Measuring Retrieval Complexity in Question Answering Systems (2024)

Abstract: In this paper, we investigate which questions are challenging for retrieval-based Question Answering (QA). We (i) propose retrieval complexity (RC), a novel metric conditioned on the completeness of retrieved documents, which measures the difficulty of answering questions, and (ii) propose an unsupervised pipeline to measure RC given an arbitrary retrieval system. Our proposed pipeline measures RC more accurately than alternative estimators, including LLMs, on six challenging QA benchmarks. Further investigation reveals that RC scores strongly correlate with both QA performance and expert judgment across five of the six studied benchmarks, indicating that RC is an effective measure of question difficulty. Subsequent categorization of high-RC questions shows that they span a broad set of question shapes, including multi-hop, compositional, and temporal QA, indicating that RC scores can categorize a new subset of complex questions. Our system can also have a major impact on retrieval-based systems by helping to identify more challenging questions on existing datasets.

heading: 1 Introduction
text: Retrieval-based approaches are a dominant paradigm in QA. They constitute a basic building for many QA pipelines, as they can gather accurate information from external sources that are useful for answering questions. Notable examples include the Retrieve and Rerank system (Gupta et al., 2018; Garg et al., 2020) and the recent Retrieval Augmented Generation (RAG) (Lewis et al., 2020b; Hsu et al., 2021). While retrieval systems effectively address questions targeting common knowledge, they can struggle with addressing novel, domain-specific questions that require
∗Work done as an intern at Amazon Alexa AI †Work completed at Amazon Alexa AI
fresh, contextually accurate information. Generative models, on the other hand, bring the ability to generate responses to such challenging questions. For instance, Bing-GPT uses retrieval to answer questions about real-time events beyond the LLMs’ training data cutoff (Dao, 2023). However, retrieval augmentation can fail for challenging questions. To address this problem, the QA community developed benchmarks to measure the performance of QA approaches on these types of questions. For example, HotPotQA (Yang et al., 2018b), ComplexWebQuestions (Talmor and Berant, 2018), and MuSiQue (Trivedi et al., 2022) challenge systems by proposing questions with "complex" shapes, such as multi-hop questions, requiring multiple steps of reasoning, e.g., "what is the GDP of the country with the tallest bridge?". While it is as-
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sumed that these question shapes are equally difficult for RAG and other QA systems, subsequent works indicate that this is not the whole picture of QA complexity. For example, Min et al. (2019a) show that nearly 61% of HotPotQA’s multi-hop questions actually have "single-hop answer solutions" - i.e., a single document that contains the correct answer - that a simple RAG system can use to answer correctly. More recent RAG-oriented benchmarks such as Fresh QA (Vu et al., 2023) further illustrate that the complexity of the answer evidence is relevant in identifying difficult questions since the evidence can become false if not recent enough.
In this paper, we introduce a novel metric named Retrieval Complexity and an unsupervised pipeline, named Reference-based Question Complexity Pipeline (RRCP) (Section 4) to recognize it. Specifically, given a query question and one or more reference answers, RRCP employs an arbitrary retriever to procure pertinent documents. Subsequently, utilizing a novel reference-based evaluator named GenEval, RRCP scores the question based on the retrieved documents and the supplied reference answers. Conceptually, RC approximates the degree to which the evidence required to answer the question is spread across documents in the retrieval batch. The intuition behind RC is that the greater the fragmentation of required information within a retrieval batch, the harder it is for a RAG system to answer the question correctly. For example, Fig. 1 shows two questions with highly similar question semantics but significantly different retrieval quality (e.g., relevance and comprehensiveness of the information) to illustrate what RC measures.
We compare RRCP with supervised and unsupervised models, demonstrating its superior accuracy in classifying RC questions. Our unsupervised approach enables applicability to new QA benchmarks, acting as a valuable resource for the QA community. RC is intimately linked to a specific retrieval corpus, capturing (i) index coverage, (ii) retrieval method quality, and (iii) varying semantics of questions into a single metric. To support this claim, we compute RRCP scores for six QA benchmarks using a state-of-the-art search engine (Bing) and reveal a strong correlation between RC scores and QA system performance. In addition, we show that our human expert assessment of question difficulty against retrieved evidence also correlates with RRCP scores. Finally, we present a qualitative
analysis of 200 high-RC questions drawn from all benchmarks. These findings indicate a connection between high RC and diverse question types, such as multi-hop (23%), comparative (10%), temporal (15%), superlative (3%), and aggregate (16%).
In summary, our paper (i) motivates the need to estimate the answering difficulty of questions given the availability of evidence, (ii) defines RC, a new metric that measures the difficulty of questions conditioned on a retrieval batch, (iii) proposes RRCP, an unsupervised pipeline to measure retrieval complexity, and (iv) empirically demonstrates that our pipeline is superior at classifying high RC questions and (v) shows that higher RC scores correlate with lower QA performance.

heading: 2 Related work
text: In this section, we introduce the related work on the main topics of our paper: question complexity, LLM-based QA, retrieval for QA, and automatic evaluation.
Notions of Question Complexity: A popular notion of question complexity in QA literature considers the number of reasoning steps (hops) required to get to the answer. Multi-hop questions (Mavi et al., 2022) - those expected to require at least two reasoning steps - are one source of complex questions. Popular benchmarks for multi-hop QA include HotPotQA (Yang et al., 2018b) and MuSiQue (Trivedi et al., 2022), which are constructed by aggregating multiple one-hop questions into a multi-hop one. Min et al. (2019b) highlight that such multihop questions may, in fact, not require multiple reasoning steps to answer, finding that many may be answered with a single snippet extracted from a relevant document. Talmor and Berant (2018) suggests a related notion, compositional complexity, that assesses the degree to which the answer must be composed from multiple pieces of evidence. Subsequent works have shown that both multi-hop and compositional questions can be decomposed into simpler sub-questions (Perez et al., 2020; Yoran et al., 2023), enabling a strong LLM to answer using chain-of-thought (CoT) (Wei et al., 2022). To conclude, prior works tried to perform some performance prediction of queries (Zhou and Croft, 2007; Datta et al., 2022) relying on evidence in the form of different characteristic patterns in the distribution of Retrieval Status Values (RSVs).
Reasoning over temporal information - i.e., information that changes quickly over time - is an-
other dimension of QA complexity, captured in benchmarks like Time-Sensitive-QA and FreshLLM (Chen et al., 2021; Vu et al., 2023). Temporal questions require systems to reflect embedded notions of temporality, which may either be explicit (e.g., Who was the president of the US in 1945?) or implicit (e.g., Who was the last president of the US?). Temporal knowledge graphs (Saxena et al., 2021; Shang et al., 2022; Sharma et al., 2023), temporal embeddings in the (Huang et al., 2022), and retrieval have all been proposed as solutions to the complexity of temporal QA (Vu et al., 2023).
LLMs for Question Answering: Transformerbased models (Vaswani et al., 2017) have become the de-facto standard for QA tasks, either in the form of encoder-only models (Devlin et al., 2019; Liu et al., 2019; Clark et al., 2020), encoderdecoder models such as T5 (Raffel et al., 2020; Lewis et al., 2020a) or decoder-only models (Radford et al., 2018), most notably ChatGPT. Despite the impressive performance of these models across a variety of QA benchmarks, answering complex and convoluted questions without hallucinations is an enduring challenge (Huang et al., 2023). RAG systems seek to address this challenge by providing retrieved information as grounding knowledge for answer generation (Lewis et al., 2020b; Gabburo et al., 2022; Borgeaud et al., 2022).
Retrieval for QA: BM25 (Crestani et al., 1998) is a traditional retrieval approach also widely used for QA. It uses an unsupervised scoring function based on a sparse bag-of-words representation of text. More recently, supervised retrieval systems that compute an approximate nearest neighbour score on dense representations of query and document have been proposed, such as DPR (Karpukhin et al., 2020) and ColBERT (Khattab and Zaharia, 2020). Other models attempt to capture the benefits of both techniques by learning a sparse representation of documents conditioned on relevant queries, such as UniCOIL (Lin and Ma, 2021) and DeepImpact (Mallia et al., 2021).
Automatic QA Evaluation: Automatically evaluating the correctness of answers is a challenging task, especially in light of the compelling hallucinations created by strong generative LLMs. Previously, token-level metrics such as BLEU (Papineni et al., 2001) and sentence-level metrics such as BERTScore (Sun et al., 2022) and BLEURT (Yan et al., 2023) have been used for this task. However,
these metrics do not correlate well with human annotation for QA tasks, as shown in (Gabburo et al., 2022). Recently, several works have proposed reference-based evaluation metrics for the QA and demonstrated that these have greater correlation with human annotations, such as AVA (Vu and Moschitti, 2021), BEM (Bulian et al., 2022), and SQuARe (Gabburo et al., 2023).

heading: 3 Retrieval Complexity of Questions
text: A retrieval system provides users with relevant and accurate information in response to their queries (Baumgärtner et al., 2022b; Rogers et al., 2023). Recently, retrieval augmentation - that is, conditioning generation on retrieved evidence - has been shown to enable generative models to address more complex, multi-faceted questions (Luo et al., 2023). We conceptualize RC, a specific notion of question complexity, which can also be used to evaluate the complexity of questions used in prior retrieval-based QA systems, e.g., RAG models.
Intuitively, a question can be considered complex for retrieval augmentation if it cannot be answered by extracting a snippet from a retrieved document. This dimension of complexity can occur for multiple reasons, such as if the answer requires multiple reasoning steps or a composition of supporting facts spread across retrieved content (Dua et al., 2019; Yang et al., 2018a). Effectively, retrieval complexity occurs when multiple pieces of information must be combined in a complex fashion to generate the correct answer, such as reasoning, comparison, or composition over multiple facts. Multiple factors can increase the retrieval complexity, including index coverage, retrieval quality, and question syntax, as each plays a role in determining whether a document containing a snippet that answers the question is retrieved.
For example, answering the question "Are lions bigger than tigers?" (Fig. 1) requires a comparison between two related entities. While this question could be considered complex, the close relation of the lions and tigers increases the probability that a single snippet talks about the size of both animals. However, the probability above is an order of magnitudes lower for a similar question, such as "Are lions bigger than freezers?".

heading: 4 Modeling Retrieval Complexity
text: To model and recognize the retrieval complexity (Section 3), we designed an unsupervised reference-
based pipeline named RRCP (reference-based RC pipeline) shown in Fig. 2. RRCP is composed of three primary components: (i) A state-of-the-art retrieval system based on multiple indexes. This, given a question Q, composes a set of supporting documents D = {d0, d1, ..., dk}. (ii) A powerful automatic evaluation system named GenEval, which, using the retrieved documents and a set of references, estimates the RC of Q, and (iii) a constraint enforcer mechanism based on two thresholds.

heading: 4.1 Retrieval System
text: The retrieval system component of RRCP is a framework that uses multiple indexes to efficiently retrieve relevant documents in response to a given question Q. This system employs state-of-the-art techniques to compose a set of supporting documents, D = d0, d1, ..., dk, where each document di is deemed relevant to the query Q. To ensure high reliability and robustness, we used a hybrid retrieval system based on BM25 (Crestani et al., 1998) and ColBERT (Khattab and Zaharia, 2020).

heading: 4.2 GenEval
text: Inspired by recent automatic evaluation systems such as BEM (Bulian et al., 2022) and SQuArE (Gabburo et al., 2023), we designed a novel model named GenEval to recognize the difficulty of a question. GenEval is an encoder-decoder model trained to understand if a document di ∈ D is relevant (e.g., contains a correct answer) given a

heading: Models AE Finetuning Accuracy
text: question Q and a set of multiple references R = {r0, r1, ..., rk}.
GenEval differs from BEM and SQuArE in two main aspects: First, both SQuArE and BEM are based on an only-encoder transformer architecture (Devlin et al., 2019; Liu et al., 2019; He et al., 2021). Using an encoder-decoder model allows for a more flexible model training starting from stateof-the-art large language models such as T5-xxl (Raffel et al., 2020).
Second, unlike the aforementioned approaches, GenEval has been trained on more reference datasets and on synthetic data, increasing flexibility to cases where ground-truth references are not available and using a two-headed architecture to predict the "answer correctness" and "tokens relevance". The first one estimates the probability of di containing an accurate answer for Q, while the second computes the relevance distribution of each token of di according to Q. RRCP uses these two inner metrics to model the Answerability and the Retrieval Completeness constraints necessary to estimate RC. We provide better details about GenEeval in Appendix A.4.
To prove the better performance of GenEval over the BEM and SQuARe, we conducted an experiment measuring the performance of the GenEval on the AE (Bulian et al., 2022) testset. Table 1 presents the comparison results of GenEval, SQuARe, and BEM on the Answer Equivalence (AE) test set in both zero-shot and fine-tuned settings. In the zero-shot setting, without fine-tuning on the target dataset, GenEval shows better accuracy with a value of 0.750 compared to SQuARe’s 0.572. In the fine-tuned setting, all models were finetuned on the target dataset, and the table shows that SQuARe and GenEval exhibit improved perfor-
mances, with the latter having an accuracy of 0.916, which is higher than both SQuARe’s 0.907 and BEM’s 0.897. These results suggest that GenEval outperforms SQuARe and BEM in terms of accuracy and correctness estimation in both settings.

heading: 4.3 RRCP Constraints
text: RRCP enforces two constraints, Answerability and Retrieval Set Completeness, to estimate RC.

heading: 4.3.1 Answerability
text: From a retrieval perspective, a requirement that makes a question complex is the probability of answering it with a single document (Sec. 3. For example, questions like "What is the capital of France?" can be easily answered by a single document and do not fit our definition of retrieval complexity. In contrast, questions like "Is Paris bigger than the capital of the US?" have a higher degree of complexity since the probability of finding a document that makes this comparison is more difficult to find.
We capture this property by setting a constraint on answerability: if the target question fails to meet this criterion, it is deemed potentially complex. Specifically, answerability is met if at least one document di ∈ D contains an accurate response to Q. To compute the probability that an answer exists in a document, we use the probability estimated by GenEval. Specifically, we define a threshold Tans ∈ [0, 1] over the probability computed by the GenEval "answer correctness" head of a document containing the correct answer si: if the score exceeds Tans, the question is answerable. Intuitively, if the question can be answered by a single retrieved document di in D, si will approach 1. As such, we model the answerability function Ans(SD) as follows:
Ans(SD) = { 0 if max(si ∈ SD) < Tans 1 if ∃ si ∈ SD ≥ Tans,
(1) where Tans is used to discriminate between not answerable questions when si < Tans, and answerable questions when si ≥ Tans.

heading: 4.3.2 Retrieval Set Completeness
text: Retrieval set completeness determines how much the information required to answer is spread across different documents. Indeed, a document could be partially relevant to the question but without
containing sufficient information to induce the correct answer (Fan et al., 2018; Baumgärtner et al., 2022a). For instance, to answer a question like "Who are the top 5 goalkeepers of the last ten years?" a two-year-old document could not contain all the information needed since there is no evidence about the scores achieved by the goalkeepers in the last two years. For this reason, the document is still relevant but not exhaustive. With the retrieval set completeness, we aim to estimate the retrieval complexity of a question by examining the heterogeneity of the retrieval set. To perform this estimation, we compute the entropy of the relevance of each document in the retrieval batch di ∈ D with each token in the question. For example, given the question "Are lions bigger than tigers?", we can expect that documents discussing lions will be more relevant to the question subparts that refer to lions, and the opposite for documents discussing about tigers. Based on this notion of relevance, we can approximate whether the knowledge relevant to each portion of the question is present in the retrieval set.
To measure completeness, we leverage the relevance distribution extracted from GenEval at the token level to generate a distinct attention distribution for each document in D. These distributions are organized into a matrix M of size |D|× |Q|, where each row represents the token tj from the question, and columns indicate the relevance Rel(di, tj) of each document di to those tokens.
Finally, to ensure comparability, we normalize the entropy for each document and compute the average normalized entropy to obtain the completeness score SD:
SD =
∑|D| i=1 ∥∥∥ ∑|Q| j=1Rel(di, tj) ∥∥∥
|D| . (2)
Similar to answerability, we apply a threshold Tcom to the completeness score:
Com(SD) = { 1 if SD ≥ Tcom 0 if SD < Tcom
(3)

heading: 4.4 Classifying Complex Questions
text: While answerability and retrieval set completeness are two standalone criteria, RRCP leverages both signals to approximate retrieval complexity (RC). Specifically, RRCP considers a question complex when the question is not answerable with a single
document and when the retrieval set is incomplete. Formally, we consider both 1 and 3, classifying a question as retrieval-complex if Ans(SD) = 0 and Com(SD) = 1. In addition to enabling RC classification, answerability and completeness scores can be used as additional diagnostic metrics.

heading: 5 Experiments
text: In this section, we focus on studying Retrieval Complexity (RC) and our RRCP framework for its detection. First, in sections 5.1 and 5.2 we describe the datasets we considered and the setup of RRCP. Then, we validate RC and RRCP by conducting both quantitative and qualitative analyses. Specifically, we first compare RRCP against a strong prompted LLM unsupervised baseline directly on a set of 4 selected datasets in, targeting the specific complexity class for each of them (Section 5.3). Secondly, in Section 5.4, we evaluate the correlation between the RC classification (complex/not complex) with LLM answer capability. This allows us to understand some possible limitations of our notion of complexity. In the third quantitative experiment (Section 5.5), we measure the answerability of the questions identified as complex by our pipeline using a state-of-the-art search engine, such as Bing. Finally, we perform a qualitative analysis to inspect the limitations and the generalizability of our approach (Section 5.7).

heading: 5.1 Datasets
text: We evaluated RRCP on the following academic benchmarks: ComplexWebQuestions (CWQ) (Talmor and Berant, 2018), HotPotQA (Yang et al., 2018b), StrategyQA (Geva et al., 2021), and MuSiQue (Trivedi et al., 2022). We used the question complexity information provided in each dataset to define "complex" or "not complex" labels. For CWQ, we labelled their simple questions as not complex and the more challenging ones composed from them as complex. For HotPotQA, we used the "difficulty level" associated with each question in the dataset. For MuSiQue and StrategyQA, we considered one-hop questions as not complex and multi-hop ones as complex.
We also used Natural Questions (Kwiatkowski et al., 2019) and QuoraQP-a (Wang et al., 2020) to evaluate our pipeline on more natural usergenerated questions. A small team of expert annotators determined complexity labels on these datasets using the instructions outlined in Appendix A.6.
Table 2 reports the complexity categories we found in some of the datasets above. Additional details regarding the distribution, size, and splits of these datasets are defined in Appendix A.2.

heading: 5.2 RRCP setup
text: We implemented RRCP (described in Section 3), with a state-of-the-art hybrid retrieval system based on BM25 (Crestani et al., 1998) and ColBERT (Khattab and Zaharia, 2020) with an index of documents containing (Wikipedia (Petroni et al., 2021), and MS MARCO (Nguyen et al., 2016)).
To implement the automatic evaluation system represented by GenEval (Sec.4.2), we trained a T5-xxl model (Raffel et al., 2020) on two existing datasets, which are WQA (Vu and Moschitti, 2021) and AE (Bulian et al., 2022). We discuss additional details regarding the experimental setting and the performance against other automatic evaluation metrics in Appendix A.4. We set thresholds Tans = 0.15 and Tcom = 0.80 based on a small set of 50 manually written test questions.

heading: 5.3 Complex Question Identification
text: To compare the ability of RRCP to detect complex questions with alternative approaches (e.g., LLMs, supervised models), we use the answerability and completeness scores to classify questions as described in Section 5.3. We compare the performance in terms of accuracy and f1-measure against a strong unsupervised baseline consisting of a prompted state-of-the-art LLM for this task. We report the results of these experiments in Table 3.
Furthermore, we ablated different configurations of the pipeline to assess the benefits given by the two constraints. Combining the answerability and the retrieval set completeness constraints proved to be beneficial, enabling a more accurate classification than the alternatives. RRCP, based only on the answerability constraint, generally demonstrates higher results than the LLM baseline. Also,
without considering the completeness constraint, the pipeline provides accurate predictions. On the other hand, the model only based on retrieval completeness achieves lower performance than the other approaches, highlighting the fact that it can not be used standalone.

heading: 5.4 LLM Performance on Complex Questions
text: In this section, we study whether RRCP predictions (complex vs. not complex) correlate with the notion of complexity of LLM-based systems (only using parametric knowledge). Specifically, we evaluate the correlation between its RC classification and LLM answer capacity (0/1 label), where the latter is computed by (i) generating an answer with LLM and (ii) manually annotating its correctness.
For each dataset in Section 5.1, we apply RRCP, employing our defined criteria to filter complex from non-complex questions. We use an end-toend QA system composed of a prompted Mistral 7B (Jiang et al., 2023) (a large language model) designed to receive input questions and generate accurate answers. Then, we evaluated each generated answer, comparing it with the original gold answers in the datasets. Finally, we measured the agreement between the detected RC and answer correctness in terms of Pearson Correlation.
We present the results of this analysis in terms of accuracy in Table 4, where we show the accuracy scores for both complex and non-complex questions across the different datasets and their Pearson Correlation. Each entry in the table represents the percentage of questions correctly answered by this LLM-based QA system.
The results confirm that our approach effectively identifies complex questions, resulting in higher answerability. Questions identified as complex by the pipeline generally exhibit higher accuracy in terms of answerability, indicating that these questions are
easier to be answered for the model. Specifically, questions categorized as complex in CWQ, HotPotQA, MuSiQue, and Natural Questions display higher accuracy than those classified as not complex. Notably, the complexity assessment in Quora and StrategyQA does not significantly impact the question answerability, suggesting a different nature of complexity in this dataset or some bias. In StrategyQA, complex questions were labelled due to limited "true/false" reference answers, impacting evaluation metrics. Modifying the prompt eliminated this artifact, highlighting the need for precise evaluation metrics. In contrast, Quora’s complexity designation was influenced by poor-quality reference answers, emphasizing caution when interpreting complexity labels in datasets with sub-optimal reference quality.

heading: 5.5 Search Engine Performance on Complex Questions
text: We further explore the quality of our pipeline by sampling a set of 500 questions from the "complex" questions of each dataset and analyzing how many of them can be answered by a state-of-the-art search engine such as Bing1. This dataset is con-
1https://www.bing.com/

heading: RRCP Answerable Not MCCClassification Answerable
text: structed by selecting 256 questions from datasets with their own notion of complexity, including CWQ, HotPotQA, StrategyQA, and MuSiQue (64 questions per dataset), and another 256 from natural datasets not specifically focused on complexity (128 each from Natural Questions and Quora). To conduct the evaluation, we select a pool of expert annotators. Their task is to determine whether a given question can be answered by examining the top 5 search engine results. If the answer is found within these results or can be inferred through reasoning based on them, the question is considered answerable. Furthermore, the annotators are tasked with evaluating whether the question aligns with our predefined notion of retrieval complexity as described in Section 3.
The results of our analysis, detailed in Table 5, reveal significant insights. Indeed, the probability of a question marked as complex by RRCP of not being answered by a state-of-the-art search engine is high (0.887). Similarly, a question marked as not complex has a high chance to be answered (0.6). In addition, the results show a good correlation between question-predicted complexity and their answerability (manually annotated), with a Matthew correlation of 0.508, indicating a moderate to strong positive correlation between the predicted classifications and the actual classifications.

heading: 5.6 Limitations of Supervised Approaches
text: In this section, we explore the limitations of employing supervised approaches to estimate question complexity. To show this finding, we trained several cross-encoder models on the datasets introduced in Section 5.1 using a supervised learning approach. The experimental setup is detailed in Appendix A.1. The outcomes of this analysis are presented in Table 6.
We assessed the resulting five models on the four datasets. Notably, Natural Questions (Kwiatkowski et al., 2019) and QuoraQP-a (Wang et al., 2020)
lack an internal definition of complexity (Table 2), making automatic evaluation and training impracticable.
Although the model trained on the merged dataset demonstrated impressive performance, individual models struggled to replicate this strong performance across datasets. This disparity implies that fine-tuning induces models to overfit on the question distribution rather than learning the intricacies of question complexity. This observation highlights the need for standard fine-tuning to develop dataset-agnostic models to detect question complexity. It is important to acknowledge that the "ALL" model performs well due to its ability to identify which dataset the test question belongs to, thanks to the distinctive topics and typical question shapes characterizing each dataset. Consequently, supervised models only capture specific properties of the data and complexity definitions.

heading: 5.7 Qualitative Analysis and Limitations
text: We further examine the behaviour of our pipeline through a rigorous qualitative evaluation. We notice that RRCP, initially designed to recognize retrieval complexity, can address other complexity classes beyond its primary scope. These complexity classes are part of a wide range of question types, such as comparative questions (e.g., "Is an elephant bigger than a cat?"), multi-hop questions (e.g., "How old is the wife of the tallest NBA player?"), questions needing the "aggregation" of multiple answers in the form of disconnected entities (e.g., "List every football player who played in the last World Championship?"), time-based questions, both implicit and explicit (e.g., "Who is the current president of the US?" and "Which movie won the Oscar for the best movie in 1992?") and
superlative questions (e.g., "What are the best countries to travel to in March?") following the distribution shown in Fig. 3.
However, our analysis also highlights notable limitations within our pipeline. We identified two primary challenges. Firstly, the reference-based nature of our approach is susceptible to the quality of the references used. Consequently, the predictive accuracy of the pipeline is significantly impacted by the quality of these references. This issue becomes evident during the examination of results from Quora, where we observed a discernible drop in performance. Despite employing a robust retrieval system, the precision of our pipeline is closely linked to the quality of the references. This finding underscores the critical role of reference quality in shaping the effectiveness of our methodology. Addressing this challenge necessitates a comprehensive evaluation of the reference sources employed and potential enhancements in the retrieval system to mitigate the adverse effects on prediction accuracy. By acknowledging and addressing these limitations, our research aims to refine the qualitative analysis pipeline, ensuring its applicability across various complexity classes and enhancing its overall robustness in handling diverse question types.

heading: 6 Retrieval Complexity Applications
text: In Section 5, we show that RRCP is a valuable tool which allows for the recognition of RC with high accuracy. This could be difficult to achieve with a reference-free approach. Although the need of references could limit the applicability of RRCP in real-world scenarios, it serves as a crucial step to-
wards understanding the potential applications and future directions of RC in the field of QA systems. Indeed, RC is a valuable diagnostic tool that can be applied to various settings, including question routing, optimizing document usage in Relevance and Ranking (RAG) systems, filtering QA datasets, and identifying interesting questions according to some complexity notion. The motivating concepts of RC are potentially applicable to many settings, as they provide insights into the underlying complexity of questions and can help reveal challenging questions in existing academic benchmarks.

heading: 7 Conclusion
text: In this paper, we introduced a novel concept of question complexity, measuring the difficulty of finding accurate answers from multiple sources. By combining a top-tier retrieval system with an effective automatic evaluation system, our approach (RRCP) demonstrated high accuracy in handling complex questions that go beyond single-source responses. We performed an extensive experimentation, conducting both quantitative and qualitative analyses on various datasets, proving the robustness of our pipeline in managing and recognizing complex question types, including multi-hop questions, time-based queries, and comparative inquiries. The results consistently showed that our approach outperformed state-of-the-art supervised transformer models and large language models in these challenging scenarios. Additionally, our benchmark evaluations underscored the superiority of our method, highlighting its capability to deliver more precise answers where traditional models struggled. The empirical evidence confirmed that our pipeline is particularly effective in classifying high retrieval complexity (RC) questions and that higher RC scores were correlated with lower QA performance, underscoring the validity of our RC metric. As future work, we plan to reduce the reference dependency of the Retrieval Complexity Pipeline (RRCP) in our evaluation system by incorporating large language models (LLMs) and parametric knowledge. This enhancement aims to increase the number of application scenarios for our framework, broadening its usability and effectiveness in diverse contexts. By leveraging these advanced models, we anticipate further improvements in the efficiency and accuracy of our system, making it even more versatile in handling a wide range of complex queries.

heading: 8 Limitations
text: While our study provides valuable insights about retrieval complexity and our framework proved to be a useful tool to determine whether a question fits with our notion of complexity, it is important to acknowledge several limitations that may impact our approach:
Corpus dependency: As mentioned in Section 4 and Section 5, the performance of our pipeline is limited by the goodness of the corpora considered to build the index. For example, this limitation is evident when thinking about a time-based question asking about recent events not covered by our index. We partially mitigate this problem by working on the completeness constraints as specified in Section 4, but we consider this limitation as an open problem, planning to address it in future work.
Reference-based approach: The core of our framework is based on a reference-based evaluation system. Although we can rely on high accuracy and human-like performance in terms of correctness evaluation, on the other hand, we are limited by the need for gold answers to get a good answerability prediction, limiting the scope of RRCP on labeled data. However, despite this limitation, we believe that larger reference-free approaches based on LLMs could soon replace the automatic evaluation component.
Quality of the retrieval system: Our methodology accuracy scales with the quality and accuracy of the retrieval system.
Thresholds: Determining Tans and Tcom is a trivial task that can be done with few examples. However, their values are critical to determine the RC with high accuracy.
As mentioned in Section 5 and Section 7, we plan to address these limitations in future work.

heading: A Appendix

heading: A.1 Modelling Details
text: The supervised model was trained on Amazon AWS P3dn.24xlarge hosts using specific hyperparameters selected after a parameter search. The model architecture utilized the roberta-base (Su et al., 2022) configuration, with a batch size (bs) of 256 instances. We used an Adam optimizer considering a learning rate (lr) of 1e − 05 during training, carried out over 10 epochs. The model selection criterion was based on achieving the highest F1 score on the development set (devset), ensuring the selection of the most effective model variant. Additionally, the training process incorporated mixed-precision arithmetic (fp16) to enhance computational efficiency and speed up the training procedure. We estimate that GPU hours used for baseline training and pipeline inference to be no more than 462 GPU hours.

heading: A.2 Datasets
text: In this section, we provide an exhaustive description of the datasets we considered in the paper to validate our approach.
ComplexWebQuestions (Talmor and Berant, 2018) is a dataset for answering complex questions that require reasoning over multiple web snippets. It contains 34686 examples in total (27368, 3518, and 3530 for train, dev and test splits), and each example presents a question, an answer, and a SPARQL query to retrieve the web snippets needed to build the context.
HOTPOTQA (Yang et al., 2018b): A QA dataset designed to contain complex questions that can not be answered without reasoning and additional context. To support this, they also added different
paragraphs for each question in the dataset that can be used as a context to provide the answer.
StrategyQA (Geva et al., 2021): StrategyQA is a question-answering benchmark focusing on opendomain questions where the required reasoning steps are implicit in the question and should be inferred using a strategy. StrategyQA includes 2,780 examples, each consisting of a strategy question, its decomposition, and evidence paragraphs. The only usable split is the "train "since it has both the decompositions and the facts.
MuSiQue (Trivedi et al., 2022): This dataset has been prepared by joining multi-hop questions with single-hop questions from different datasets using a bottom-up approach. Differently from BREAK, the decomposed questions here look more natural.
Natural Questions (Kwiatkowski et al., 2019): Large scale dataset made considering real Google queries. Each query is paired with a corresponding Wikipedia page and the relevant passage containing the answer. By definition, this dataset does not contain questions that fit our definition of complexity (Section 3) since, for construction, the majority of the questions have answers that can be answered by a single passage. However, studying this dataset is helpful to recognize the limitations of the retrieval system used by the pipeline and to study the correlations between what is complex for a human and for a QA system.
QuoraQP-a (Wang et al., 2020), is a questionanswering dataset made pairing existing questions from Quora Question Pairs (QQP) with their original answers.

heading: A.3 Supervised results
text: For completeness, in Table 7, we report the complete results obtained by the supervised approach measured in terms of Accuracy, Precision, Recall, and F1.

heading: A.4 GenEval details
text: The GenEval is an encoder-decoder transformer model based on the T5-XXL (Raffel et al., 2020). We trained the model on three datasets, WQA (Gabburo et al., 2023), and AE (Bulian et al., 2022) and ASNQ (Garg et al., 2020). Differently from the original SQuArE, we used a variable number of references during the training, considering also generated ones (we generated these references using a GenQA model (Gabburo et al., 2022)). We

heading: Trained on All

heading: Trained on CWQ

heading: Trained on HOTPOTQA

heading: Trained on MUSIQUE

heading: Trained on StrategyQA
text: experimented with different parameters, and we found the best combination of parameters training the model for 20 epochs on every dataset using a batch size of 32, fp32, and Adam as optimizer with a learning rate equal to 5e− 05. We select the best checkpoint by evaluating the AUROC (Area Under the Curve) on the validation set.

heading: A.5 Mistral 7B Evaluation Prompt
text: To perform the automatic evaluation on LLM, we are considering the following prompt: 

"Consider the following question Q: {s}. Is question Q complex according to the provided definition? A complex question cannot be answered by a single document; it necessitates reasoning over different snippets due to the low probability of finding the answer within existing sources. Examples of complex questions include inquiries like ’Is a cup of tea bigger than an elephant?’ where the comparison is unlikely to be found in a single document. In contrast, questions such as ’Is an elephant bigger than a lion?’ are not complex because ’elephant and lions’ can be part of the same
document with high probability. Please respond with ’yes’ if the question is complex and ’no’ if it is not. Ensure your reply is concise, strictly limited to ’yes’ or ’no’." 


heading: A.6 Manual annotation
text: To perform the manual annotation described in Section 5.5, we employed a set of 5 voluntary international experts (from the US, Brazil, India, and Italy) in the QA domain to annotate the data. We instruct each of them on the task, providing the notion of retrieval complexity 3 and a set of examples to reference during the annotation. Specifically, for each question present in our evaluation set, the annotation has been done by presenting the question to the annotator, the top−5 web pages retrieved by the search engine, and the top document retrieved using our retrieval system. Then, for each question, the annotators determine whether the question is answerable by one or more Bing search results (applying or inferring reasoning if needed). During the annotation process, the annotator was unaware of the RC assigned by RRCP.

heading: Future Work
text: We partially mitigate this problem by working on the completeness constraints as specified in Section 4, but we consider this limitation as an open problem, planning to address it in future work. Reference-based approach: The core of our framework is based on a reference-based evaluation system. Although we can rely on high accuracy and human-like performance in terms of correctness evaluation, on the other hand, we are limited by the need for gold answers to get a good answerability prediction, limiting the scope of RRCP on labeled data. However, despite this limitation, we believe that larger reference-free approaches based on LLMs could soon replace the automatic evaluation component. Quality of the retrieval system: Our methodology accuracy scales with the quality and accuracy of the retrieval system. Thresholds: Determining Tans and Tcom is a trivial task that can be done with few examples. However, their values are critical to determine the RC with high accuracy. As mentioned in Section 5 and Section 7, we plan to address these limitations in future work