Generative Pre-trained Ranking Model with Over-parameterization at Web-Scale (Extended Abstract)^†^†thanks: This work was accepted by the Sister Conference Track of IJCAI 2024.

Yuchen Li^1,2 Haoyi Xiong² Linghe Kong¹ Jiang Bian² Shuaiqiang Wang²
Guihai Chen¹&Dawei Yin²
¹Shanghai Jiao Tong University, China ²Baidu Inc., China
{yuchenli, linghe.kong, gchen}@sjtu.edu.cn, [email protected],
{jiangbian03, shqiang.wang}@gmail.com, [email protected]

Abstract

Learning to rank (LTR) is widely employed in web searches to prioritize pertinent webpages from retrieved content based on input queries. However, traditional LTR models encounter two principal obstacles that lead to suboptimal performance: (1) the lack of well-annotated query-webpage pairs with ranking scores covering a diverse range of search query popularities, which hampers their ability to address queries across the popularity spectrum, and (2) inadequately trained models that fail to induce generalized representations for LTR, resulting in overfitting. To address these challenges, we propose a Generative Semi-Supervised Pre-trained (GS²P) LTR model. We conduct extensive offline experiments on both a publicly available dataset and a real-world dataset collected from a large-scale search engine. Furthermore, we deploy GS²P in a large-scale web search engine with realistic traffic, where we observe significant improvements in the real-world application.

1 Introduction

The booming increase of internet users and web content surges the demands on web search. In the current digital epoch, large-scale search engines manage an impressive archive of trillions of webpages, providing service to hundreds of millions of active users daily while handling billions of queries Xiong et al. (2024a); Liao et al. (2024); Chen et al. (2024h); Lyu et al. (2022a). The search procedure commences with a user query, often a text string, necessitating keyword or phrase extraction to comprehend user attempting Zhao et al. (2010); Li et al. (2023d); Chen et al. (2024c); Chen and Xiao (2024); Lyu et al. (2024b). Post identification of keywords, search engines evaluate the relation between the query and webpages, subsequently retrieving highly relevant ones from their vast databases Huang et al. (2021); Yu et al. (2018); Lyu et al. (2022b). These webpages are then sorted based on content attributes and click-through rates, positioning the most relevant ones on top of the result Li et al. (2023a); Xiong et al. (2024b); Chen et al. (2023e, 2024e, 2024f); Lyu et al. (2023).

The optimization of the user experience, achieved by catering to information needs, largely depends on the effective sorting of retrieved content. In this realm, Learning to Rank (LTR) becomes instrumental, requiring a considerable amount of query-webpage pairings with relevancy scores for effective supervised LTR Li et al. (2023b); Qin and Liu (2013); Li et al. (2023c); Lyu et al. (2020); Peng et al. (2024); Wang et al. (2024b). Nevertheless, the commonplace scarcity of well-described, query-webpage pairings often compels semi-supervised LTR, harnessing both labeled and unlabeled samples for the process Szummer and Yilmaz (2011); Zhang et al. (2016); Zhu et al. (2023); Peng et al. (2023). Recent years have seen the integration of deep models in LTR, aimed at end-to-end ranking loss minimization Li et al. (2020); Wang et al. (2021); Li et al. (2022); Yang and Ying (2023); Chen et al. (2024g, 2022b). However, these models occasionally falter in learning generalizable representations from structural data due to limited or noisy supervision, sometimes resulting in performance that is weaker compared to statistical learners Bruch et al. (2019); Lyu et al. (2024a); Wang et al. (2024a); Chen et al. (2023d). Further discussion on this subject can be found in a comprehensive review available in a recent scholarly work Werner (2022); Chen et al. (2023c, a, b, 2024d).

Refer to caption — Figure 1: The framework of GS²P.

In order to tackle the above issues, we propose a Generative Semi-Supervised Pre-trained LTR (GS²P) model. The proposed GS²P first generates high-quality pseudo labels for every unlabeled query-webpage pair through co-training of multiple/diverse LTR models based on various ranking losses, then learns generalizable representations with a self-attentive network using both generative loss and discriminative loss. Finally, given the generalizable representations of query-webpage pairs, by incorporating an MLP-based ranker with Random Fourier Features (RFF), GS²P pushes LTR models into so-called interpolating regime Belkin (2021); Song et al. (2023); Chen et al. (2022a, 2024a); Cai et al. (2023) and obtains superb performance improvement. To demonstrate the effectiveness of GS²P, we conduct comprehensive experiments on a publicly available LTR dataset Qin and Liu (2013); Chen et al. (2024b) and a real-world dataset collected from a large-scale search engine. We also deploy GS²P at the search engine and evaluate the proposed model using online A/B tests in comparison with the online legacy system.

2 Methodology

2.1 Preliminaries

Given a set of search queries $\mathcal{Q}=\{q_{1},~{}q_{2},$ $\dots\}$ and all archived webpages $\mathcal{W}=\{w_{1},w_{2},\dots\}$ , for each query $q_{i}\in\mathcal{Q}$ , the search engine retrieves a set of relevant webpages denoted as $W_{i}=\{w^{i}_{1},w^{i}_{2},\dots\}\subset\mathcal{W}$ . After annotating, each query $q_{i}$ is assigned with a set of relevance scores $\bm{y}_{i}=\{y^{i}_{1},y^{i}_{2},\dots\}$ . In this work, we follow the settings in Qin and Liu (2013); Li et al. (2023e) and scale the relevance score from 0 to 4 to represent levels of relevance, which represents whether the webpage w.r.t. the query is bad (0), fair (1), good (2), excellent (3) or perfect (4). We denote a set of query-webpage pairs with relevance score annotations as $\mathcal{T}^{L}=\{(q_{1},W_{1},\bm{y}_{1}),~{}(q_{2},W_{2},\bm{y}_{2}),\dots\}$ . The core problem of semi-supervised LTR is to leverage unlabeled pairs, i.e., $\mathcal{T}^{U}=\{(q^{\prime}_{1},W^{\prime}_{1}),~{}(q^{\prime}_{2},W^{\prime}_{2}),\dots\}\subset\mathcal{Q}$ and $|\mathcal{T}^{U}|\gg|\mathcal{T}^{L}|$ , in the training process.

2.2 Semi-supervised Pseudo-Label Generation

Given the overall set of queries $\mathcal{Q}$ and the set of all webpages $\mathcal{W}$ , GS²P first obtains every possible query-webpage pair from both datasets, denoted as $(q_{i},w_{i}^{j})$ for $\forall q_{i}\in\mathcal{Q}$ and $\forall w_{i}^{j}\in W_{i}\subset\mathcal{W}$ , i.e., the $j^{th}$ webpage retrieved for the $i^{th}$ query. For each query-webpage pair $(q_{i},w_{i}^{j})$ , GS²P further extracts an $m$ -dimensional feature vector $\bm{x}_{i,j}$ representing the features of the $j^{th}$ webpage under the $i^{th}$ query. Then, the labeled and unlabeled sets of feature vectors can be presented as $\mathcal{D}^{L}=\{(\bm{x}_{i,j},\bm{y}^{i}_{j})|\forall(q_{i},W_{i},\bm{y})\in\mathcal{T}^{L}~{}\text{and}~{}\forall w_{j}^{i}\in W_{i}\}$ and $\mathcal{D}^{U}=\{\bm{x}_{i,j}|\forall(q_{i},W_{i})\in\mathcal{T}^{U}\}$ . Inspired by Li et al. (2023e), GS²P leverages a semi-supervised learning LTR manner to generate high-quality pseudo labels for unlabeled samples.

2.3 Self-attentive Representation Learning via Denoising Autoencoding

Denoised Self-attentive Autoencoder. Given an $m$ -dimensional feature vector $\tilde{\bm{x}}_{i,j}$ of a query-webpage pair $(\tilde{\bm{x}}_{i,j},\bm{y}^{i}_{j})$ in combined data, GS²P aims to utilize a self-attentive encoder to learn a generalizable representation $\bm{z}_{i,j}$ . Specifically, given a vector $\tilde{\bm{x}}_{i,j}$ generated from Semi-supervised Pseudo-Label Generation, GS²P (1) passes it through a fully-connected layer and produces a hidden representation. Then, GS²P (2) feeds the hidden representation into a self-attentive autoencoder, which consists of $B$ encoder blocks of Transformer Vaswani et al. (2017). In particular, each encoder block incorporates a multi-head attention layer and a feed-forward layer, both followed by layer normalization. Eventually, GS²P (3) generates the learned representation $\bm{z}_{i,j}$ from the last encoder block. For each original feature vector $\tilde{\bm{x}}_{i,j}$ , the whole training process can be formulated as $\bm{z}_{i,j}=f_{\tilde{\theta}}(\tilde{\bm{x}}_{i,j})$ , where $\tilde{\theta}$ is the set of parameters of the self-attentive encoder.

Given the learned representation $\bm{z}_{i,j}$ , GS²P leverages an MLP-based decoder for the reconstruction task. Specifically, for each representation $\bm{z}_{i,j}$ produced from the self-attentive autoencoder, GS²P uses the MLP-based decoder to map $\bm{z}_{i,j}$ to a generalizable representation $\bm{z}^{{\prime}}_{i,j}$ , which has the same dimension with the original feature vector. The whole training process can be formulated as $\bm{z}^{{\prime}}_{i,j}=g_{\theta^{\prime}}(\bm{z}_{i,j})$ , where the $\theta^{\prime}$ is the set of parameters of the MLP-based decoder. Finally, GS²P jointly optimizes the parameter sets $\tilde{\theta}$ and $\theta^{\prime}$ to minimize the generative loss as $\mathcal{L}_{\text{G}}=\frac{1}{|\mathcal{Q}|}\frac{1}{|W_{i}|}\sum_{i=1}^{|\mathcal{Q}|}\sum_{j=1}^{|W_{i}|}\ell_{\text{G}}\left(\tilde{\bm{x}}_{i,j},\bm{z}^{{\prime}}_{i,j}\right)$ , where $\ell_{\text{G}}$ is the squared error, which could be presented as $\ell_{\text{G}}\left(\tilde{\bm{x}}_{i,j},\bm{z}^{{\prime}}_{i,j}\right)=\|\tilde{\bm{x}}_{i,j}-\bm{z}^{{\prime}}_{i,j}\|^{2}$ .

Pre-trained Ranker. Given the learned vector $\bm{z}_{i,j}$ generated from Denoised Self-attentive Autoencoder, GS²P leverages a fully-connected layer to obtain predicted scores $\bm{r}_{i,j}$ as $\bm{r}_{i,j}=k_{\theta}(\bm{z}_{i,j})$ , where $\theta$ is the set of discriminative parameters of Pre-trained Ranker. Against the ground truth, GS²P utilizes the discriminative loss function $\mathcal{L}_{\text{D}}$ to compute the loss of ranking prediction as $\mathcal{L}_{\text{D}}=\frac{1}{|\mathcal{Q}|}\frac{1}{|W_{i}|}\sum_{i=1}^{|\mathcal{Q}|}\sum_{j=1}^{|W_{i}|}\ell_{\text{D}}\left(\bm{y}^{i}_{j},\bm{r}_{i,j}\right)$ , where $\ell_{\text{D}}$ is denoted as the standard LTR loss function. Then, GS²P jointly optimizes the discriminative loss $\mathcal{L}_{\text{D}}$ and the generative loss $\mathcal{L}_{\text{G}}$ to accomplish both discriminative (LTR) and generative (denoising autoencoding for reconstruction) tasks simultaneously as $\mathcal{L}_{\text{Final}}=\alpha\mathcal{L}_{\text{D}}+\beta\mathcal{L}_{\text{G}}$ , where $\alpha,\beta\in[0,1]$ are weight coefficients to balance two terms.

Methods	5%		10%		15%		20%
Methods	$@{4}$	$@{10}$	$@{4}$	$@{10}$	$@{4}$	$@{10}$	$@{4}$	$@{10}$
XGBoost	31.76	34.10	36.72	39.12	39.93	41.01	42.60	45.84
LightGBM	35.72	39.32	39.89	42.05	43.90	45.67	46.56	48.52
RMSE	34.82	38.02	38.75	41.95	42.97	45.65	45.75	48.86
RankNet	34.06	37.43	38.12	41.32	42.24	45.08	45.01	47.89
LambdaRank	35.28	38.50	39.32	42.47	43.40	46.23	46.26	49.56
ListNet	34.36	37.94	38.31	41.76	42.51	45.40	45.32	48.42
ListMLE	33.47	36.95	37.52	40.84	41.53	44.43	44.39	47.26
ApproxNDCG	33.98	37.20	37.94	41.01	42.09	44.70	44.94	47.50
NeuralNDCG	35.15	38.26	39.07	42.10	43.32	45.97	46.08	49.20
$\rm{CR_{RMSE}}$	36.04	38.54	39.52	42.48	43.67	46.25	46.86	49.75
$\rm{CR_{RankNet}}$	35.90	38.42	39.44	42.37	43.45	45.98	46.70	49.61
$\rm{CR_{LambdaRank}}$	36.45	38.93	40.03	43.10	44.36	46.88	47.57	50.47
$\rm{CR_{ListNet}}$	37.53	40.08	41.28	44.21	45.17	47.73	48.35	51.24
$\rm{CR_{ListMLE}}$	35.67	38.16	39.40	42.35	43.28	45.86	46.62	49.48
$\rm{CR_{ApproxNDCG}}$	37.93	40.41	41.47	44.32	45.53	48.03	48.81	51.69
$\rm{CR_{NeuralNDCG}}$	37.26	40.65	40.76	43.69	44.85	47.52	48.16	51.13
GS²P_RMSE	39.02	40.88	41.80	44.72	45.72	48.22	48.72	51.40
GS²P_RankNet	38.15	40.42	40.03	44.21	44.93	47.85	47.85	50.98
GS²P_LambdaRank	39.47	41.43	42.17	45.20	46.07	48.89	49.15	51.97
GS²P_ListNet	39.53	41.62	42.28	45.42	46.15	49.16	49.18	52.20
GS²P_ListMLE	37.66	39.87	39.80	43.70	44.52	47.28	47.41	50.24
GS²P_ApproxNDCG	39.57	41.76	42.39	45.65	46.31	49.31	49.25	52.25
GS²P_NeuralNDCG	39.72	41.97	42.56	45.83	46.38	49.53	49.36	52.47

Table 1: Results for Web30K on NDCG across diverse labeled data percentages.

2.4 LTR via Over-parameterized MLP

Given the learned representation $\bm{z}_{i,j}\in\mathcal{R}^{n}$ generated from Self-attentive Representation Learning via Denoising Autoencoding, GS²P converts this representation vector into an $N$ -dimensional version, represented as $\bm{h}_{i,j}=\mathbf{h}(\bm{z}_{i,j})$ . This step is implemented using the feature transformation $\mathbf{h}(z)$ . In this procedure, GS²P utilizes a transformation rooted in random Fourier features to execute $\mathbf{h}(z)$ Rahimi and Recht (2007), thereby mapping the original features of LTR into a higher dimensional feature space. An important point to consider is that increasing the number of dimensions ( $N$ ) leads to over-parameterization of the LTR model via the addition of more input features. This scenario brings about a feature-wise ’double descent’ phenomenon in predicting generalization errors Belkin et al. (2019); Belkin (2021). GS²P sets the optimal value for $N$ , stemming from cross-validation performed on the labeled dataset to ensure the best generalization performance. Therefore, incorporating $\bm{h}_{i,j}$ for every pair of query-webpage paves the path for an over-parameterized LTR model. This advanced model operates in the interpolating regime and is projected to exhibit excellent generalization performance Belkin (2021). In this way, GS²P transforms $\bm{z}_{i,j}$ into a high-dimensional vector $\bm{h}_{i,j}$ and constructs a Ranker (i.e., MLP-based LTR model) for the LTR task with several popular ranking loss functions.

3 Experiments

3.1 Experimental Setup

Datasets. We carry out the offline experiments on a standard and publicly available dataset Web30K Qin and Liu (2013) and a real-world dataset commerical dataset collected from Baidu search engine. Specifically, the commercial Dataset contains 50,000 queries. The dataset is annotated by a group of professionals on the crowdsourcing platform, who assign a score between 0 and 4 to each query-document pair.

Metrics. To assess the performance of various ranking systems comprehensively, we leverage the following metrics. Normalized Discounted Cumulative Gain (NDCG) Järvelin and Kekäläinen (2017) is a standard listwise accuracy metric, which has been commonly used in research and industrial community. For our online evaluation, we utilize the Good vs. Same vs. Bad ( $\mathrm{GSB}$ ) Zhao et al. (2011), which is an online pairwise-based evaluation methodology evaluated by annotators. Considering the confidentiality of commercial information, we only report the difference between the results of GS²P and the online legacy system.

Methods	5%		10%		15%		20%
Methods	$@{4}$	$@{10}$	$@{4}$	$@{10}$	$@{4}$	$@{10}$	$@{4}$	$@{10}$
XGBoost	48.39	52.12	52.83	56.45	56.14	60.03	58.03	62.61
LightGBM	50.48	53.50	54.13	59.04	57.00	62.14	60.47	65.82
RMSE	49.73	53.42	54.13	57.86	57.43	61.34	59.42	64.76
RankNet	49.32	53.07	53.76	57.37	57.08	60.92	59.17	64.25
LambdaRank	50.82	54.24	55.07	58.62	58.16	62.05	61.12	65.28
ListNet	50.26	53.61	54.52	58.04	57.81	61.47	59.74	64.82
ListMLE	48.73	52.46	53.08	56.70	56.32	60.25	58.42	63.68
ApproxNDCG	49.08	52.75	53.44	57.02	56.79	60.61	58.84	64.01
NeuralNDCG	50.68	53.89	54.88	58.31	58.02	61.82	61.03	64.97
$\rm{CR_{RMSE}}$	50.43	53.63	54.52	58.70	56.90	61.74	60.42	65.22
$\rm{CR_{RankNet}}$	50.86	54.06	54.98	58.26	57.32	61.82	60.83	65.61
$\rm{CR_{LambdaRank}}$	52.47	55.67	56.13	59.84	58.90	63.79	61.87	66.59
$\rm{CR_{ListNet}}$	52.45	55.64	56.08	59.82	58.74	63.24	62.28	67.09
$\rm{CR_{ListMLE}}$	51.05	54.30	54.76	58.46	57.53	62.01	61.04	65.83
$\rm{CR_{ApproxNDCG}}$	51.92	55.08	55.68	59.40	58.42	62.87	62.00	66.75
$\rm{CR_{NeuralNDCG}}$	52.06	55.31	55.87	59.61	58.67	63.20	62.18	66.84
GS²P_RMSE	52.72	55.48	55.89	59.60	58.82	63.13	61.92	66.24
GS²P_RankNet	53.13	55.93	56.20	59.92	58.94	63.41	62.28	66.67
GS²P_LambdaRank	53.67	56.72	56.90	60.76	59.58	64.19	62.95	67.65
GS²P_ListNet	54.00	57.18	57.28	61.04	59.93	64.50	63.38	67.96
GS²P_ListMLE	53.41	56.24	56.51	56.51	59.20	63.72	62.50	66.88
GS²P_ApproxNDCG	54.23	57.32	57.44	61.12	60.12	64.62	63.58	68.05
GS²P_NeuralNDCG	54.36	57.43	57.62	61.25	60.28	64.76	63.72	68.12

Table 2: Results for Commercial Dataset on NDCG across diverse labeled data percentages.

	GS²P_ApproxNDCG		GS²P_NeuralNDCG
	Random	Long-Tail	Random	Long-Tail
$\Delta GSB$	+3.00%	+4.00%	+5.50%	+6.50%

Table 3: Performance improvements of GS²P with ApproxNDCG loss and GS²P with NeuralNDCG loss for the online evaluation.

Loss Functions and Competitor Systems In this work, we leverage the following advanced ranking loss functions to evaluate the proposed model comprehensively, such as RMSE, RankNet Burges et al. (2005), LambdaRank Burges et al. (2006), ListNet Cao et al. (2007), ListMLE Xia et al. (2008), ApproxNDCG Qin et al. (2010), and NeuralNDCG Pobrotyn and Białobrzeski (2021).

As for the ranking model, we choose the following state-of-the-art ranking models as the competitor for GS²P, such as MLP, Context-aware Ranker (CR) Pobrotyn et al. (2020), XGBoost Chen and Guestrin (2016) and LightGBM Ke et al. (2017).

3.2 Offline Experimental Results

Overall Results. Table 1 and 2 present the average results for offline evaluation, where GS²P is compared with competitors on Web30K and the commercial dataset. Intuitively, we could observe GS²P outperforms all competitors with different losses under various ratios of labeled data on two datasets. More specifically, GS²P with NeuralNDCG gets 3.60% and nearly 3.57% higher NDCG $@4$ and NDCG $@10$ on Web30K dataset, compared with the pointwise-based self-trained MLP model with NeuralNDCG. On Commercial Dataset, GS²P on average obtains nearly 2.84% and 3.14% improvement on NDCG $@4$ and NDCG $@10$ , when compared with NeuralNDCG. GS²P+NeuralNDCG could gain the most improvement under the less ratio of labeled data on both metrics on two datasets, which demonstrates the effectiveness of GS²P under low-resource situations.

3.3 Online Evaluation

To comprehensively evaluate our proposed model, we conduct a manual comparison experiment. Intuitively, manual comparison results are presented in Table 3. In particular, we observe that our proposed model outperforms the online legacy system by a large margin for random and long-tail (i.e., the search frequency of the query is lower than 10 per week) queries. Specifically, GS²P with NeuralNDCG loss achieves the largest improvement compared with the legacy system with 5.50% and 6.50% for random and long-tail queries, respectively. Moreover, GS²P with ApproxNDCG loss also improves the performance for random and long-tail queries. Figure 2 illustrates the relative performance between GS²P and the base model, expressed via $\Delta NCDG@4$ . Logically, GS²P shows marked enhancement in performance across all days when compared to the base system, evidencing its practical capability in upgrading the efficacy of a large-scale search engine. Even more impressively, GS²P has shown substantial growth on this large-scale platform. A prominent highlight is GS²P outperforming the online base model by a significant margin of 0.61% relative improvement on $\Delta NCDG@4$ , a feat achieved by the NeuralNDCG loss-trained model using a nominal 5% labeled data ratio. GS²P has showcased consistent performance across both online and offline platforms.

4 Related Works

To enhance the user experience in search results, ranking the retrieved content is a crucial step in which the LTR model plays a significant role. Based on the loss function, LTR models can be categorized into three families: pointwise, pairwise Burges et al. (2005, 2006), and listwise Cao et al. (2007); Qin et al. (2010). For the pointwise loss, the LTR problem is formulated as a regression task Zhou (2024b). The pairwise approach converts the problem into binary classification by considering document pairs. Besides, the listwise approach treats the entire document list as a single sample and directly optimizes the evaluation metrics Zhou et al. (2024); Wang et al. (2023c, a).

The core principle of data reconstruction involves learning the joint probability distribution of samples from the training data. Variational autoencoder architectures Kingma and Welling (2014); Tran et al. (2017); Liang et al. (2024) have been utilized for data reconstruction in prior studies Liu et al. (2024); Lu et al. (2024). For instance, Tran et al. (2017) employed a cascaded residual autoencoder inspired by the denoised autoencoder Vincent et al. (2010); Zhou (2024c); Weng and Wu (2024a) to estimate residuals and reconstruct corrupted multimodal data sequences.

The issue of balancing under-parameterization and over-parameterization has received increasing attention from researchers Belkin et al. (2019); Zhou (2024a); Chen et al. (2022c); Xin et al. (2024); Wang et al. (2024c). To address LTR tasks, Szummer and Yilmaz (2011); Jin et al. (2024c, b, a) proposes a parameter learning-based approach, which has shown that over-parameterization can achieve superior performance on test data under certain conditions in the ”interpolation regime” with the double descent curve Shangguan et al. (2021); Zheng et al. (2021); Liang et al. (2021). Random Fourier Feature Rahimi and Recht (2007); Jin et al. (2023); Ding et al. (2024); Ni et al. (2024); Weng and Wu (2024b, b); Chen et al. (2023f) method utilizes a kernel technique to generate features for most inner product-based models, which has demonstrated significant improvements Jiang et al. (2024); Xie et al. (2024); Fu et al. (2024); Wang et al. (2023b).

5 Conclusion

In this work, we design, implement and deploy a generative semi-supervised pre-trained model GS²P on a real-world large-scale search engine to address the problems of LTR under semi-supervised settings. We substantiate the effectiveness of GS²P through comprehensive offline and online analyses, juxtaposed against an extensive lineup of rivals. The offline trials denote a considerable leap in GS²P’s performance relative to other baselines. Furthermore, GS²P significantly enhances the online ranking efficacy in practical applications, mirroring the positive outcomes observed in the offline experiments.

Acknowledgments

This work was initially presented at the 10th IEEE International Conference on Data Science and Advanced Analytics (DSAA) in 2023 and Machine Learning (MLJ) in 2024 Li et al. (2024).

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Generative Pre-trained Ranking Model with Over-parameterization at Web-Scale (Extended Abstract)††thanks: This work was accepted by the Sister Conference Track of IJCAI 2024.