer is wrong because previous sub-questions were answered incorrectly either because such a question has multiple correct answer, or simply because the model could not understand the question correctly.

Context: … Roger David Casement (1 September 1864 - 3 August 1916), formerly known as Sir Roger Casement …. In collaboration with Roger Casement, Morel led a campaign against slavery in the Congo Free State, founding the Congo Reform Association …. The association was founded in March, 1904, by Dr. Henry Grattan Guinness (1861-1915), Edmund Dene Morel, and Roger Casement … Question: When was the date of birth of one of the founder of Congo Reform Association? True Answer: 1 September 1864 Generated Answer: 18 October 1914 Decomposed Question 1: Who is the founder of the Congo Reform Association? True Answer: Roger Casement Generated Answer: Henry Grattan Guinness Decomposed Question 2: When was #1 born? True Answer: 1 September 1864 Generated Answer: 1861 Above is an example from HotpotQA. As can be seen from the context, Congo Reform Association had multiple founders. GPT3 did give a correct answer among a set of correct answers whereas the ground truth answer provided by the dataset was some other correct option.

Below is an example of incorrect retrieval. The answer generated for the first decomposed question incorrectly returns cities taken by Ottomans as well instead of just the Venetians. Hence, the final decomposed questions returns the incorrect count. Context: In the Morean War, the Republic of Venice besieged Sinj in October 1684 and then again March and April 1685, but both times without success. In the 1685 attempt, the Venetian armies were aided by the local militia of the Republic of Poljica, who thereby rebelled against their nominal Ottoman suzerainty that had existed since 1513. In an effort to retaliate to Poljica, in June 1685, the Ottomans attacked Zadvarje, and in July 1686 Dolac and Srijane, but were pushed back, and suffered major casualties. With the help of the local population of Poljica as well as the Morlachs, the fortress of Sinj finally fell to the Venetian army on 30 September 1686. On 1 September 1687 the siege of Herceg Novi started, and ended with a Venetian victory on 30 September. Knin was taken after a twelve-day siege on 11 September 1688. The capture of the Knin Fortress marked the end of the successful Venetian campaign to expand their territory in inland Dalmatia, and it also determined much of the final border between Dalmatia and Bosnia and Herzegovina that stands today. The Ottomans would besiege Sinj again in the Second Morean War, but would be repelled. On 26 November 1690, Venice took Vrgorac, which opened the route towards Imotski and Mostar. In 1694 they managed to take areas north of the Republic of Ragusa, namely Čitluk, Gabela, Zažablje, Trebinje, Popovo, Klobuk and Metković. In the final peace treaty, Venice did relinquish the areas of Popovo polje as well as Klek and Sutorina, to maintain the pre-existing demarcation near Ragusa. Question: How many cities did Venice try to take? True Answer: 10 Generated Answer: 3 Decomposed Question 1: Which cities did Venice try to take? True Answer: Sinj, Knin, Vrgorac, Čitluk, Gabela, Zažablje, Trebinje, Popovo, Klobuk and Metković Generated Answer: Sinj, Zadvarje, Dolac, Srijane, Knin, Vrgorac, Čitluk, Gabela, Zažablje, Trebinje, Popovo, Klobuk and Metković Decomposed Question 2: What is the count of the cities mentioned in #1? True Answer: 10 Generated Answer: 14 The samples for QASC are provided without context. Without the context, the answers to some of the decomposed questions can be open ended. Certain options can be unambiguously wrong and some are unambiguously correct. Below is an example: Question: What can knowledge of the stars be used for? (A) travel (B) art (C) as a base (D) safety (E) story telling (F) light source (G) vision (H) life True Answer: travel Generated Answer: art Decomposed Question: Can the knowledge of stars be used for the following: #? The decomposed question for each option is posed as a yes or no question to GPT3. It returns yes for art and story telling but not for travel.

Appendix C Examples, Results and Details for Automation

We attempt to automate the process of decomposition using GPT3. We use the examples from manual decomposition in the prompts given to GPT3, some of which are presented below. The results obtained from the experiments are presented in Table 6. The generated decompositions are answered using RoBERTa-base finetuned on SQuAD 2.0 dataset.

In this section, we present the prompts we used while attempting to automatically generate decomposed questions using GPT3. The prompt for generating decompositions for DROP was as follows: Decompose a given question by breaking it into simpler sub-questions. The answer to each subsequent sub-question should lead towards the answer of the given question. To do so, use the context provided and look at the examples. Here are some helpful instructions:

If the given question compares two things, best strategy is to generate sub-questions that finds the answer to each of those things and compare them in the last sub-question.

Some sub-questions must contain phrases like "answer of sub-question 1".

If a sub-question is an arithmetic operation, then the sub-question should be framed as operation ! "answer of sub-question 1" ! "answer of sub-question 2".

The operation used in 3) is always one of the following: summation, difference, greater, lesser.

Example 1: Context: Mehmed built a fleet to besiege the city from the sea .Contemporary estimates of the strength of the Ottoman fleet span between about 110 ships , 145 , 160 , 200-250 to 430 . A more realistic modern estimate predicts a fleet strength of 126 ships comprising 6 large galleys, 10 ordinary galleys, 15 smaller galleys, 75 large rowing boats, and 20 horse-transports.:44 Before the siege of Constantinople, it was known that the Ottomans had the ability to cast medium-sized cannons, but the range of some pieces they were able to field far surpassed the defenders’ expectations. Instrumental to this Ottoman advancement in arms production was a somewhat mysterious figure by the name of Orban , a Hungarian. One cannon designed by Orban was named B̈asilicaänd was 27 feet long, and able to hurl a 600 lb stone ball over a mile . Question: How many ordinary galleys and large rowing boats is estimated from the fleet strength? Sub-question 1: How many ordinary galleys were there? Sub-question 2: How many large rowing boats were there?" Sub-question 3: summation ! "answer of sub-question 1" ! "answer of sub-question 2" Example 2: Context: As of the census of 2000, there were 14,702 people, 5,771 households, and 4,097 families residing in the county. The population density was 29 people per square mile (11/km²). There were 7,374 housing units at an average density of 14 per square mile (6/km²). The racial makeup of the county was 98.02% Race (United States Census), 0.69% Race (United States Census) or Race (United States Census), 0.35% Race (United States Census), 0.11% Race (United States Census), 0.05% Race (United States Census), 0.08% from Race (United States Census), and 0.71% from two or more races. 0.44% of the population were Race (United States Census) or Race (United States Census) of any race. Question: How many more people than households are reported according to the census? Sub-question 1: As of the 2000 census, how many people are residing in the country? Sub-question 2: As of the 2000 census, how many households are reported? Sub-question 3: difference !"answer of sub-question 1" ! "answer of sub-question 2" Example 3: Context: As of the census of 2000, there were 49,129 people, 18,878 households, and 13,629 families residing in the county. The population density was 88 people per square mile (34/km2). There were 21,779 housing units at an average density of 39 per square mile (15/km2). The racial makeup of the county was 74.4% Race (United States Census), 20.4% Race (United States Census) or Race (United States Census), 0.60% Race (United States Census), 1.1% Race (United States Census), 0.15% Race (United States Census), 1.3% from Race (United States Census), and 2.2% from two or more races. 3.4% of the population were Race (United States Census) or Race (United States Census) of any race. 2.85% of the population reported speaking Spanish language at home, while 1.51% speak German language. Question: How many more people are there than families? Sub-question 1: How many people are there in the 2000 census? Sub-question 2: How many families are recorded in the 200 census? Sub-question 3: difference ! "answer of sub-question 1" ! "answer of sub-question 2" Context: <> Question: <> <

> The prompt for HotpotQA was similar, except replacing the examples with instances from HotpotQA. For SVAMP, since the context was much smaller, we could give more examples. The prompt for SVAMP is as shown below: Decompose a given question by breaking it into simpler sub-questions. The answer to each subsequent sub-question should lead towards the answer of the given question. To do so, use the context provided and look at the examples. Here are some helpful instructions:

If the given question compares two things, best strategy is to generate sub-questions that finds the answer to each of those things and compare them in the last sub-question, 2) Some sub-questions must contain phrases like "answer of sub-question 1".

Some sub-questions must contain phrases like "answer of sub-question 1".

If a sub-question is an arithmetic operation, then the sub-question should be framed as operation ! "answer of sub-question 1" ! "answer of sub-question 2".

The operation used in 3) is always one of the following: summation, difference, greater, lesser

Example 1: Context: Jessica had 8.0 quarters in her bank . Her sister borrowed 3.0 of her quarters. How many quarters does Jessica have now? Sub-question 1: How many quarters did Jessica have in her bank initially? Sub-question 2: How many quarters did Jessica’s sister borrow? Sub-question 3: difference ! "answer of sub-question 1" ! "answer of sub-question 2" Example 2: Context: Shawn has 13.0 blocks. Mildred has with 2.0 blocks. Mildred finds another 84.0. How many blocks does Mildred end with? Sub-question 1: How many blocks does Mildred start with? Sub-question 2: How many blocks does Mildred find? Sub-question 3: summation ! "answer of sub-question 1" ! "answer of sub-question 2" Example 3: Context: Dave was helping the cafeteria workers pick up lunch trays, but he could only carry 9.0 trays at a time. If he had to pick up 17.0 trays from one table and 55.0 trays from another. how many trips will he make? Sub-question 1: How many trays did Dave have to pick up from the first table? Sub-question 2: How many trays did Dave have to pick up from the second table? Sub-question 3: summation ! "answer of sub-question 1" ! "answer of sub-question 2" Sub-question 4: How many lunch trays could Dave carry at a time? Sub-question 5: division ! "answer of sub-question 3" ! "answer of sub-question 4" Example 4: Context: Paco had 93.0 cookies. Paco ate 15.0 of them. How many cookies did Paco have left? Sub-question 1: How many cookies did Paco start with? Sub-question 2: How many cookies did Paco eat? Sub-question 3: difference ! "answer of sub-question 1" ! "answer of sub-question 2" Example 5: Context: 43 children were riding on the bus. At the bus stop some children got off the bus. Then there were 21 children left on the bus. How many children got off the bus at the bus stop? Sub-question 1: How many children were on the bus at the beginning? Sub-question 2: How many children were left on the bus? Sub-question 3: difference ! "answer of sub-question 1" ! "answer of sub-question 2" Example 6: Context: 28 children were riding on the bus. At the bus stop 82 children got on the bus while some got off the bus. Then there were 30 children altogether on the bus. How many more children got on the bus than those that got off? Sub-question 1: How many children were on the bus at the beginning? Sub-question 2: How many children were left on the bus? Sub-question 3: difference ! "answer of sub-question 1" ! "answer of sub-question 2" Example 7: Context: They decided to hold the party in their backyard. If they have 11 sets of tables and each set has 13 chairs, how many chairs do they have in the backyard? Sub-question 1: How many tables are there in the backyard? Sub-question 2: How many chairs are on each table? Sub-question 3: multiplication ! "answer of sub-question 1" ! "answer of sub-question 2" Context: <> The examples of decompositions generated for HotpotQA, DROP and SVAMP are shown in Table 7

Appendix D Results

We tabulate the results we get for all the datasets for baseline and our proposed mechanism.