A DVERSARIAL R ETRIEVER - R ANKER FOR DENSE TEXT RETRIEVAL
Anonymous authors
Paper under double-blind review
A BSTRACT
Current dense text retrieval models face two typical challenges.
First, it adopts a siamese dual-encoder architecture to encode query and document independently for fast indexing and searching, whereas neglecting the ﬁner-grained term-wise interactions.
This results in a sub-optimal recall performance.
Second, it highly relies on a negative sampling technique to build up the negative documents in its contrastive loss.
To address these challenges, we present A dversarial R etrieverR anker (AR2), which consists of a dual-encoder retriever plus a cross-encoder ranker.
The two models are jointly optimized according to a minimax adversarial objective: the retriever learns to retrieve negative documents to cheat the ranker, while the ranker learns to rank a collection of candidates including both the ground-truth and the retrieved ones, as well as providing progressive direct feedback to the dual-encoder retriever.
Through this adversarial game, the retriever gradually produces harder negative documents to train a better ranker, whereas the cross-encoder ranker provides progressive feedback to improve retriever.
We evaluate AR2 on three benchmarks.
Experimental results show that AR2 consistently and signiﬁcantly outperforms existing dense retriever methods and achieves new state-of-the-art results on all of them.
This includes the improvements on
Natural Questions R@5 to 77 .
9% ( +2 .
1% ), TriviaQA R@5 to 78 .
2% ( +1 . 4% ), and MS-MARCO MRR@10 to 39 .
5% ( +1 . 3% ).
We will make our code, models, and data publicly available.
I NTRODUCTION
Dense text retrieval (Lee et al., 2019; Karpukhin et al., 2020) has achieved great successes in a wide variety of both research and industrial areas, such as search engine (Brickley et al., 2019;
Shen et al., 2014), recommendation system (Hu et al., 2020), open-domain question answering (Chen et al., 2017; Liu et al., 2020), etc.
A typical dense retrieval model adopts a dual-encoder (Huang et al., 2013) architecture to encode queries and documents into low-dimensional embedding vectors, and the relevance between query and document is measured by the similarity between embeddings.
In the real-world dense text retrieval applications, it pre-computes all the embedding vectors of documents in the corpus, and leverages the approximate nearest neighbor (ANN) (Johnson et al., 2019) technique for efﬁciency.
To train a dense retriever, contrastive loss with negative samples is widely applied in the literature (Xiong et al., 2021; Karpukhin et al., 2020).
During training, it utilizes a negative sampling method to obtain negative documents for a given query-document pair, and then minimizes the contrastive loss which relies on both the positive document and the sampled negative ones (Shen et al., 2014;
Chen et al., 2017; Radford et al., 2021).
Recent studies on contrastive learning (Xiong et al., 2021; Karpukhin et al., 2020) show that the iterative “hard-negative” sampling technique can signiﬁcantly improve the performance compared with “random-negative” sampling approach, as it can pick more representative negative samples to learn a more discriminative retriever.
In the work (Qu et al., 2021), it suggests to leverage crossencoder model to heuristically ﬁlter “hard-negative” samples to further improve performance and shows the importance of sampling technique in the contrastive learning.
On the other hand, the model architecture of dual-encoders enables the encoding of queries and documents independently which is essential for document indexing and fast retrieval.
However, this
… … … … query document relevance … … … …
query document relevance (a) Retriever … … … … query document relevance … query document relevance
[Figure]
Ranker ignores the modeling of ﬁner-grained interactions between query and document which could be a sub-optimal solution in terms of retrieval accuracy.
Motivated by these phenomenons, we propose an A dversarial R etriever-
R anker (AR2) framework.
The intuitive idea of AR2 is inspired by the “retriever-ranker” architecture in the classical information retrieval systems.
AR2 consists of two modules: a dual-encoder model served as the retrieval module in Figure 1a and a cross-encoder model served as the ranker module in Figure 1b.
The crossencoder model takes the concatenation of query and document as input text, and could generate more accurate relevance scores compared with the dual-encoder model, since it can fully explore the interactions between query and document through a self-attention mechanism using a conventional transformer model (Vaswani et al., 2017).
Instead of training “retriever-ranker” modules independently in some IR systems (Manning et al., 2008; Mitra & Craswell, 2017), AR2 constructs a uniﬁed minimax game for training the retriever and ranker models interactively, as shown in Figure 2. [Figure] e
[Figure]
Docs 𝑞 𝑑 𝔻 (cid:3044)(cid:2879)
In particular, AR2 adopts a minimax objective from the adversarial game (Goodfellow et al., 2014) where the retrieval model is optimized to produce relevant documents to fool the ranker model, whereas the ranker model learns to distinguish the ground-truth relevant document and retrieved ones by its opponent retrieval model.
Within the adversarial “retriever-ranker” training framework, the retrieval model receives the smooth training signals from the ranker model which helps alleviate the harmful effects of “false-negative” issues.
For example, a “false-negative” example which is rated as high-relevance by the ranker model, will also be granted with high probability by retrieval model in order to fool the ranker, meanwhile the ranker model with better generalization capability is more resistant to label noises compared with the retrieval model.
In the empirical studies of AR2, we further introduce a distillation regularization approach to help stabilize/improve the training of the retriever.
Intuitively, the retriever would be converged to a sharp conditionalprobabilities over documents given a query within the adversarial training framework, i.e., high retrieval probabilities for the top relevant documents and near-zero retrieval ones for the rest.
However, it is not a desirable property as it might impede exploring different documents during training.
Thus, we incorporate the distillation loss between the retriever and ranker models as a smooth term for further improvement.
In experiments, we evaluate AR2 on three widely-used benchmarks for dense text retrieval: Natural
Questions, Trivia QA and MS-MARCO.
Experimental results show that AR2 achieves state-of-theart performance on all these datasets.
Meanwhile, we provide a comprehensive ablation study to demonstrate the advantage of different AR2 components.
PRELIMINARIES
Dense Text Retrieval: we mainly consider a contrastive-learning paradigm for dense text retrieval in this work, where the training set consists of a collection of text pairs.
C =
{ ( q 1 , d 1 ) , ..., ( q n , d n ) } .
In the scenario of open-domain question answering, a text pair ( q, d ) refers to a question and a corresponding document which contains the answer.
A typical dense retrieval model adopts a dual encoder architecture, where questions and documents are represented as dense vectors separately and the relevance score s θ ( q, d ) between them is measured by the similarity between their embeddings:
[Equation]
where E ( · ; θ ) denotes the encoder module parameterized with θ , and (cid:104)·(cid:105) is the similarity function, e.g., inner-product, euclidean distance, etc.
Based on the embeddings, existing solutions generally leverage on-the-shelf fast ANN-search (Johnson et al., 2019) for efﬁciency.
A conventional contrastive-learning algorithm could be applied for training the dual encoders (Shen et al., 2014; Chen et al., 2017; Liu et al., 2020).
For example, given a training instance ( q, d ) , we select n negative irrelevant documents ( d − 1 , ..., d − n ) (denoted as D − q ) to optimize the loss function of the negative log likelihood of the positive document:
[Equation]
where τ is a hyper-parameter to control the temperature.
In the previous works (Shen et al., 2014;
Chen et al., 2017; Liu et al., 2020), it presents an effective strategy on negative document sampling, called “In-Batch Negatives” where negative documents are randomly sampled from a collection of documents which are within the same mini-batch as question-document training pairs.
Recently, some studies e.g., ANCE (Xiong et al., 2021), Condenser (Gao & Callan, 2021b) have shown that selecting “hard-negatives” in the training can signiﬁcantly improve the retrieval performance in open-domain question answering.
For example, instead of sampling negative document randomly, “hard-negatives” are iteratively sampled based on previous checkpoints of dual encoder model.
However, a more recent work RocketQA
(Qu et al., 2021) continues to point out that the retrieved “hard-negatives” could potential be “false-negatives” in some cases, which might limit the performance.
Generative Adversarial Network : GANs have been widely studied for generating the realisticlooking images in computation vision (Goodfellow et al., 2014; Brock et al., 2018).
In the past years, the idea of GANs has been applied in information retrieval (Wang et al., 2017).
For example,
IRGAN (Wang et al., 2017), proposes an minimax retrieval framework which constructs two types of IR models: a generative retrieval model and a discriminative retrieval model.
The two IR models are optimized through a minimax game: the generative retrieval model generates relevant documents that look like ground-truth relevant documents to fool the discriminative retrieval model, whereas the discriminative retrieval model learns to draw a clear distinction between the ground-truth relevant documents and the generated ones made by its opponent generative retrieval model.
The minimax objective is formulated as:
[Equation]
(3) where G θ ( ·| q ) and D φ ( d − , q ) denote the generative retrieval model and discriminative retrieval model in IRGAN, respectively.
It is worth noting the original IRGAN model doesn’t work for dense text retrieval tasks as it doesn’t contain the dual-encoder model for document indexing or fast retrieval.
M ETHOD
In this section, we introduce the proposed adversarial retriever-ranker ( AR2 ) approach.
It consists of two modules: the dual-encoder retriever module G θ as in Figure 1a, and the cross-encoder ranker module D φ as in Figure 1b.
G θ and D φ computes the relevance score between question and document as follows:
[Equation]
where E θ ( · ) and E φ ( · ) are language model encoders which can be initialized with any pre-trained language models, w φ is the linear projector in D φ and [ q, d ] is the concatenation of question and document.
In AR2 , the retriever and ranker modules are optimized jointly through a contrastive minimax objective:
[Equation]
where D − q : { d − i } ni =1 is the set of n negative documents sampled by G θ ( q, · ) given q , and p φ ( d | q ; D q ) denotes the probability of selecting the ground-truth document d from the document set D q ( D q = { d } ∪ D − q ) by the ranker module D φ :
[Equation]
According to the objective function (Eqn. 5), the dual-encoder retrieval model G θ ( q, · ) would try to sample the high-relevant documents to fool the ranker model, whereas the ranker model D φ ( q, · ) is optimized to draw distinction between ground truth passage and the ones sampled by G θ ( q, · ) .
We present the illustration of the AR2 framework in Figure 2.
In order to optimize the minimax objective function, we adopt a conventional iterative-learning mechanism to optimize the retriever and ranker modules coordinately.
3. T RAINING R ANKER D φ
Given the ﬁxed retriever G θ , the ranker model D φ is updated by maximizing the log likelihood of selecting ground-truth d from set D q given a query q :
[Equation]
where D q consists of ground-truth document d and negative document set D − q . D − q is sampled by G θ according to Eqn. 5.
In experiments, we ﬁrst retrieve top- 100 negative documents, and then randomly sample n examples from them to obtain D − q .
3. T RAINING R ETRIEVER G θ
With ﬁxing the ranker D φ , the model parameters θ ∗ for retriever G θ is optimized by minimizing the expectation of log likelihood of function.
In particular, by isolating θ from the minimax function (Eqn. 5), the objective for the retriever can be written as:
[Equation]
However, it is intractable to optimize θ directly through Eqn. 8, as the computation of probability D − q ∼ G θ ( q, · ) is not following a close form.
Thus, we seek to minimize an alternative upper-bound of the loss criteria:
[Equation]
The detailed deviation of Eqn. 9 is provided in the Appendix A.1.
Therefore, the gradient of parameter θ can be computed as the derivative of ˆ J θ with respect to θ :
[Equation]
Here, the same approach is applied to obtain set D − q as in Eqn. 7.
Regularization: we further introduce a distillation regularization term in G θ ’s training, which encourages the retriever model to distill from the ranker model.
[Equation]
H ( · ) is the cross entropy function.
p φ ( ·| q ; D ) and p θ ( [Equation] | q ; D ) denote the conditional probabilities of document in the whole corpus D by the ranker and the retriever model, respectively.
In practice, we also limit the sampling space over documents be a ﬁxed set, i.e., D q = { d } ∪ D − q .
Thus the regularization loss for the retriever model can be rewritten as:
[Equation]
3. I NDEX REFRESH
During each training iteration of retriever and ranker models in AR2, we refresh the document index to keep the retrieved document set updated.
To build the document index, we take the document encoder from the retrieval model to compute the embeddings E ( d ; θ ) for every document d from the corpus: d ∈ C , and then build the inner-product based ANN search index with FAISS tool (Johnson et al., 2019).
In summary, Algorithm 1 shows the full implementation details of the proposed AR2.
E XPERIMENTS 4. D ATASETS :
We conduct experiments on three popular benchmarks: Natural Questions (Kwiatkowski et al., 2019), Trivia QA (Joshi et al., 2017), and MS-MARCO Passage Ranking (Nguyen et al., 2016).
Their detailed statistics are presented in Table 1.
Train(Original) Train(Processed)
Dev
Test
Documents
Natural Questions 79, 58, 8, 3, 21,015,
Trivia QA 78, 60, 8, 11, 21,015,
MS-MARCO 502, 502, 6, 6, 8,841,
Natural Questions (NQ) collects real questions from Google search engine and each question is paired with an answer span and golden passages in Wikipedia pages.
In NQ, the goal of the retrieval stage is to ﬁnd positive passages from a large passage pool.
We report Recall of top- k
(R@k), which represents the proportion of top k retrieved passages that contain the answers.
Trivia QA is a reading comprehension corpus authored by trivia enthusiasts.
Each sample is a (cid:104) question, answer, evidence (cid:105) triple.
In the retrieval stage, the goal is to ﬁnd passages that contains the answer.
We also use Recall of top- k as the evaluation metric for Trivia QA.
MS-MARCO Passage Ranking is widely used in information retrieval.
It collects real questions from Bing search engine.
Each question is paired with several web documents.
Following previous works (Ren et al., 2021; Qu et al., 2021), we report MRR@10, R@50, R@1k on the dev set.
Mean
[Table]
Reciprocal Rank(MRR) is the mean of Reciprocal Rank(RR) across questions, calculated as the reciprocal of the rank where the ﬁrst relevant document was retrieved
[Table]
4. I MPLEMENTATION D ETAILS
First step
[Table]
we follow the experiments in (Sachan et al., 2021b; Gao & Callan, 2021a) to continuous pre-training the
Second step, we follow the experiment settings of DPR (Karpukhin et al., 2020) to train a warm-up dual-encoder retrieval model G 0 .
It is initialized with the continuous pretrained ERNIE-2.0-based model as we obtained in step one.
Then we train a warm-up cross-encoder model D 0 initialized with the ERNIE-2.0-Large.
D 0 learns to rank the Top-k documents selected by G 0 with contrastive learning.
The detailed hyper-parameters in training are listed in Appendix A.3.
Third step, we iteratively train the ranker (AR2- D ) model initialized with ERNIE-2.0-large and retriever (AR2- G ) initialized with G 0 according to Algorithm 1.
The number of training iterations is set to 10.
During each iteration of training, the retriever model is scheduled to train withmini-batches, while the ranker model is scheduled to train with 500 mini-batches.
The document index is refreshed after each iteration of training.
The other detailed hyper-parameters are shown in
Appendix A.3.
All the experiments in this work run on 8 NVIDIA Tesla A100 GPUs.
The implementation code of
AR2 is based on Huggingface Transformers (Wolf et al., 2020) with utilizing gradient checkpointing (Chen et al., 2016), Apex 1 , and gradient accumulation to reduce GPU memory consumption.
4. R ESULTS
Performance of Retriever AR2- G : The comparison of retrieval performance on NQ, Trivia QA, and MS-MARCO are presented in Table 2.
We compare AR2- G with previous state-of-the-art methods, including sparse and dense retrieval models.
The top block shows the performance of sparse retrieval methods.
BM25 (Yang et al., 2017)
[Table] [Table]
[Table] [Table]
is a traditional sparse retriever based on the exact term matching.
DeepCT (Dai & Callan, 2019) uses
BERT to dynamically generate lexical weights to augment BM25 Systems.
doc2Query
(Nogueira et al., 2019b), docTTTTTQuery (Nogueira et al., 2019a), and GAR (Mao et al., 2021a)
use text generation to expand queries or documents to make better use of BM25.
The middle block lists the results of strong dense retrieval methods, including DPR (Karpukhin et al., 2020), ANCE (Xiong et al., 2021), RDR (Yang & Seo, 2020), RocketQA (Qu et al., 2021), Joint and Individual Top-k (Sachan et al., 2021b), PAIR (Ren et al., 2021), DPR-PAQ (O ˘ guz et al., 2021), Condenser (Gao & Callan, 2021b).
coCondenser (Gao & Callan, 2021a), ME-BERT (Luan et al., 2021), CoIL (Gao et al., 2021).
These methods improve the performance of dense retrieval by constructing hard negative samples, jointly training the retriever and downstream tasks, pre-training, knowledge distillation, and muti-vector representations.
The bottom block in Table 2 shows the results of proposed AR2 models.
AR2- G 0 refers to the warm-up retrieval model in AR2 (details can be found in section 4.2) which leverages the existing continuous pre-training technique for dense text retrieval tasks.
i.e., It shows better performance compared with DPR (Karpukhin et al., 2020) and ANCE (Xiong et al., 2021), etc approaches that don’t adopt the continuous pre-training procedure.
We also observed that AR2- G : the retrieval model trained with the adversary framework, signiﬁcantly outperforms the warm-up AR2- Gmodel, and achieves new state-of-the-art performance on all three datasets.
4. A NALYSIS
In this section, we conduct a set of detailed experiments on analyzing the proposed AR2 training framework to help understand its pros and cons.
Performance of Ranker AR2- D : To evaluate the performance of ranker AR2- D on NQ, we ﬁrst retrieve top- 100 documents for each query in the test set with the help of dual-encoder AR2- G model, and then re-rank them with the scores produced by the AR2- D model.
The results are shown in Table 3.
“-” represents without ranker.
AR2- D 0 refers to the warm-up ranker model in AR2.
The results show that the ranker obtains better performance compared with only using retriever.
It suggests that we could use a two-stage ranking strategy to further boost the retrieval performance.
Comparing the results of AR2- D and AR2- D 0 .
We further ﬁnd that the ranker AR2- D gets a signiﬁcant gain with adversarial training.
Impact of Negative Sample Size: In the training of AR2, the number of negative documents n would affect the model performance and training time as well.
In Table 4, we show the performance and the training latency per batch with different negative sample size n .
In this setting, we evaluate AR2 without the regularization term.
We observe the improvement over R@1 and R@ by increasing n from 1 to 7 , and marginal improvement when keep increasing n from 7 to 15 .
The latency of training per batch is almost linear increased by improving n .
Comparison with IRGAN : The original IRGAN (Wang et al., 2017) doesn’t work for dense text retrieval task as it doesn’t contain the dual-encoder retrieval model for fast document indexing and
[Figure] [Figure]
Retriever
Ranker [Table]
[Table]
GAR
[Table]
(Mao
[Table]
, 2021a)
[Table]
GAR + (Mao et al., 2021a) [Table] GAR + (Mao et al., 2021a)
[Table]
GAR + (Mao et al., 2021a)
[Table]
search.
However, it provides an conventional GAN framework for training the generative and discriminative models jointly for IR tasks.
To compare the proposed AR2 with IRGAN, we replaced the generative and discriminative models in IRGAN with the retriever and ranker models in AR2, respectively.
Therefore, with the conﬁguration of the same model architectures for generator(retriever) and discriminator(ranker), The performance of the retriever is shown in Table 5.
We see that AR outperforms IRGAN signiﬁcantly.
Effect of Regularization : To study the effectiveness of regularization, we conducted ablation studies by removing the regularization term in the training of retrieval model.
In Table 6, “ R ” refers to the regularization item, it shows that the regularization approach help to improve the R@1 and R@ evaluation metrics.
In additional, we compute the average entropy of distribution p θ ( ·| q, d, D q ) on the NQ test set, here D q is the retrieved top- 15 documents.
The average entropy measures the sharpness of distribution p θ ( ·| q, d, D q ) .
In experiments, the average entropies for with R and w/o R in
AR2- G are 2 .
10 and 1 .
70 respectively.
It indicates that the regularization term could help smooth the prediction of probabilities in retriever.
Visualization of the Training Procedure: We visualize the changes of R@5 during the AR2- G training.
The result is shown in Figure 3.
We see that R@5 of both AR2-retriever and AR2-ranker gradually increases, as adversarial iteration increases.
AR2-retriever has the most signiﬁcant improvement after the ﬁrst iteration, about 4.5%.
While the training advance closer to the convergence, the improvement of R@5 also gradually slows down.
In the end, AR2-retriever is improved by approximately 8% and AR2-ranker is improved by approximately 3%.
Adversarial Training versus Iterative Hard-Negative Sampling :
To give a fair comparison of
AR2 and ANCE (Xiong et al., 2021), we retrain the ANCE model by initializing it with the same warm-up AR2- G 0 which leverages the advantage of continuous pre-training technique.
In experiments, ANCE trains the retriever with an iterative hard-negative sampling approach instead of adversarial training in AR2.
In Figure 4, we observe that AR2 steadily outperforms ANCE during training in terms of R@5 and R@10 evaluation metrics with the same model-initialization.
It shows that AR2 is a superior training framework compared with ANCE.
Performance of the Pipeline: We evaluate the performance of the retrieve-then-rank pipeline on
NQ dataset.
The results are shown in Table 7.
GAR + is a sparse retriever which ensembles
GAR (Mao et al., 2021a) and DPR (Karpukhin et al., 2020).
BERT (Nogueira & Cho, 2019),
BART (Nogueira et al., 2020), and RIDER (Mao et al., 2021b) are three ranking methods.
BERT ranker is a cross-encoder, which makes a binary relevance decision for each query-passage pair.
BART ranker generates relevance labels as target tokens in a seq2seq manner.
RIDER re-ranks the retrieved passages based on the lexical overlap with the top predicted answers from the reader.
The results show that AR2 pipeline signiﬁcantly outperforms existing public pipelines.
R ELATED WORK
Text Retrieval: Text retrieval aims to ﬁnd related documents from a large corpus given a query.
Retrieve-then-rank is the widely-used pipeline (Huang et al., 2020; Zou et al., 2021).
For the ﬁrst stage retrieval, early researchers use sparse vector space models, e.g. BM25 (Yang et al., 2017) as the retriever which are based on the exact term matching.
Recently, some works improve the traditional sparse retriever with neural network, e.g. Dai & Callan (2019) use BERT to dynamically generate term weights, doc2Query
(Nogueira et al., 2019b), docTTTTTQuery (Nogueira et al., 2019a), and GAR (Mao et al., 2021a) use text generation to expand queries or documents to make better use of BM25.
Recently, dense retrieval methods have become a new paradigm for the ﬁrst stage of retrieval.
Various methods have been proposed to enhance dense retrieval, e.g. DPR (Karpukhin et al., 2020) and ME-BERT (Luan et al., 2021) use in-batch negatives and contruct hard negatives by
BM25; ANCE (Xiong et al., 2021), UniK-QA (Oguz et al., 2021), RocketQA (Qu et al., 2021) and ADORE (Zhan et al., 2021) improve the hard negative sampling by iterative replacement, denoising, and dynamic sampling; PAIR (Ren et al., 2021) leverages passage-centric similarity relation into training object; FID-KD (Izacard & Grave, 2020) and RDR (Yang & Seo, 2020) distill knowledge from reader to retriever; Guu et al.
(2020) and Sachan et al.
(2021b) enhance retriever by jointly training with downstream tasks.
Some researches focus on the pre-training of dense retrieval, such as ICT (Lee et al., 2019), Condenser (Gao & Callan, 2021b) and coCondenser (Gao & Callan, 2021a).
For the second stage ranking, previous works typically use cross-encoder based methods.
The crossencoder models which capture the token-level interactions between the query and the document (Guo et al., 2016; Xiong et al., 2017), have shown to be more effective.
Various methods are proposed to enhance ranker, e.g. Nogueira & Cho (2019) use BERT to makes a binary relevance decision for each query-passage pair; Nogueira et al.
(2020) adopt BART to generate relevance labels as target tokens in a seq2seq manner; Khattab & Zaharia (2020) and Gao et al.
(2020) adopt the lightweight interaction based on the representations of dense retrievers to reduce computation.
However, negative samples are statically sampled in these works.
In AR2, negative samples for training the ranker will be dynamically adjusted with the progressive retriever.
Generative Adversarial Nets: Generative Adversarial Nets (Goodfellow et al., 2014) have been widely studied in the generation ﬁeld, i.e., image generation (Brock et al., 2018), text generation (Yu et al., 2017).
With a minimax game, GAN aims to train a generative model to ﬁt the real data distribution under the guidance of a discriminative model.
Few works study GAN to text retrieval.
A related work is IRGAN (Wang et al., 2017).
It proposes a minimax retrieval framework that aims to unify the generative and discriminative retrieval models.
C ONCLUSION
In this paper, we introduce AR2, an adversarial retriever-ranker framework to jointly train the endto-end retrieve-
then-rank pipeline.
In AR2, the retriever retrieves hard negatives to cheat the ranker, and the ranker learns to rank the collection of positives and hard negatives while provides progressive rewards to the retriever.
AR2 can iteratively improve the performance of both retriever and ranker because (1) the retriever is guided by the progressive ranker; (2) the ranker learns better through the harder negatives sampled by the progressive retriever.
AR2 achieves new state-of-the-art performance on all three competitive benchmarks.
A A PPENDIX A. P ROOF
Proof of Eqn.
9: Suppose d − i ∈ D − q is sampled by p θ ( ·| q ; D − q ) , thus
[Equation]
where D − q indicates the set of negative documents sampled by G θ ( q, · ) . In practice [Equation]
we approximate D − q by sampling n documents from the top- K retrieved negative set. Therefore
[Equation] we could further obtain the following approximately equation in implementation [Equation]
of Eqn. 10:
[Equation]
) (cid:3) (15)
A. E FFICIENCY R EPORT
We list the time cost of training and inference in Table 8.
The evaluation is made with 8 NVIDIA
A100 GPUs.
The max step of ANCE training is from the ANCE’s open-source website 2 .We estimate the overall training time without taking account of the time of continuous pre-training step and warming-up step.
[Table] [Table]
[Table] [Table]
[Table] [Table]
[Table] [Table]
[Table] [Table]
[Table]
We list the detailed conﬁguration of AR2 and baseline models in Table 10.
[Table]
Table 11 shows the results of our method with different initial models. We see that ERNIE-Base as the initial model achieves a little better performance than BERT-Base.
And AR2-G using BERTBase as the initial model still achieves better performance than other methods under the same initial model. Meanwhile, ICT pre-training improves the performance of AR2-G
[Table] [Table]
Xiong
[Table]
RocketQA (
[Table]
Table 12 shows the comparison of AR2 and several existing retrieval approaches. “Extra Label” refers to whether the answer label is used. AR2 jointly optimizes both the retriever and the ranker according to a principle adversarial objective, which is the key difference with previous works
[Table]
[Table]
A. P ERFORMANCE OF THE PIPELINE
Table 13 shows the performance of the retrieve-then-rank pipeline on Trivia QA and MS-MARCO. From the results of Table 7 and Table
[Table]
we ﬁnd that the ranker AR2-D improves the performance on all three benchmarks including NQ, Trivia QA, and MS-MARCO. Meanwhile, the pipeline based on AR2 achieves state-of-the-art performances on all benchmarks
[Table] [Table]