summaries: Many Information Retrieval systems rely on two components: a retriever that identifies a small set of "support" documents from a large corpus, followed by a reader that re-scores these support documents more finely. For retrievers, metrics like BM25 were once common but they are increasingly replaced by machine learned components. However, most datasets do not provide direct supervision information for the retriever. The paper targets an important problem in open-domain QA - the training of the retriever for the purpose of determining a segment that may contain the answer. In the most traditional setting, the retriever is just a traditional IR system such as BM25. In some existing work, the retriever has been trained to locate the documents containing the answer (e.g. inverse cloze task, or DPR). This paper goes in the same direction. The difference is that it uses the attention weights as relevance signals to train the retriever, instead of the inclusion of the answer in the passage. The authors propose a training technique for information retrieval models in the context of (open domain) question answering. Assuming the existence of some reader model, the idea is to use internal information of that model as a training signal for a retriever. Specifically, they use the attention activations over the input documents as synthetic labels for the retriever.
abstractText: The task of information retrieval is an important component of many natural language processing systems, such as open domain question answering. While traditional methods were based on hand-crafted features, continuous representations based on neural networks recently obtained competitive results. A challenge of using such methods is to obtain supervised data to train the retriever model, corresponding to pairs of query and support documents. In this paper, we propose a technique to learn retriever models for downstream tasks, inspired by knowledge distillation, and which does not require annotated pairs of query and documents. Our approach leverages attention scores of a reader model, used to solve the task based on retrieved documents, to obtain synthetic labels for the retriever. We evaluate our method on question answering, obtaining state-of-the-art results.
authors.name: QUESTION ANSWERING
authors.name: Gautier Izacard
authors.name: Edouard Grave
references.authors: Wei-Cheng Chang Felix X Yu Yin-Wen Chang Yiming Yang Sanjiv Kumar
references.title: Pre-training tasks for embedding-based large-scale retrieval
references.venue: arXiv preprint arXiv:2002.03932,
references.authors: Danqi Chen Adam Fisch Jason Weston Antoine Bordes
references.title: Reading Wikipedia to answer opendomain questions
references.venue: In Proc. ACL,
references.authors: Scott Deerwester Susan T Dumais George W Furnas Thomas K Landauer Richard Harshman
references.title: Indexing by latent semantic analysis
references.venue: Journal of the American society for information science,
references.authors: Mostafa Dehghani Hamed Zamani Aliaksei Severyn Jaap Kamps W. Bruce Croft
references.title: Neural ranking models with weak supervision
references.venue: In Proceedings of the 40th International ACM SIGIR Conference on Research and Development in Information Retrieval,
references.authors: Jacob Devlin Ming-Wei Chang Kenton Lee Kristina Toutanova
references.title: BERT: Pre-training of deep bidirectional transformers for language understanding
references.venue: In Proc. NAACL,
references.authors: Daniel Gillick Alessandro Presta Gaurav Singh Tomar
references.title: End-to-end retrieval in continuous space
references.venue: arXiv preprint arXiv:1811.08008,
references.authors: Kelvin Guu Kenton Lee Zora Tung Panupong Pasupat Ming-Wei Chang
references.title: Realm: Retrievalaugmented language model pre-training
references.venue: arXiv preprint arXiv:2002.08909,
references.authors: Geoffrey Hinton Oriol Vinyals Jeff Dean
references.title: Distilling the knowledge in a neural network
references.authors: Po-Sen Huang Xiaodong He Jianfeng Gao Li Deng Alex Acero Larry Heck
references.title: Learning deep structured semantic models for web search using clickthrough data
references.venue: In Proceedings of the 22nd ACM international conference on Information & Knowledge Management,
references.authors: Samuel Humeau Kurt Shuster Marie-Anne Lachaux Jason Weston
references.title: Poly-encoders: Transformer architectures and pre-training strategies for fast and accurate multi-sentence scoring
references.authors: Gautier Izacard Edouard Grave
references.title: Leveraging passage retrieval with generative models for open domain question answering
references.venue: arXiv preprint arXiv:2007.01282,
references.authors: Jeff Johnson Matthijs Douze Hervé Jégou
references.title: Billion-scale similarity search with gpus
references.venue: IEEE Transactions on Big Data,
references.authors: Karen Sparck Jones
references.title: A statistical interpretation of term specificity and its application in retrieval
references.venue: Journal of documentation,
references.authors: Mandar Joshi Eunsol Choi Daniel S. Weld Luke Zettlemoyer
references.title: Triviaqa: A large scale distantly supervised challenge dataset for reading comprehension
references.venue: In Proc. ACL,
references.authors: Vladimir Karpukhin Barlas Oğuz Sewon Min Ledell Wu Sergey Edunov Danqi Chen Wen-tau Yih
references.title: Dense passage retrieval for open-domain question answering
references.venue: arXiv preprint arXiv:2004.04906,
references.authors: Omar Khattab Christopher Potts Matei Zaharia
references.title: Relevance-guided supervision for openqa with colbert
references.authors: Diederik P Kingma Jimmy Ba
references.title: Adam: A method for stochastic optimization
references.venue: arXiv preprint arXiv:1412.6980,
references.authors: Tomáš Kočiskỳ Jonathan Schwarz Phil Blunsom Chris Dyer Karl Moritz Hermann Gábor Melis Edward Grefenstette
references.title: The NarrativeQA reading comprehension challenge
references.authors: Tom Kwiatkowski Jennimaria Palomaki Olivia Redfield Michael Collins Ankur Parikh Chris Alberti Danielle Epstein Illia Polosukhin Matthew Kelcey Jacob Devlin Kenton Lee Kristina N. Toutanova Llion Jones Ming-Wei Chang Andrew Dai Jakob Uszkoreit Quoc Le Slav Petrov
references.title: Natural Questions: a benchmark for question answering research
references.venue: TACL,
references.authors: Kenton Lee Ming-Wei Chang Kristina Toutanova
references.title: Latent retrieval for weakly supervised open domain question answering
references.venue: In Proc. ACL,
references.authors: Mike Lewis Yinhan Liu Naman Goyal Marjan Ghazvininejad Abdelrahman Mohamed Omer Levy Ves Stoyanov Luke Zettlemoyer
references.title: BART: Denoising sequence-to-sequence pretraining for natural language generation, translation, and comprehension
references.authors: Mike Lewis Marjan Ghazvininejad Gargi Ghosh Armen Aghajanyan Sida Wang Luke Zettlemoyer
references.title: Pre-training via paraphrasing
references.venue: arXiv preprint arXiv:2006.15020,
references.authors: Patrick Lewis Ethan Perez Aleksandara Piktus Fabio Petroni Vladimir Karpukhin Naman Goyal Heinrich Küttler Mike Lewis Wen-tau Yih Tim Rocktäschel
references.title: Retrieval-augmented generation for knowledge-intensive nlp tasks
references.venue: arXiv preprint arXiv:2005.11401,
references.authors: Ilya Loshchilov Frank Hutter
references.title: Decoupled weight decay regularization
references.venue: In International Conference on Learning Representations,
references.authors: Yi Luan Jacob Eisenstein Kristina Toutanova Michael Collins
references.title: Sparse, dense, and attentional representations for text retrieval
references.venue: arXiv preprint arXiv:2005.00181,
references.authors: Christopher D Manning Hinrich Schütze Prabhakar Raghavan
references.title: Introduction to information retrieval
references.venue: Cambridge university press,
references.authors: Rodrigo Nogueira Kyunghyun Cho
references.title: Passage re-ranking with bert
references.venue: arXiv preprint arXiv:1901.04085,
references.authors: Hamid Palangi Li Deng Yelong Shen Jianfeng Gao Xiaodong He Jianshu Chen Xinying Song Rabab Ward
references.title: Deep sentence embedding using long short-term memory networks: Analysis and application to information retrieval
references.venue: IEEE/ACM Transactions on Audio, Speech, and Language Processing,
references.authors: Colin Raffel Noam Shazeer Adam Roberts Katherine Lee Sharan Narang Michael Matena Yanqi Zhou Wei Li Peter J Liu
references.title: Exploring the limits of transfer learning with a unified text-to-text transformer
references.venue: arXiv preprint arXiv:1910.10683,
references.authors: Pranav Rajpurkar Jian Zhang Konstantin Lopyrev Percy Liang
references.title: SQuAD: 100,000+ questions for machine comprehension of text
references.venue: In Proc. EMNLP,
references.authors: Stephen E Robertson Steve Walker Susan Jones Micheline M Hancock-Beaulieu Mike Gatford
references.title: Okapi at TREC-3
references.venue: NIST Special Publication Sp,
references.authors: Yelong Shen Xiaodong He Jianfeng Gao Li Deng Grégoire Mesnil
references.title: Learning semantic representations using convolutional neural networks for web search
references.venue: In Proceedings of the 23rd international conference on world wide web,
references.authors: James Thorne Andreas Vlachos Christos Christodoulopoulos Arpit Mittal
references.title: Fever: a large-scale dataset for fact extraction and verification
references.venue: arXiv preprint arXiv:1803.05355,
references.authors: Ashish Vaswani Noam Shazeer Niki Parmar Jakob Uszkoreit Llion Jones Aidan N Gomez Ł ukasz Kaiser Illia Polosukhin
references.title: Attention is all you need
references.venue: In Advances in Neural Information Processing Systems
references.authors: Ellen M Voorhees
references.title: The TREC-8 question answering track report
references.venue: In TREC,
references.authors: Sohee Yang Minjoon Seo
references.title: Is retriever merely an approximator of reader
references.venue: arXiv preprint arXiv:2010.10999,
references.authors: Wei Yang Yuqing Xie Aileen Lin Xingyu Li Luchen Tan Kun Xiong Ming Li Jimmy Lin
references.title: End-to-end open-domain question answering with BERTserini
references.venue: In Proc. NAACL (Demonstrations),
sections.heading: 1 INTRODUCTION
sections.text: Information retrieval is an important component for many natural language processing tasks, such as question answering (Voorhees et al., 1999) or fact checking (Thorne et al., 2018). For example, many real world question answering systems start by retrieving a set of support documents from a large source of knowledge such as Wikipedia. Then, a finer-grained model processes these documents to extract the answer. Traditionally, information retrieval systems were based on hand-crafted sparse representations of text documents, such as TF-IDF or BM25 (Jones, 1972; Robertson et al., 1995). Recently, methods based on dense vectors and machine learning have shown promising results (Karpukhin et al., 2020; Khattab et al., 2020). Deep neural networks based on pre-training, such as BERT (Devlin et al., 2019), have been used to encode documents into fixed-size representations. These representations are then queried using approximate nearest neighbors (Johnson et al., 2019). These techniques have lead to improved performance on various question answering tasks.
  A challenge of applying machine learning to information retrieval is to obtain training data for the retriever. To train such models, one needs pairs of queries and the corresponding list of documents that contains the information corresponding to the queries. Unfortunately, hand-labeling data to that end is time consuming, and many datasets and applications lack such annotations. An alternative approach is to resort to heuristics, or weakly supervised learning, for example by considering that all documents containing the answer are positive examples. However, these approaches suffer from the following limitations. First, frequent answers or entities might lead to false positive examples. As an example, consider the question “where was Ada Lovelace born?”. The sentence “Ada Lovelace died in 1852 in London” would be considered as a positive example, because it contains the answer “London”. A second limitation is that for some tasks, such as fact checking or long form question answering, such heuristics might not be applicable directly.
  In this paper, we propose a procedure to learn retriever systems without strong supervision in the form of pairs of queries and documents. Following previous work (Chen et al., 2017), our approach uses two models: the first one retrieves documents from a large source of knowledge (the retriever), the second one processes the support documents to solve the task (the reader). Our method is inspired by knowledge distillation (Hinton et al., 2015), and uses the reader model to obtain synthetic labels to train the retriever model. More precisely, we use a sequence-to-sequence model as the reader, and use the attention activations over the input documents as synthetic labels to train the retriever. Said otherwise, we assume that attention activations are a good proxy for the relevance of
  documents. We then train the retriever to reproduce the ranking of documents corresponding to that metric.
  We make the following contributions:
  • First, we show that attention scores from a sequence-to-sequence reader model are a good measure of document relevance (Sec. 3.2) ;
  • Second, inspired by knowledge distillation, we propose to iteratively train the retriever from these activations, and compare different loss functions (Sec. 3.4) ;
  • Finally, we evaluate our method on three question-answering benchmarks, obtaining stateof-the-art results (Sec. 4).
  Our code is available at: github.com/facebookresearch/FiD.
sections.heading: 2 RELATED WORK
sections.text: We briefly review information retrieval based on machine learning. We refer the reader to Manning et al. (2008) and Mitra et al. (2018) for a more exhaustive introduction to the subject.
  Vector space models. In traditional information retrieval systems, documents and queries are represented as sparse vectors, each dimension corresponding to a different term. Different schemes have been considered to weigh the different term, the most well known being based on inverse document frequency, or term specificity (Jones, 1972). This technique was later extended, leading to the BM25 weighting scheme which is still widely used today (Robertson et al., 1995). A limitation of sparse representations is that the terms of the query need to match the terms of the returned documents. To overcome this, Deerwester et al. (1990) proposed to use latent semantic analysis for indexing, leading to low-dimension dense representations of documents.
  Neural information retrieval. Following the success of deep learning for other natural processing tasks, neural networks were applied to the task of information retrieval. Huang et al. (2013) proposed a deep bag-of-words model, where queries and documents were embedded independently, a technique known as bi-encoder. Documents were then ranked by using the cosine similarity with the query, and the model was trained on clickthrough data from a search engine. This technique was later extended by using convolutional neural networks (Shen et al., 2014) and recurrent neural networks (Palangi et al., 2016). A limitation of independently embedding documents and query is that it does not capture fine-grained interactions between the query and documents. This lead Nogueira & Cho (2019) and Yang et al. (2019) to use a BERT model to jointly embed documents and query, a technique known as cross-encoder.
  End-to-end retrieval. Most of the methods described in the previous paragraph were used to rerank a small number of documents, usually returned by a traditional IR systems. In the context of ad-hoc document retrieval, Gillick et al. (2018) showed that bi-encoder models could be competitive with traditional IR systems. For open domain question-answering, Karpukhin et al. (2020) introduced dense passage retrieval (DPR), which uses dense embeddings and nearest neighbors search. More precisely, question and passage embeddings are obtained using a BERT-based biencoder model, which is trained on a small dataset of question and passage pairs. Then, the full knowledge source (Wikipedia) is encoded using this model, and passages are queried by computing the k-nearest neighbors of the embedding of the question. Jointly embedding the query and documents makes the application of cross-encoder models intractable to large database. To address this limitation, Humeau et al. (2019) introduced the poly-encoder architecture, in which each documents is represented by multiple vectors instead of one. Similarly, Khattab et al. (2020) proposed a scoring function where each term of the query and documents is represented by a single vector. To make the method tractable, their system retrieves documents with an approximate score, which are then re-ranked with the exact one. Finally, Luan et al. (2020) conducts a theoretical and empirical study of sparse, dense and cross-attention information retrieval systems.
  Unsupervised learning. Closest to our work, there is growing body of work trying to learn information retrieval systems from unsupervised data. Lee et al. (2019) introduced the inverse cloze task
  for pre-training retrievers, which can then be fine-tuned end-to-end on question-answering tasks. This pre-training scheme was later evaluated for ad-hoc document retrieval by Chang et al. (2020). Guu et al. (2020) proposed to augment language model pre-training with a retriever module, which is trained using the masked language modeling objective. Similarly, Lewis et al. (2020a) introduced a sequence-to-sequence model that is pre-trained by generating a target text, after retrieving a set of related texts. Lewis et al. (2020b) further train the retriever obtained in Karpukhin et al. (2020) by backpropagating to the retriever the error between the generated output and the gold answer.
  Simultaneously to our work, Yang & Seo (2020) proposes to train a retriever with knowledge distillation. The main difference with our method is the nature of the synthetic labels that are used to train the retriever. Yang & Seo (2020) uses the DPR reader, which includes a classifier that predicts which passage contains the answer, and can be seen as a cross-encoder reranker. This technique thus performs the distillation of a cross-encoder retriever to a bi-encoder retriever. In contrast, our method uses the internal attention scores of the reader, which does not require additional supervision besides pairs of question and answer.
sections.heading: 3 METHODOLOGY
sections.text: Our system is composed of two modules, the retriever and the reader, following the standard pipeline for open-domain question answering. Given an input question these modules are used in a two-step process to generate an answer. First the retriever selects support passages in a large knowledge source. Then these passages are processed by the reader, along with the question, to generate an answer. For the reader module we use the Fusion-in-Decoder model (Izacard & Grave, 2020), which achieves state-of-the-art performance when combined with BM25 or DPR (Karpukhin et al., 2020). It is based on a sequence-to-sequence architecture, and is initialized from pre-trained models such as T5 or BART (Raffel et al., 2019; Lewis et al., 2019).
  The focus of this work is to train the retriever without strong supervision or weakly supervised learning based on heuristics. For this we propose to train the retriever by learning to approximate the attention score of the reader. The training scheme outlined here can be seen as a student-teacher pipeline, where the teacher, the reader module, produces targets which are used to train a student network, the reader. By doing so, we hope to leverage the signal extracted from the question-answer pairs by the reader. Since the goal of the retriever is to retrieve the most relevant passages, by training the retriever to estimate the reader attention scores, we implicitly make the assumption that these scores are a good proxy for the usefulness of a passage to answer the question.
  In this section we will first describe the Fusion-in-Decoder architecture, before elaborating on the signal which is used to train the retriever, the design of the retriever, and how this module is trained.
sections.heading: 3.1 CROSS-ATTENTION MECHANISM
sections.text: First, let us briefly review the Fusion-in-Decoder model (FiD, Izacard & Grave, 2020). The underlying architecture is a sequence-to-sequence model, composed of an encoder and a decoder. The encoder independently processes np different text inputs (sk)1≤k≤np . In the case of open-domain question answering based on Wikipedia, each input sk is the concatenation of the question q and a support passage, with special tokens question:, title: and context: added before the question, the title of the Wikipedia article and the text of each passage. The output representations of the encoder are then concatenated to form a global representation X of dimension ( ∑ k `k) × d, where `k is the length of the k-th segment and d is the dimension of the embeddings and hidden representations of the model. Then, the decoder processes this representation as a regular autoregressive model, alternating self-attention, cross-attention and feed-forward modules.
  Only the cross-attention module explicitly takes as input the global output representation X of the encoder. If H ∈ Rd denotes the output of the previous self-attention layer of the decoder, the crossattention operation consists in the following operations. First, queries Q, keys K and values V are computed by applying linear transformations:
  Q = WQH, K = WKX, V = WVX.
  Then a similarity score between the query at position i, Qi, and the key at position j, Kj , is obtained by computing the dot-product between these two elements, and normalized over the dimension:
  αi,j = Q T i Kj , α̃i,j = exp(αi,j)∑ m exp(αi,m) .
  A new representation is obtained as a sum of the values, weighted by the attention probabilities, before going through a final linear transformation Wo:
  Oi = WO ∑ j α̃i,jVi,j
  The operations described above are performed in parallel with different linear transformations in the case of multi-head attention. Finally a normalization layer is applied, and this pipeline is wrapped by a skip connection. See Vaswani et al. (2017) for more details on the structure of Transformers.
sections.heading: 3.2 CROSS-ATTENTION SCORE AS A RELEVANCE MEASURE FOR PASSAGE RETRIEVAL
sections.text: In some sense, the attention scores α:,j involving the j-th key measures the importance of this key, and corresponding value, to compute the next representation. We hypothesize that it is good proxy to estimate the relevance of a passage — the more the tokens in a text segment are attended to, the more relevant the text segment is to answer the question.
  Given the reader model, an input question q and a corresponding set of support passages Dq = (pk)1≤k≤n, we obtain relevance scores (Gq,pk)1≤k≤n for each passage by aggregating attention scores. In particular, the score Gq,pk is obtained by averaging the pre-attention scores α0,: over all the tokens in the input sk corresponding to the passage pk, all the layers and all the heads of the decoder. Note that the FiD decoder jointly processes the passages, and thus the score Gq,pk depends on the other support passages. We consider other pooling operators, such as max, to aggregate attention scores over layers, heads and tokens and empirically compare them in Sec. 5.2.
  Before we proceed, let us consider the following simple experiment, which is a first indication that reader attention scores are indeed a strong relevance signal. Given a question and 100 passages retrieved with DPR, our goal is to select the 10 best passages. When using the top 10 passages from DPR instead of the top 100, the performance of our reader drops from 48.2 EM to 42.9 EM. On the other hand, if we select the top 10 documents according to the attention scores, the performance only drops to 46.8 EM.
sections.heading: 3.3 DENSE BI-ENCODER FOR PASSAGE RETRIEVAL
sections.text: Ideally, we would like to rank passages according to the reader cross-attention scores. In practice however, since the passages and the question need to be processed simultaneously by the reader module it is impractical to query a large knowledge source this way. Thus, we use a retriever model composed of an embedder functionE that maps any text passage to a d-dimensional vector, such that the similarity score between a question q and a passage p is defined as Sθ(q, p) = E(q)TE(p). This similarity metric enables us to index all passages in the knowledge source as a preprocessing step. Then at runtime, passages with the highest similarity score with the input question are retrieved, by using an efficient similarity search library such as FAISS (Johnson et al., 2019).
  For the embedder we use BERT and follow DPR by considering that the encodings E(q) and E(p) are obtained by extracting the representation of the initial [CLS] token. This leads to a representation of dimension d = 768 in the case of a base model. Differently from DPR, we use the same encoding function E for the questions and passages by sharing parameters.
sections.heading: 3.4 DISTILLING THE CROSS-ATTENTION SCORE TO A BI-ENCODER
sections.text: In this section, we describe how to train the retriever model, based on the relevance scores obtained in Sec. 3.2. For the training objective of the retriever, we propose to minimize the KL-divergence between the output Sθ(q, p) and the score Gq,p after normalization:
  LKL(θ,Q) = ∑
  q∈Q,p∈Dq
  G̃q,p(log G̃q,p − log S̃θ(q, p)),
  where
  G̃q,p = exp(Gq,p)∑
  p′∈Dq exp(Gq,p′) , S̃θ(q, p) = exp(Sθ(q, p))∑ p′∈Dq exp(Sθ(q, p ′)) .
  In Sec. 5.1 we present results obtained when using alternatives to this training objective. We consider two other objectives which have been used in Dehghani et al. (2017), where BM25 is used as a teacher model to train a neural ranker. A first option consists in training the retriever with a regression approach by minimizing the mean squared error:
  LMSE(θ,Q) = ∑
  q∈Q,p∈Dq
  (Sθ(q, p)−Gq,p)2.
  The second option we consider is to use a max-margin loss that explicitly penalizes inversions in the ranking estimated by the retriever:
  Lranking(θ,Q) = ∑
  q∈Q,p1,p2∈Dq
  max (0, γ − sign(Gq,p1 −Gq,p2)(Sθ(q, p1)− Sθ(q, p2))) .
  In words, if p1 is more relevant to answer the question q than p2 , i.e. Gq,p1 > Gq,p2 , the loss pushes the retriever score of p1 to be larger than the score of p2 by at least a margin of γ.
sections.heading: 3.5 ITERATIVE TRAINING
sections.text: In this section, we explain how iterative training can be used with the student-teacher scheme described in the previous section, similarly to Khattab et al. (2020). This iterative procedure can be interpreted as using the current retriever to sample negative examples, in order to train a new retriever. When learning a retriever with discriminative training, negative samples play an important role, and various strategies have been considered in previous work. Karpukhin et al. (2020) compared random sampling with using the top-k passages from BM25 which do not contain the answer and with using the positive passages from other queries. Consider that for each question, we have an initial set of support documents D0q . We propose to use an iterative pipeline where each iteration can be described as the following 4-step process:
  1. Train the reader R using the set of support documents for each question D0q . 2. Compute aggregated attention scores (Gq,p)q∈Q,p∈D0q with the reader R.
  3. Train the retriever E using the scores (Gq,p)q∈Q,p∈D0q .
  4. Retrieve top-passages with the new trained retriever E.
  This multi-step procedure can be repeated multiple times. A critical point of the training procedure is the initial set of documents corresponding to each question. In Sec. 4, we compare retrievers obtained by starting from documents obtained using BM25 or cosine similarity from a BERT model. In particular, we show that while the initial performance with BERT is low, the iterative procedure allows to greatly improve the performance of the model.
sections.heading: 4 EXPERIMENTS
sections.text: In this section we evaluate the student-teacher training procedure from the previous section. We show that we obtain competitive performance without strong supervision for support documents.
sections.heading: 4.1 EXPERIMENTAL SETTING
sections.text: Datasets. We perform experiments on TriviaQA (Joshi et al., 2017) and NaturalQuestions (Kwiatkowski et al., 2019), two standard benchmarks for open-domain question answering. TriviaQA is made of questions from trivia and quiz league websites, and does not contain gold support documents. NaturalQuestions contains questions corresponding to web search queries, and gold support documents from Wikipedia. Following the setting from Lee et al. (2019); Karpukhin
  et al. (2020), we use the original evaluation set as test set, and keep 10% of the training data for validation. We use the Wikipedia dump from Dec. 20, 2018 for support documents, splitting articles into non-overlapping passages of 100 tokens, and applying the same preprocessing as Chen et al. (2017).
  We also evaluate on NarrativeQuestions (Kočiskỳ et al., 2018), using a publicly available preprocessed version.1 This is a reading comprehension dataset built on a corpus of books and movie scripts. For each story, questions are generated by human annotators based on a summary of the given document. We consider the full story setting, where the task is to answer questions given the entire story and not the summary used to generate question-answer pairs. Here the knowledge source is not the same for all questions: given a question the retrieval operation is performed on all passages of the associated story. These passages are obtained by dividing the story in chunks of 100 words. These stories are long documents, with an average of 60k words. While part of the documents could be processed entirely by the Fusion-in-Decoder module, it is interesting to limit the number of support passages to reduce the computational cost of the reading step.
  While answers in TriviaQA and NaturalQuestions are short, NarrativeQA answers are about five words long on average, with medium length answers such as ”He dismantles it and attaches it to his mother’s jeep” which answers the question ”What does Mark do with his radio station?”. Notably a significant number of answers do not correspond to spans in the story. It is thus not straightforward to train the retriever with heuristics using question-answer pairs. In our case we use the same pipeline as for TriviaQA and NaturalQuestions, demonstrating the flexibility of our approach.
  Evaluation. The model performance is assessed in two ways. First, following previous work such as DPR and ColbertQA, we report the top-k retrieval accuracy (P@k), which is the percentage of questions for which at least one passage of the top-k retrieved passages contains the gold answer. It is unclear how well this metric evaluates the retriever performance, since the answer can be contained in a passage without being related to the question. This is notably true for common words or entities.
  We also report the final end-to-end performance of the question answering system composed of the retriever and reader modules. This is the metric we are fundamentally interested in. For TriviaQA and NaturalQuestions, predicted answers are evaluated with the standard exact match metric (EM), as introduced by Rajpurkar et al. (2016). For NarrativeQA we report the metrics proposed in the original paper: ROUGE-L, BLEU-1, BLEU-4 and METEOR.
sections.heading: 4.2 TECHNICAL DETAILS
sections.text: Initialization. Similarly to DPR, we initialize the retriever with the BERT base model, pretrained with uncased text. The Fusion-in-Decoder reader is initialized with the T5 base model. A critical component of the iterative training procedure is the initialization of the support passages D0q asso-
  1https://cs.nyu.edu/˜kcho/NarrativeQA
  ciated with each question q. For this we consider different options. The first one is to use passages retrieved using BM25. We use the implementation from Apache Lucene2 with default parameters, and tokenize questions and passages with SpaCy3. We also use passages obtained with BERT as a retriever without fine-tuning, this leads to poor initial performance. Finally in Table 2 we show that initializing D0q with passages obtained with DPR (Karpukhin et al., 2020) outperforms the two previous initializations. We train all retrievers using 100 passages. For the reader, we use 100 passages for NaturalQuestions and TriviaQA and 20 passages for NarrativeQA.
  Iterative training. We apply the iterative training procedure on each dataset independently. Both the reader and the retriever are fine-tuned using the ADAM algorithm (Kingma & Ba, 2014), with a batch of size 64. The reader is trained for 10k gradient steps with a constant learning rate of 10−4, and the best model is selected based on the validation performance. The retriever is trained with a constant learning rate of 5 ·10−5 until the performance saturates. To monitor the performance of the retriever during training, we measure the similarity between the reader and the retriever rankings. At each new training iteration the reader is reinitialized from T5 base, while we pursue the training of the retriever. We found that restarting from T5 base is important for the first iterations when starting with BERT documents. We have not tried to reinitialize the retriever between each iteration. More details on the hyperparameters and the training procedure are reported in Appendix A.2.
sections.heading: 4.3 RESULTS
sections.text: In Table 1, we report the performance of our approach for different number of self-training iterations. Generally, we observe that the accuracy of our system increases with the number of iterations, obtaining strong performance after a few iterations. Interestingly, while the initial performance with documents retrieved with BERT is very poor, our method still reach competitive scores on TriviaQA, and to a lesser extent, NaturalQuestions. However, a second observation is that the quality of the initial document sets plays an important role on the performance of the end system. Indeed, we observe that starting the procedure from BM25 documents, which are higher quality as indicated by the performance of the system at iteration 0, leads to stronger results than using BERT documents. An interesting research question would be to explore pre-training of the initial BERT model for retrieval, for example by using the inverse cloze task.
  In Table 2, we report the performance of our approach, as well as existing state-of-the-art systems on TriviaQA and NaturalQuestions. In addition to initializing our method with documents retrieved with BM25 and BERT, we also train a system by starting from DPR documents. First, we observe that our method improve the performance over the state-of-the-art, even when starting from BM25 documents. This validates our assumption that it is possible to obtain strong retrievers without the need of supervision for the documents. Second, when starting from DPR passages, our method leads to a +4.5 EM improvement on TriviaQA and +2.3 EM improvement on NaturalQuestions when the final evaluation is carried out with a large reader.
  2lucene.apache.org 3spacy.io
  In Table 3, we report the performance of our method on the NarrativeQA dataset. We use the setting where the knowledge source corresponds to the whole document, and in particular, we do not use the summary. We compare our results to the best ones reported in the original paper for this setting. Similar to results obtained on NaturalQuestions and TriviaQA, we observe that training the retriever by using the attention scores of the reader leads to improvements, compared to the BM25 baseline.
sections.heading: 5 ABLATIONS
sections.text: In this section, we investigate design choices regarding two key elements of our approach: the training objective and the aggregation of cross-attention scores. For all experiments, we consider a simplified experimental setting: a single training iteration is performed on NaturalQuestions, starting from BM25 passages.
sections.heading: 5.1 TRAINING OBJECTIVES
sections.text: In Table 4 we report the performance of our model trained with the different training objectives described in Sec. 3.3. We observe that using the KL-divergence between the aggregated scores of the reader and the scores of the retriever outperforms the other objective functions.
sections.heading: 5.2 HOW TO AGGREGATE CROSS-ATTENTION SCORES?
sections.text: In Section 4 the cross-attention scores α are aggregated in a specific way, in order to obtain a single scalar used to train the retriever. Formally let us denote by αi,j,k,h the cross-attention scores between token i of the output and token j of the input, for the k-th layer and h-th head. Then, the scores Gq,p for p ∈ Dq used in Section 4 are computed as follows:
  Gq,p = mean j,k,h α0,j,k,h,
  where j describes the input tokens corresponding to p. In Table 5 we explore alternatives to this choice by considering different aggregation schemes. In particular, we consider (1) taking the max over the input tokens corresponding to passage p instead of the average, (2) taking the average over the output tokens instead of taking the score of the first token, (3) taking the mean over the last six layers instead of all the layers, (4) taking the max over the layers instead of the average, (5) taking the max over the heads instead of the average. We observe that the performance of our approach is relatively stable to the choice of aggregation, and that the best result is obtained by averaging, except over the output tokens where it is best to only consider the first token.
sections.heading: 6 CONCLUSION
sections.text: In this paper, we introduce a method to train an information retrieval module for downstream tasks, without using pairs of queries and documents as annotations. Our approach is inspired by knowledge distillation, where the retriever module corresponds to the student model and the reader module corresponds to the teacher model. In particular, we use the cross-attention scores, from a sequenceto-sequence reader, to obtain synthetic targets for the retriever. We compare different ways to aggregate the scores, as well as different training objectives to learn the retriever. We show that iteratively training the reader and the retriever leads to better performance, and obtain state-of-the-art performance on competitive question answering benchmarks. In the future, we would like to explore better pre-training strategies for the retriever module, as well as better scoring functions for the retriever.
sections.heading: A EXPERIMENTAL DETAILS
sections.text: A.1 SETTING
  For NaturalQuestions and TriviaQA we follow the standard open-domain question answering setting used in Lee et al. (2019); Karpukhin et al. (2020). In this setting the original development set is used as test set, and 10% of the training set is used for development purpose. Moreover, for NaturalQuestions, all questions with answers longer than five tokens are discarded.
  For TriviaQA we use the unique human-generated answer to train the reader. In this dataset part of the answers are in uppercase. We normalize uppercase answers by converting the first letter in each word to uppercase and remaining characters to lowercase using the title Python string method.
  For NarrativeQA, questions and answers in uppercase are converted to lowercase.
  A.2 TRAINING
  For every datasets, both the reader and the retriever are fine-tuned with a dropout rate of 10%. All models at the exception of the large reader are trained using the ADAM algorithm (Kingma & Ba, 2014) with a constant learning rate of 10−4 for the base reader and 5 · 10−5 for the retriever. The base reader is trained for 10k gradient steps with a batch size of 64. We train the large reader with the ADAMW algorithm (Loshchilov & Hutter, 2019) with a peak learning rate of 5 · 10−5 and a linear warmup for 600 gradient steps followed by a linear decrease of the learning rate for 14.4k gradient steps.
  We perform model selection on the validation performance. The retriever is trained until its performance saturates with a batch size of 64. To monitor the performance of the retriever during training, we measure the similarity between the ranking obtained with the reader score, and the ranking of the retriever. We use different metrics for this: the number of inversions between the two rankings, the proportion of passages in the retriever top-k that are also in the reader top-k and the number of passages to obtain all top-k passage of the reader.
  During training and at test time, each text input of the encoder is restricted to be at most 250 token long. For NaturalQuestions and TriviaQA, we use wikipedia as a knowledge source, thus for each passage there is an associated article title. Each input is composed of the concatenation of a question, title and support passage with special tokens question:, title: and context: added before the question, the title and the text of each passage. In the case of NarrativeQA, the question and each passage are concatenated to form the different inputs.
  A.3 INFERENCE
  At test time, for TriviaQA and NaturalQuestions we use greedy decoding, and Beam Search with 3 beams for NarrativeQA.