HPSERec: A Hierarchical Partitioning and Stepwise Enhancement Framework for Long-tailed Sequential Recommendation
Authors: Xiaolong Xu
Xudong Zhao
Haolong Xiang
Xuyun Zhang
Wei Shen
Hongsheng Hu
Lianyong Qi
Venue: NeurIPS 2025 poster ()
Keywords: Sequential Recommendation; Long-tail Problem; Transfer Learning
Primary area: deep_learning

Abstract: The long-tail problem in sequential recommender systems stems from imbalanced interaction data, resulting in suboptimal model performance for tail users and items. Recent studies have leveraged head data to enhance tail data for diminish the impact of the long-tail problem. However, these methods often adopt ad-hoc strategies to distinguish between head and tail data, which fails to capture the underlying distributional characteristics and structural properties of each category. Moreover, due to a substantial representational gap exists between head and tail data, head-to-tail enhancement strategies are susceptible to negative transfer, often leading to a decline in overall model performance. To address these issues, we propose a hierarchical partitioning and stepwise enhancement framework, called HPSERec, for long-tailed sequential recommendation. HPSERec partitions the item set into subsets based on a data imbalance metric, assigning an expert network to each subset to capture user-specific local features. Subsequently, we apply knowledge distillation to progressively improve long-tail interest representation, followed by a Sinkhorn optimal transport-based feedback module, which aligns user representations across expert levels through a globally optimal and softly matched mapping. Extensive experiments on three real-world datasets demonstrate that HPSERec consistently outperforms all baseline methods. The implementation code is available at https://anonymous.4open.science/r/HPSERec-2404.

HPSERec: A Hierarchical Partitioning and Stepwise Enhancement Framework for Long-tailed Sequential Recommendation
Xiaolong Xu', Xudong Zhao', Haolong X :uyun Zhang?, Wei Shen Hongsheng Hu', Lianyong Qi
Schooo of Software, Nanjing University of Information Science and Technology. China SScooo of computing. Macquarie University, Australia Independent Researcher, China
"School of Information and Physical Sciences, University of Newcastle, Australia College of Computer Science and Technology, China University of Petroleum (East China), China
Abstract
The long-tail problem in sequential recommender systems stems from imbalanced interaction data, resulting in suboptimal model performance for tail users and items. Recent studies have leveraged head data enhance tail data for diminish the impact of the long-tail problem. However, these methods often adopt ad-hoc strategies distinguish between head and tail data, which fails capture the underlying distributional characteristics and structural properties of each category. Moreover, due a substantial representational gap exists between head and tail data, head-to-tail enhancement strategies are susceptible to negative transfer, often leading to a decline in overall model performance. To address these issues, we propose a hierarchical partitioning and stepwise enhancement framework, called HPSERee, for long-tailed sequential recommendation. HPSERec partitions the item set into subsets based on data imbalance metric, assigning expert network to each subset capture user-specific local features. Subsequently, we apply knowledge distillation to progressively improve long-tail interest representation, followed by a Sinkhorn optimal transport-based feedback module, which aligns user representations across expert levels through globally optimal and softly matched mapping. Extensive experiments on three real-world datasets demonstrate that HPSERec consistently outperforms all baseline methods. The implementation 23/HPSE.ec..
code is available at
Introduction
Recommender systems have been widely adopted across various online platforms to suggest items that users likely to engage with. Despite their remarkable success in numerous applications, the loig-tail problem associated with both users and items remains a significant challenge, hindering the further development of recommender systems. On the user side, small number of head users dominate interactions, far surpassing the engagement levels of the majority of tail users (I). As head users, which ultimately reduces the platform's
result, models tend to focus disproportionately ability to retain new users. On the item side, most user interactions are concentrated on limited number of popular items (2), leaving the majority of less popular items with minimal engagement. This concentration on popular items narrows the diversity of recommendations and fosters the emergence of filter bubbles
CCorresponding author. Email: hixiang @ nuist.edu.cn
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Head Ite
Talliion
Tell foo
Tree Hovd itom
# of Consumption
# of Consumption
200
16
(00)
200-
76
200
192
100
Sorted item index
Sorted item index
(a) Yelp
(b) MovieLens-200
Figure 1: The number of consumed items on Yelp and MovieLens-20M
Recent studies focused on addressing the long-tail problem in sequential recommender systems (SRS). Several approaches address the long-tail problem from the user perspective, tackling the challenge of tail users by employing adversarial training to map head and tail users into shared latent space, or by extending the interaction sequences of tail users ()) Other methods focus on the item perspective, aiming to enhance the representation of tail items through attention mechanisms or
by assigning higher weights to tail items during training 7α, In addition, certain works incorporate large language models (LL.s) to capture user sequence features and rich semantic information, enhancing the performance of long-tail data (9) 10
12).
Most existing methods follow standard pipeline comprising data preprocessing, model training, and evaluation deal with the long-tail problem, while those methods share common limitations.
During data preprocessing, most existing studies adopt a fixed-ratio approach to distinguish between head and tail data. For example, define the top 20% of items with the highest number of interactions as head items, and the remaining 80% as tail items. However, this ratio is largely based empirical assumptions and may not generalize well across different application scenarios. As illustrated in Figure ((a) and Figure T(b), the item interaction distribution in the Moviel
Arbitrary Partitioning:
dataset exhibits much stronger long-tail effect compared the Amazon Yelp dataset. This variability suggests that fixed-ratio partitioning schemes may not generalize well across datasets, potentially leading suboptimal modeling and recommendation performance.
Flawed Head-Tail Augmentation: During model training, a common approach to mitigate the long-tai tail problem is to augment tail data using the rich information available in head data. For instance, information from head users is often transferred to tail users through shared or similar interaction sequences. However, due to the significant disparity in information density between head and tail entities, the presence superficially similar patterns does not necessarily imply representational similarity. As result, such augmentation may introduce noise rather than useful signal, ultimately degrading model performance.
To address the above problems, propose Hierarchical Partitioning and Stepwise Enhancement Framework for Long-tailed Sequential Recommendation (HPSERec), which leverages imbalance- aware partitioning, expert-based modeling, and distribution-levè alignment to achieve balanced and effective recommendation. Our method comprises three modules: the distribution balance module, the feedforward module, and the feedback module. The distribution balance module addresses the problem of Arbitrary Partitioning by introducing a novel imbalance metric and a corresponding partitioning algorithm to ensure more balanced data subsets. The feedforward module tackles Flawed Head-Tail Augmentation by assigning expert networks to each subset and using progressive knowledge distillation to share tail item knowledge across the dataset. The feedback module further addresses this issue by refining upstream experts through soft distribution--lvel alignment using optimal transport, enabling adaptive updates without strict one-to-one matching.
Through this approach, HPSERee achieves more accurate recommendations for tail items without compromising recommendation performance for head items.
Contributions. The contributions this study are summarized as follows:
We define a metric to quantify data imbalance and design algorithm to partition the item set based on this metric. The algorithm ensures that each subset minimizes data imbalance while maintaining sufficient total number of interactions to preserve data utility.

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Distribution
Peodforward
Erbokling
Dabodinn lays
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03
Cousling
Citt
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Feedback Madale
Ranking
Dala Preprocesing
Model Training
Evalustion
Figure 2: The overall architecture of HPSERec. Distribution balancing module splits the item set into subsets to reduce long-tail effects and improve training. Feedforward module boosts long-tail item representations with contrastive learning and refines global expert performance via knowledge distillation. Feedback module transfers head item information to long-tail experts using an annealing algorithm, expanding their receptive field.
We propose a novel framework, called the Hierarchical Partitioning and Stepwise Enhancement Framework for Long- tailed Sequential Recommendation (HPSERec), which aims to address the long-tail problem SRS.
We the first address the long-tail problem in the recommendation domain by segmenting items and users into multiple subsets based on their long-tail characteristics, rather than merely classifying them into head and tail categories.
We conduct extensive experiments three real-world datasets, demonstrating that our approach improves the performance tail items without compromising the performance of head items. Remarkably, its effectiveness surpasses even SRS integrated with LLM.
2 Problem Definition
Let U and V represent the sets of users and items. The historical interaction sequence of u E is represented as:
S. = [U
Um]
(I)
where m = |Su| indicates the length of the sequence Sg, and represents the k-th item in the sequence. The embedding representations
user u and an item u are denoted as en E Rd and e, Rdd where d represents the dimensionality of the hidden space. The goal of SRS is predict the next likely item uss +1 based on the user's interaction sequence S,, and a sequence encoder fe(-). Formally, this process can be expressed as:
e fo((s) = arg max P(um+1 v1.(Sa),
(2)
vLEV
where e,, representation u. By performing a product between e,, and e,, we obtain ranked list y = [/,, .2,..... V/v]l where y, represents the probability that v is the next item will interact with. The top-K items with the highest probabilities in y are selected the output of the recommender system.
3

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3 Methodology
3.1 Overview
In this section, we introduce HPSERec, a framework designed to enhance traditional SRS by strengthening the representation of users' interests in long-tail items. HPSERec consists of three modules, including the distribution balancing module. the feedforward module, and the feedback module. The distribution balancing module (Section 3.2) partitions the set of items V into multiple subsets with minimal long-tailed characteristics, ensuring that each subset can achieve optimal performance during subsequent training. The feedforward module (Section (3.)) enhances the embedding of long-tail items through contrastive learning-basse data augmentation. This is followed by knowledge distillation, which transfers knowledge between expert networks to improve the long- tail performance of the global expert. The feedback module (Section 3.4) refines upstream experts via distribution-les alignment. It aligns current upstream user embeddings to a target distribution by minimizing the entropic regularized optimal transport cost using the Sinkhorn algorithm. Finally, describe the overall training strategy of the framework (Section 3.5 The complete architecture of our model is illustrated in Figure 2
3.2 Distribution Balancing Module
To more effectively address the intrinsic complexity of the long-tail phenomenon commonly observed in real-world recommendation datasets, we propose novel and practical imbalance metric to precisely quantify the skewness in item interaction distributions.
The item set is denoted as V = {11, , UnJ. count c. Assume that the items in V are sorted in descending order according their interaction frequencies. Our objective is to partition V into L disjoint item subsets { {V/1 V/,,.., VzJ, where each subset V&2 is defined as:
where each item u; is associated with an interaction
V (UT, 1 (r,
where (Ti...., .T....,TT_11. } are index-based splitting points, with To = 0 and Ty. n. For given subset Vk, we define the normalized interaction probability distribution as:
kk)
GS
4
ΣjEV 9
To quantify the concentration level of interactions within the subset, we introduce the following non- non-linear aggregation functional:
P (
4 = Σ LEVA
(5)
The value of 4 reflects the dispersion item interactions within Vg. A smaller 4y indicates a more uniform distribution of interactions across items, while a larger & signifies that interactions are highly concentrated on few dominant items. The parameter a is a tunable hyperparameter. When 1, Φ is more sensitive tail items, and when a becomes more responsive head items.
To avoid extremely imbalanced partition sizes during the segmentation process, we further introduce regularization term defined as:
2 Se (Se-m)²
B₁
1
Sy denotes the expected average size of a partition, and Sş is the size of subset Vg. This where 14 L regularization term B, penalizes partitions that deviate significantly from the target size μt, ensuring that each subset remains balanced not only in the interaction distribution but also in size.
Accordingly, for any given subset Vk. define the overall imbalance score
J(v.) log&; BB

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where 7 E +oc) is a hyperparameter that controls the strength of the regularization penalty. Thus, the optimal partitioning strategy can be formalized as the following discrete optimization problem:
min
Σ J(Vi).
This formulation jointly controls interaction skewness and subset size, yielding balanced item groups for more effective head-tail modeling. The algorithm and proof details of the item subset partitioning process, based on our defined item interaction imbalance metric and implemented with dynamic programming and pruning, are provided in the Appendix A.
3.3 Feedforward Module
To enhance the performance of long-tail items, we initiate training by focusing on users' interests in long-tail items and gradually expand their preferences to encompass all items, while maintaining strong performance specifically on long-tail items. We design distinct expert networks to process corresponding datasets. For clarity, in the following sections, refer to the expert responsible for inferring users' long-tail interests as the upstream expert and the expert responsible for inferring users' global interests as the downstream expert. Unlike traditional MOE models (13), where datasets assigned to each expert are statically partitioned, our approach progressively expands the datasets for each expert. For expert Es, the user emhedding et represents the user's interest in tail items after excluding certain head items. Although e,, does not fully capture the user's global preferences, it serves guiding signal for training subsequent experts.
We adopt a knowledge distillation approach (4), transferring knowledge from upstream experts to downstream experts. To mitigate performance degradation caused by substantial differences in the capacities of expert models, we restrict the knowledge distillation process to adjacent expert networks. This design ensures that downstream models effectively learn from upstream models without being adversely affected by significant capability gaps.
The distillation loss is computed using softened target distribution, where the smoothness of the logits controlled by a temperature parameter т. The distillation loss is defined as:
CKD
1
Σ KL (ISofiimax(2)= Softmax(z///))
[V
VEV;
where =1-1 and at are the logits produced by experts E and E,, respectively.
3.4 Feedback Module
To enhance the representation quality of users in lower-level experts, we propose Sinkhorn-based (15) [66 Feedback Module that adaptively transfers knowledge from higher-level experts via a principled optimal transport framework. This module aligns user representations across expert layers by computing a soft matching plan that minimizes the overall transport cost, thereby enabling fine-grained and globally optimal feedback supervision.
Let the user representation sets from two adjacent expert levels be denoted as U = [ui, uš,.... n and U++1 = {uf+1 un u,, }, where each vector is normalized. We define the transport cost matrix C E Ra*a as:
Cjj = 1 cos(u (uf, /
(10)
which captures the pairwise dissimilarity between user representations across levels using cosine distance. Through this distance-based cost matrix, we formulate the entropy-regularic optimal transport problem as:
min (ET 3.
EnssCij - Σ Ti log Tig iJ
(11)
where 7 E Buxn the transport plan, > 0 is a regularization parameter, and μ = v are uniform marginals. This formulation enables efficient, differentiable, and globally consistent feedback propagation via Sinkhorn iterations, facilitating stable optimization and improving representation alignment across expert layers in long-tailed scenarios.
5

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The feedback supervision is imposed through the expected cost under the transport plan:
Dback
Co..
(12)
This loss encourages each user representation in the current expert to softly align with structurally similar representations from the higher-level expert, thus enhancing representation consistency and improving learning in sparse regions of the long-tail distribution. Unlike hard matching schemes, our soft alignment mechanism, grounded in optimal transport theory, offers greater flexibility and robustness by leveraging its ability to model structured correspondences under distributional shifts, especially beneficial for handling noisy sparse signals. The detailed proof of this module is provided in the Appendix A.2
3.5 Training Strategy
The HPSERec framework adopts dual-stage training paradigm to leverage the interaction between the upstream and downstream expert models. In the forward stage, HPSERec emphasizes the use of upstream models to guide downstream models in discovering latent user features, particularly those associated with toig-tail interests. In contrast, in the feedback stage, HPSERec aims to enhance user representations in upstream models by leveraging the global interest features extracted by downstream models. We have designed an alternating two-stage training strategy for the entire framework.
Feedforward Stage. During this stage, the training process starts with the top-level expert model and gradually incorporates adjacent downstream expert models. The downstream experts are treated as student networks, guided by the knowledge distilled from the upstream models. The overall loss function for this stage defined as:
Liow= = Lree + BBCKD
(13)
where Lree denotes the recommendation loss, and LKD corresponds to the knowledge distillation loss. The weight 3 controls the weighting of the user's long-tail interest representation relative to the global interest.
Feedback Stage. this stage, the training direction is reversed. This phase starts from the bottommost global expert and proceeds sequentially to the upstream adjacent experts. The goal is to address the knowledge gaps in the long-tail experts, improving their ability to capture users' long-tail interests. The loss function for this stage is Loock which can be calculated by Eq.(1 The detailed training procedure is outlined Appendix A.3.
Experiment
4.1
Experimental Settings
Datasets. We compare HPSERec with baseline models using three real-world datasets from online services: Yelp, Amazon Beauty, and Amazon Music. For data pre-processing, we follow previous studies by excluding users with less than five interactions. More details about the datasets and preprocessing can be seen in Appendix B.1
Evaluation Metrics. Performance is evaluated using top-k ranking metries, specifically Hit Rate (HR @ 10) and Normalized Discounted Cumulative Gain (NDCG@ 10) (7). Consistent with prior research SAS, randomly select 100 items that the user has engaged with serve negative samples 18 19), paired with the ground truth, for metric computation.
Compared Methods. To assess the effectiveness of HPSERec, we compared it with two standard SRS models: SASRec (18) and BERT4Rec (17), two traditional enhancement framework for the long-tailed sequential recommendation: CITIES (7) and MELT (2), and three large model-based SRS
approaches: RLMRec (0)), LLMInit 122 20) and LLM-ESR 21). The more details about baselines
put in Appendix B.2
To assess the effectiveness each method, we initially identified the best hyperparameters with single seed applied to the validation set. Subsequently, each method was trained with the selected hyperparameters across five different random seeds. More details about the datasets and preprocessing can be seen in Appendix B.3
Implementation Details.

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Table 1: The overall results of competing baselines and our HPSERec. The boldface refers to the highest score and the underline indicates the next best result of the models. "e" indicates the
statistically significant improvements (L.., two-sided t-test with p < 0.05) over the best baseline.
Dataset
Model
HR
Overall
ND@10
HR@ 10
Tail Item
ND
HR@10
Head Item
ND 10
HR
Tail User
ND@10
HR 10
Head User
ND@10
Improv.
BenARRc
0.3945
0.2453
0.0312
0.0085
0.1917
0.2922
0.3845
0,2384
0.4593
0.2941
33.9%
SASRe:
0.4488
0.2861
0.1593
0.0856
0.7187
0.4815
0.4236
0.2690
0.5261
0.3611
17.7%
CITIES
0.3894
0.2462
0.1127
0.0013
0.4974
0.2745
0.3852
0.2249
04584
0.2594
35.0%%
Beauty
RLMRec
MELT
0.4077
0.4869
0.2565
0.3144
0.1924
0.1598
0.1660
0.0628
0.8055
0.6302
0.4657
0.5595
0.4356
0,4719
0.3021
0.3016
0.4892
0.5523
0.3345
0.3679
29.5%
8,5%
M.I.
0.4351
0.2914
0.2714
0.0708
0.6984
0.5198
0.4919
0.3117
0.5430
0.3632
21.4%
LLM-ESR
0.4945
0,3275
0,2986
0.1713
0.7270
0.5232
0,4821
0,3103
0,5501
0.3425
6.8%
HPSERee
0.5281
0.3665
0.3203
0.2060
0.7306
0.5229
0.5163
0.3557
0,5799
0.4148
BenA/Re
0.5307
0.3025
0.0131
0.0045
0.3913
0.5319
0.5251
0.2978
SASRec
0.5866
0.3536
0.0890
0.0386
0.8002
0.4888
0.5848
0.3525
0.5945
0.3585
16.4%
CITIES
0.5745
0.3404
0.077
0.341
0.7648
0,4573
0.5751
0.3416
0.5891
0.3419
18. 88%
Yelp
MLMRec
MELT
0.6038
0.5306
0.3909
0.0697
0.0104
0.0263
0.0140
0.7683
0,4568
0.5041
0.6037
0.5351
0.3065
0.6042
0.5137
0.2936
28. 7%
MIIi
0.66999
0.3781
0.0874
0.0330
0.7766
0,4797
0.6204
0.3795
0.6187
0.3823
11. 11.9%
LLM-ESR
0.6190
0.1584
0.0670
0.5055
0.6331
HPSERee
0.6827
0
0.3252
0.1832
0
0.5261
0.6884
0.4280
0.6583
0.4027
Ben-4itee
0.4721
0.3056
0.1222
0.9944
0 0,8299
0.5929
0.4475
0.2870
0 0.5638
0.3752
39. 6%%
SASRee
0.5031
0,2243
0.6124
0.6317
CITIES
0.4421
0.2710
0.0824
0.0312
0,8347
0.539]
0.4192
0.2609
0.5082
0.3085
49. 19.1%
Music
RLMRec
MELT
0.5442
0.38332
0.2473
0.3271
0,1405
0.1539
0.8531
0,511
0.6292
0.6256
0.4946
0,5070
0.3374
0.6677
0.6604
0.4722
21. 1%
LLMInit
0.5537
0.3877
0.3024
0,1574
0.8312
0.6426
0.5145
0.3591
0.6843
0.4746
19. 19.1%
L.
0.59.88
0.4013
0.2318
0.1548
0.996
0.6835
0.5622
0. 0,3824
0. 70699
0.4846
10.0%
HPSERce
0.4786
0.4425
0.6806
0.4701
0.7144
0.5069
0.652
0.47
0.059
0.479
NRg10
0.642
NDCG@10
0.450
HR:810
0.003
NDCG910
0.473
0.032
0.443
0.647
0.467
0.62]
0.429
0.641
0.162
0611
2.416
0.836
0.40
0.8
0.9
1.0
1.1
1.2
0.8
0.9
3.0
1.1
1.2
3.0
3.1
1.2
3.3
1.4
1.0
1.1
1.2
1.3
1.
B
B
7
Figure 3: The syper-parameter experiments on the weight of user's long-tail interest representation and distillation temperature т. The result are based on the Music dataset with the SASRec model.
4.2 Overall Performance Comparison
The comparative evaluation of HPSERec and other baseline models in three datasets is shown in Table [ which includes overall recommendation performance along with specific performance metries for head and tail users, as well as head and tail items. For the sake of comparison, we categorize the top 20% as head data and the remaining data as tail data.
Upon examining the table, we find that HPSERec significantly improves overall performance across all datasets. Specifically, in terms of HR @ 10, HPSERec outperforms the best baseline model, LLM-ESR, by 6.8% (Beauty), 10.3% (Yelp) and 10.6% (Music).
Compared to models specifically designed for the long-tail problem. HPSERec delivers substantial performance gains for both head and tail items, with especially notable improvements for tail items. Although HPSERec lacks a dedicated module for enhancing user representations, it still achieves optimal performance for both head and tail users. This suggests that enhancing both item and user performance is not always necessary. Since users and items share the same vector space, improving item performance also benefits user performance.
HPSERec significantly enhances the performance of tail items while maintaining strong performance for head items. In contrast, CITIES demonstrates a trade-off, as it often sacrifices the performance of head items across most datasets to boost the performance of tail items, creating seesaw problem. This stark contrast underscores the advantage of HPSERee, which effectively balances performance across both head and tail groups, addressing the long-tai tail challenge more comprchensively and equitably.
7

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50000
25000
0.55
Frequency
50000
Frequency
20000
H1G 10
HR@@
0,50
20000
HPPSI3
LPPSER LL3CESR
L13GESR
10000
10000
MASRec
5000
0
7-15
16-24 24 25-33
34-42
45-51
51-
5-9
15-19
20-
25-29 30-
(a) Item
(b) User
Figure 4: The results of the proposed HPSERec and competing baselines in user and item groups. The results are based on the Beauty dataset with the SASRec model.
Table 2: The ablation study the Amazon Music dataset with SASRec as the backbone SRS model. The boldface refers to the highest score and the underline indicates the next best result of the models. (DB: Distribution Balancing Module, FF: Feedforward Module, FB: Feedback Module)
Danaset
Raw
DB
FF
FB
HR@10
Overall
ND@10
HR
Head User
ND@ 10
HR
10
Tail User
ND#:0
HR@
Head Item
ND#10
HR@10
Tail Item
ND@
015149
2
0.5889
0.3917
0.6661
0.4659
0.5401
0.3875
0.8655
0.6341
0.3461
0.1982
Music
0.6094
0.4163
0.6729
0.4921
0.5803
0.4127
0.8730
0.6631
0.3640
0.2174
0.4314
0,7020
0.5726
0.2399
0.6524
0.4696
0.7212
0.5248
0.6175
0.4314
0.8943
0.6798
0.4154
0.2765
4.3 Hyper-parameter Analysis
To investigate the effects of the hyper- Syper-parameters in HPSERec, we show the performance trend along with their changes in Figure 3 The hyper-parameter /3 controls the weighting of the user's long-tail interest representation relative to the global interest. With / ranging from 0.8 to 1.2, the recommending accuracy rises first and drops then. A larger value of 3 leads to suboptimal performance because it overemphasizes the user's long-tail representations, thereby compromising the recommendation accuracy for head items. Conversely, smaller 3 weakens capture long-tair maig-tallle item characteristics, ultimately degrading overall performance. As for the distillation temperature т. the optimal value is found to 1.2. This is because a smaller limits the amount of informative signal conveyed by the upstream expert outputs, while larger makes it more difficult for the downstream expert to effectively learn from the softened distributions. Additional experimental results be found in Appendix C.I
model's ability to
4.4
Group Analysis
To conduct a more detailed analysis of HPSERec's performance, we divided users and items into seven groups based user sequence lengths and item popularity, the performance of each group is shown in Figure 4 From the results, we find that HPSERec consistently outperforms the baseline across all sequence lengths. This indicates that, although our model does not explicitly optimize for tail users, the enhancement of item representations also strengthens user embeddings. On the item side, we observe that MELT achieves optimal performance in the head group but underperforms the extreme long-tail. In contrast, HPSERec demonstrates superior performance in the extreme long-tail while maintaining strong performance in the head group. Compared the LLM-ESR, HPSERec achieves significant improvements, highlighting the advantage of our framework in enhancing the performance of tail items. Additional experimental results can be found in Appendix C22
4.5 Ablation Studies
The results of the ablation study are presented in Table 2 First, to evaluate the impact of the Distribution Balancing Module, we replaced with a conventional classification scheme that separates head and tail classes based on item popularity, where the top 20% most interacted items are considered head items and the remaining are classified as tail items. comparison between Rows and as well Rows 3 and 5, demonstrates that proposed method, which quantifies data imbalance

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and enables knowledge transfer across subgroups, significantly improves overall performance. This improvement confirms the effectiveness of our subclass partitioning strategy, which is based on the imbalance characteristics defined earlier in the paper. Next, we examined the effect of the Feedback Module by removing from two variants: one with the Distribution Balancing Module and one without, while keeping other components unchanged. Comparing Rows 2 and 3, as well as Rows 4 and 5, shows that the Feedback Module further enhances performance, working complementarily with the Feedforward Module. These results validate the design rationale of each module in HPSERec. Additional experimental results can be found in Appendix
5 Related work
Sequential Recommendation. The goal of sequential recommendation is to predict the next po-
tential interaction item based on a user's historical interactions (22) 23 24, 25 26). These models designed to capture the evolving preferences of users users over time. Traditional sequential recommendation systems often rely on Markov chain models (27), which excel at modeling user-item interactions. However, Markov models are limited to capturing short-term dependencies, making them less effective in real-world recommendation scenarios. Subsequent research has shifted to- ward neural networks the primary approach for sequence modeling. GRU4Rec (28) employs recurrent neural networks to capture the sequential relationships in user-item interaction histories, enabling the prediction of the next potential item of interest. In contrast. SASRec (18) leverages attention mechanisms to model user sequences and capture global user interests. Bert4Rec (17) introduces the Cloze task to the sequential recommendation, training bidirectional model to extend SASRec. TempRec (29) introduces a time- time-diversity ddiversity-snnsiiive sensitive approach to news recommendation, using Transformer- based sequential modeling to capture temporal patterns effectively. However, these methods overlook the long-tail tail problem inherent in recommendation systems, resulting in poor performance on tail data.
Despite significant progress in SRS, the long-tail problem remains underexplored. Regarding the issue of long-tail tail users, INSERT (5) formulates the recommendation task as a Few-Shot Learning problem, seeking similar sequences from other users and leveraging useful prior knowledge from different sessions enhance recommendations for long-tail users. Similarly, ASREP (6) addresses this issue by generating pseudo-prior items through training with reversed sequences, effectively augmenting the sequence data for long-tail users. For long-tail items, CITIES (7) employs a self-attention mechanism to enhance the performance of tail items by leveraging head items, while Tail-Net (8) explicitly weights items within each user's sequence during inference based on the ratio of head to tail items. Among these works, MELT (2) is the only approach that simultaneously addresses both challenges, mitigating the issues of user and tail item by enabling mutual enhancement between user and item embeddings.
Long-tail Recommendation.
Due to their powerful reasoning and learning capabilities. LLMs have recently garnered significant attention in the field of long-tail recommendation (30) Many researchers have explored leveraging LLMs to enhance the representations of long-tail items and users. RLMRee (TO) utilizes LLMs to generate user and item profiles, effectively capturing their interaction preferences. LLMInit (12 20) employs L.M--genrrted embeddings initialize the embedding layer in SRS models. Additionally, LLM-ESR (21) adopts dual-view modeling framework augmented with a retrieval-enhanced self- distillation method, improving the performance of long-tail users and items.
However, these methods overlook two critical aspects: (1) how to leverage the characteristics of the data to partition head and tail classes effectively, and (2) how to divide items into multiple subsets to reduce semantic disparities among them, thereby enabling more effective data augmentation.
Conclusion
In this work, we propose HPSERec, a novel framework to address the challenges posed by the long-tail problem in SRS. First, we define metrics to quantify the long-tail characteristics of the data and design dynamic programming algorithm to partition the dataset, ensuring that the resulting subsets are as balanced as possible. HPSERec prioritizes learning the features of tail items and subsequently employs a combination of MoF and knowledge distillation techniques to transfer knowledge effectively, Following this, an annealing algorithm is applied to enhance the representation

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of long-tail tail interests. This enhancement leverages users' global preferences, guided by the model's training progress and the similarity of interaction sequences between adjacent experts. Experimental results three publicly available datasets demonstrate that HPSERec outperforms all baselines, including sequential recommendation models integrated with L.M. Furthermore, ablation studies confirm that HPSERec significantly enhances the performance of both tail items and tail users.
Acknowledgments
This work was supported in part by the National Natural Science Foundation of China under Grant 92267 104, and Jiangsu Provincial Major Project on Basic Research of Cutting-edge and Leading Technologies, under grant no. BK20232032.
References
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A Supplement to Method
In this section, the details prompt design and the HPSERec procedures are addressed.
A.1 Distribution Balancing Module
we introduced the formulation of data imbalance. In this section, we provide a detailed description of the algorithmic procedure used to partition the item set into balanced subsets.
In Section 3.2
Let (()) = Ek= [VE), where = , T is the set of threshold.
Algorithm I describes the dynamic programming approach used to identify the optimal threshold values that minimize the overall imbalance score / (()).
Algorithm 1: Distribution Balancing Module
Data: An array V storing the set of items, and array N storing the interaction counts for items in the set. Result: The list of thresholds O.
Sort V in descending order based on item interaction counts;
2 Initialize dp(0: [V],0 L] +- oo; Initialize path 0: |V], L] -1;
for 1 < to do
for i < 1 to [ do
for j to do
Caleulate J(V[j= : i]) by Eq. (7);
if HVVj : + dp -
dp then dp i [1] < H(V :1) dp 1];
10
0| 1| +| +;
11
end
12
end
end
end
15 return θ;
Based on the threshold set O, the item subsets V/. Vg...., V S V are generated after partitioning. To better enable long-tail experts to guide the training of downstream experts, we propose that gradually expanding the range of input items for each expert, rather than providing disjoint item sets, more effective in allowing long-tail experts to play active role in subsequent training. The final subset assigned each expert model is defined as:
V4 - V f=1
(14)
where Vi: represents the item input range for the k-th expert F& in the feedforward module. When approaches 1, the input user sequence contains only tail items, causing the model to focus on capturing the user's tail-item preferences. Conversely, approaches L, the input user sequence closely resembles the user's complete interaction history, prompting the model to capture the user's global interests.
A.2 Feedback Module
In this section, present detailed proof of the feedback module. For clarity of exposition, begin by redefining the following notations.
User embeddings produced by the !-th expert can be defined as:
U,
)
(15)
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while user embeddings produced by the t + 1-th expert can be defined as:
U² = c 1+1 ++1
(16)
We define the cost matrix C' E R using cosine distance:
Cij = (u 1
E [0,2]
(17)
+
Since sampled uniformly during training, assume that both user distributions are uniform:
v/
E
(18)
We consider the following entropy regularzee optimal transport objective:
min (7, 0) - =H) +Ell(u.))
(19)
where E 1
in is the transport plan, H(7) = - Eis Vai log Vej is the Shannon entropy, and I1e 2) (r Raxn 1 = -=
Let f(7) = (7, =H()).
Lemma The objective function f(7)) is strictly convex over its domain.
Proof. The cost term (7: C. is linear in 7, and the entropy term H()) strictly concave. Therefore, the regularized term (7) is strictly convex. The sum of linear and strictly convex function remains strictly convex.
Lemma The feasible M) C Raxx is non-emply, closed, convex, and compact.
The constraints 71 μ4, 1 vs and y define convex polytope. The entries of ry are bounded within the interval [0, 1] and their total sum is constant, ensuring compactness. The set is non-empty since uw? is a valid coupling that satisfies the marginal constraints.
Proof.
Proposition 1
The entropy-regularizee optimal transport problem
min (7,C) - cH())
(20)
TEll(u.))
admits a unique optimal solution " E ((
Proof. From Lemmas and 2, the objective function strictly convex and the feasible set is compact and non-empty. Therefore, by the fundamental theorem of convex optimization, unique global minimizer exists.
Proposition 2 The unique minimizer 7 has the following closed-form structure:
7" diag(u) K -diag()) K = exp ( (-C)
(21)
for some positive scaling vectors u, RT.
Proof. Consider the Lagrangian:
() EnsOit - Σ C(v,a, =
Mi 1og Vij +
Σ ai
44 - Σ Vis
1is
Σ
33
1/- Σ Yis
i.j
i
(22)
Taking the derivative with respect to Viy and setting it to zero yields:
a; + B, Otj -1) u, Kij Uj
Vij = exp
(23)
where u, = expp (op_))))) Vi = exp (2))
20

---

Theorem
Given positive matrix K E R4 and marginal distributions Jr, E An there exist scaling vectors u, Rt such that:
7 diag(u) diag(u) Mi v)
(24)
and the vectors u, v can be computed via the following iterative updates:
(k+1)
p
(25)
Kv(k) + K ((kt) +
n (b++))
V
(26)
where 8 a small constant ensure numerical stability.
A.3 Training Strategy
For a clearer illustration of the training and inference process, we conclude them in Algorithm
2
Algorithm 2: HPSERec
Data: S, u E U, learning rate ir, hyperparameters o, 33 7, Result: Last expert model parameters Wz.
Get item sets Vi,...V VE by Algorithm 1;
for 4- to E (number of epochs) do
/* Feedforwart stage
for - L do
if then
Calculate LKD by Eq. (9);
end
Set Lforw by Eq. (13);
Apply Adam optimizer Lorww
Perform back- prop-propaggtion to forw getting gradients G:
Update W, based 9; end
/* Feedback stage for j + to do
12
13
Calculate Lback by Eq. (12);
Perform back proppapppantiion to Lback getting gradients G;
15
Update W, based on G;
end 16
end
18
return WL:
B Experimental Settings
In this section, we will refer more details about the experimental settings.
B.1 Dataset and Preprocessing
We compare HPSERec with baseline models using three real-world datasets from online services: Yelp, Amazon Beauty, and Amazon Music. For data pre-processing, we follow prior research by filtering out users with fewer than five interactions. T presents the statisties of the datasets after pre-processing.
B.2 Backbone and Baseline
We compare proposed method with the following baseline methods.
SASRec employs self-attention mechanism to model the user's entire interaction sequence and predict the next potential item for interaction.
21

---

Table 3: Statistics of datasets, #Int denotes interaction.
Dataset
#ltems
#Users
#lnt
Avg IS
Beauty
57,289
52,204
394,908
5.6
Yelp
15,720
4,722
192,214
3.8
Music
20,356
20,165
132,595
5.1
0.031
0.458
0.059
0.479
HRg00
0.642
NDCog30
0.46
0.045
NDCG@10
0.473
8.63
0.483
0.618
V
Figure 5: The hyper-paramede parameter experiments on the weight of number of subsets L and the weight of the regularization penalty 7y. The result based on the Music dataset with the SASRec model.
BERT4Rec adopts the Cloze task to train bidirectional model, extending SASRec for better sequential modeling.
CITIES applics a self-attention mechanism, leveraging head items to improve the represen- tation of tail items.
MELT optimizes the representation of both long-tailed items and users, marking its first effort in this area.
RLMRee leverages LLMs generate user and item profiles, effectively capturing their interaction preferences.
LLMInit uses LLM embeddings to initialize the embedding layer the element in the SRS model.
LLM-ESR enhances both long-tailed items and users through a dual view modeling frame- work combined with a aetrieval-augmenn self-distillation method.
B.3 Implementation Details
We conduct all experiments on an Intel Core i7-1 700KKF platform with dual NVIDIA GeForce RTX 3090 (24GB) GPUs. Besides, the implementation is based on Python 3.8.19 19 and PyTorch 2.0.0. For the backbone SRS models, the number of GRU layers is set to I for GRU4Rec, while the number of self-attention layers fixed
for SASRec and Bert4Rec. Also, the dropout rate 0.6 for Bert4Rec. We use the Adam optimizer for parameter optimization with a learning rate of 1 x 10-4 The embedding size is 128 for all baselines, We choose the Adam as the optimizer. For Eq. (5), the default value of a is set to 0.6. For Eq. (6), the default value of L is set to 4. For Eq. (7), the default value of y is set 1.2. Eq. (9), the default value of 7 is set to 1.2. For Eq. (13), the default value of B is set to 1.
C More Experimental Results
C.1 Hyper-parameter Analysis
Figure [egure5lilian illusstrates the impact of several key hyperparameters on the performance of HPSERec. The hyperparameter L controls the number item subsets generated by the Distribution Balancing module. As L increases from to 6, the recommendation accuracy initially improves and then gradually declines. The suboptimal performance with a small can be attributed to the large representational disparity between subsets, while an excessively large L may degrade the representation quality of upstream item subsets due to data sparsity. Regarding the regularization weight 7, which controls the penalty term in the partitioning objective, the optimal value is found to be 1.2. A smaller 7 results in imbalanced subset sizes, whereas larger overly suppresses the influence of item-level imbalance. thus impairing the quality of the learned partitions.
22

---

088
107
Frequeney
6000
Frequency
4000)
4000
HPSSIR LL3-ESR
LIPSER LL3CESR
2000
MASRe
MASRe
0
0
7-8
11-12
4-6
10
12
13-15
16-18
(a) Item
(b) User
Figure 6: The results of the proposed HPSERec and competing baselines in user and item groups. The results are based on the Music dataset with the SASRec model.
8000
0.70
6000
5000
0.65
Proquency
HR@
Feequency
4000
0.60
H
4000
3000
ITSTTRa
0.55
2000
2000
MELT 122
MELT
SASRez
1000
SASRc
310
11-20
21-30
31
4] 51-60
54
5-8
9-12
13-16
17-20
21-24
(a) Item
(b) User
Figure 7: The results of the proposed HPSERec and competing baselines in user and item groups. The results based on the Yelp dataset with the SASRec model.
C.2 Group Analysis
To further evaluate the effectiveness of HPSERec, we conduct group-wise performance analysis on two additional datasets, Music and Yelp. The results presented in Figures Figures 7 From the results, we observe that the LLM-based framework consistently improves performance across all user and item groups. Moreover, HPSERec demonstrates clear advantage under extreme long-tail scenarios, while maintaining competitive performance on head users and items, indicating its ability to enhance tail representations without compromising head accuracy.
C.3 Ablation Studies
In this section, we present additional ablation experiments two benchmark datasets, Yelp and Beauty, with results summarized in Table Specifically, Row corresponds to the baseline SASRec. Row shows the performance when head and tail classes are partitioned using conventional frequency- based heuristics, and data augmentation is applied via the Feedforward module. Building on this, Row 3 incorporates the Feedback module further enhance tail-side representations. Row reflects the effect of applying our proposed Distribution Balancing module for data partitioning, coupled with Feedforward based augmentation. Finally, Row adds the Feedback module to Row 4, forming the complete HPSERec framework. Notably, although HPSERec does not include a dedicated module targeting tail users, we observe consistent performance gain for this group. This is because user and item representations are embedded in the same vector space, and user embeddings are computed based on the items they interact with thus, improving item representations inherently enhances user representations well. Moreover, unlike many long-tail recommendation methods that favor tail performance at the cost of head accuracy, HPSERee achieves balanced improvements across head and tail users/items. The full model leads to consistent performance gains in both head and tail segments, demonstrating effective representation alignment and knowledge propagation across levels of data sparsity.
23

---

Table 4: The ablation study the Yelp and Amazon Beauty dataset with SASRec as the backbone SRS model. The boldface refers to the highest score and the underline indicates the next best result of the models.
Dataset
Row
Overall
Head User
Tail User
Head Item
Thil Item
HR
ND0 10
HR
ND8
HR
ND0
0.5866
0.3536
0.5945
0.3585
0.5848
0.3591
0.8002
0.4888
0.0890
0.0386
0.6181
0.3799
0.6335
0.3784
0.612
0.3807
0.8055
0.4941
0.1061
0.0582
Yelp
0.6313
0.3974
0.6237
0.3897
0.6311
0,4008
0.8130
0.5031
0.1440
0.0874
0.6719
0.4255
0.6410
0.4065
0.6738
0.4258
0.5243
0.5206
0.3200
0.1797
0.6827
0.4231
0.6883
0.4027
0,6884
0,4280
0.8361
0.5261
0.3252
0.1832
0.4488
0.2861
0.5261
0.3611
0:4236
0.2690
0.7187
0-8155
0.1593
0.0856
0.4606
0.2917
0.5461
0.3873
0.4367
0.2875
0.7195
0.4844
0.1872
0.1083
Beaury
0.4826
0.3209
0.5522
0.4898
0.7257
0.5026
0.2152
0.14.9
/
0.5047
0.7271
0.1712
0.5281
0.3665
0.5799
0.4148
0.5163
0.3557
0.7306
0.5229
0.3203
0.2060
D Limitation
Two potential limitations of this work should be noted. First, the proposed framework involves number of hyperparameters, and identifying optimal configurations for specific tasks may require considerable tuning effort. Second, the subset partitioning algorithm in the Distribution Balancing module incurs relatively high computational complexity, making it more suitable for scenarios with moderate number of items. In practical applications with large-scale item sets, further optimization or integration with incremental learning strategies may be necessary.
24


Reviews:
[{"review_id": "G4m6w89fuo", "reviewer": "Reviewer_SjUj", "summary": "This paper addresses the long-tail problem in Sequential Recommendation Systems (SRS) by proposing HPSERec, a framework combining (1) an imbalance-aware hierarchical partitioning of items, (2) a feedforward knowledge distillation mechanism to enhance tail item representations, and (3) a feedback module using Sinkhorn-based optimal transport to align user representations across different expert levels. The framework aims to boost the performance on tail items and users while maintaining recommendation quality for head items. Extensive experiments on three real-world datasets show that HPSERec consistently outperforms both traditional and large language model-enhanced baselines in overall performance and long-tail recommendation accuracy.", "questions": "- How sensitive is the performance of HPSERec to the number of partitions (L)? Have you explored adaptive or learned partitioning beyond static imbalance-based splitting?", "limitations": "The key limitations are summarized in the weaknesses section above.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths\n\n- The hierarchical design with imbalance-based partitioning, stepwise knowledge transfer via distillation, and global alignment via optimal transport is novel, well-integrated, and mathematically sound, with clear theoretical grounding.\n\n- The proposed method shows consistent improvements over competitive baselines, including recent LLM-based methods, across multiple datasets and scenarios (tail users/items, overall ranking), with solid ablations validating each module’s contribution.\n\nWeaknesses\n\n- While the proposed distribution balancing algorithm improves over fixed-ratio partitioning, it still assumes static, discrete partitions of items and users. The method does not address temporal dynamics, gradual shifts in item popularity, or cross-group interactions, which are common in real-world recommendation scenarios. This limits the generalizability of the approach beyond the datasets and static environments tested.\n\n- The use of multiple expert models, stepwise distillation, and computationally expensive Sinkhorn optimal transport introduces non-negligible computational overhead. The paper lacks a detailed analysis of training and inference efficiency, particularly on large-scale datasets or in real-time scenarios.", "was_revised": false, "final_justification": "", "rebuttal": "Thank you. We've made responses (Res) to all weaknesses (W) and Questions (Q):\n\n***W1:** While the proposed distribution balancing algorithm improves over fixed-ratio partitioning, it still assumes static, discrete partitions of items and users. The method does not address temporal dynamics, gradual shifts in item popularity, or cross-group interactions, which are common in real-world recommendation scenarios. This limits the generalizability of the approach beyond the datasets and static environments tested.*\n\n**Res to W1:** Thank you for your insightful question. Our method is not intended for modeling temporal dynamics or behavioral evolution, but rather focuses on constructing a more reasonable data partitioning structure to enable subsequent models to better utilize tail data. In our future work, we can incorporate the time factor by combining \"sliding window partitioning\" or \"incremental re-grouping\" methods, and integrate incremental learning recommendation algorithms to further enhance the practicality of the method.\n\n***W2:** The use of multiple expert models, stepwise distillation, and computationally expensive Sinkhorn optimal transport introduces non-negligible computational overhead. The paper lacks a detailed analysis of training and inference efficiency, particularly on large-scale datasets or in real-time scenarios.*\n\n**Res to W2:** Thank you for your valuable comment. We agree that computational overhead is a critical factor in assessing the practicality of recommendation systems. Compared to recent long-tail recommendation methods that incorporate large language models, our method introduces significantly lower computational complexity.\n\nThe training complexity of our method is\n$\\mathcal{O}(E \\cdot T^2 \\cdot d \\cdot L_T) + \\mathcal{O}(m^2 \\cdot (d + t)),$\nwhere $E$ is the number of expert modules, $T$ is the sequence length, $d$ is the embedding dimension, $L_T$ is the number of Transformer layers, $m$ is the user batch size, and $t$ is the number of Sinkhorn iterations.\n\nThe inference complexity is $\\mathcal{O}(T^2 \\cdot d \\cdot L_T),$\nwhich matches that of standard Transformer-based recommenders, as only the final expert is used during inference.\nWe will include the complete theoretical analysis of computational complexity in the appendix of the final version of the paper.\n\n***Q1:** How sensitive is the performance of HPSERec to the number of partitions (L)?*\n\n**Res to Q1:** We thank you for your insightful question. In the hyperparameter analysis section of our paper (Appendix B.2), we systematically investigate the impact of the number of partitions L on model performance. Specifically, we evaluate the model on the Yelp and Beauty datasets by varying L from 2 to 6, and observe the following trends:\n\n1. When L ranges from 2 to 4, the model exhibits notable improvements in HR@10 and NDCG@10, indicating that appropriately partitioning the item space facilitates tail representation enhancement and alleviates data imbalance.\n2. When L > 4, the performance gains become marginal or slightly degrade. This is primarily due to over-segmentation, which results in fewer interactions per upstream subset. Consequently, the representation quality deteriorates, diminishing the effectiveness of knowledge distillation.\n\nOverall, HPSERec exhibits moderate sensitivity to the choice of $L$, but maintains stable performance within a reasonable range, making it practical and easy to tune in real-world applications.\n\n***Q2:** Have you explored adaptive or learned partitioning beyond static imbalance-based splitting?*\n\n**Res to Q2:** Thank you for your thoughtful question. We have indeed explored adaptive or learned partitioning methods, such as incorporating clustering losses to guide subset construction via deep learning. However, these approaches did not yield satisfactory results and introduced substantial computational overhead to the overall framework.\nTo further evaluate the necessity and effectiveness of our method, we conducted experiments with two additional variants: 1) HPSERec-QSplit adopts a simpler quantile-based partitioning strategy that statically divides items based on their interaction counts. This comparison helps evaluate whether the use of more complex partitioning algorithms is justified in practice. 2) HPSERec-DPPrune incorporates a pruning-based optimization into our original dynamic programming framework. While this variant does not guarantee finding the global optimum, it substantially improves computational efficiency.\nThe corresponding experimental results are presented below.\n\n|      Model      | Dataset | Overall |         | Head user |         | Tail user |        | Head item |        | Tail item |         |\n|:---------------:|:-------:|:-------:|:-------:|:---------:|:-------:|:---------:|:------:|-----------|--------|-----------|---------|\n|                 |         | HR@10      | NDCG@10    | HR@10        | NDCG@10    | HR@10        | NDCG@10   | HR@10        | NDCG@10  | HR@10        | NDCG@10    |\n| HPSERec         |  Music  | **0.6592**  | **0.4786**  | **0.7144**    | **0.5069**  | **0.6428**    | **0.4701** | **0.8989**    | **0.6806** | **0.4425**    | **0.2959**  |\n| HPSERec-QSplit  |         | 0.5847  | 0.4151  | 0.6717    | 0.4682  | 0.5588    | 0.3993 | 0.8442    | 0.6287 | 0.3501    | 0.2220   |\n| HPSERec-DPPrune |         | 0.6280   | 0.4423  | 0.7112    | 0.5028  | 0.6088    | 0.4311 | 0.8943    | 0.6798 | 0.3871    | 0.2407  |\n| HPSERec         |   Yelp  | **0.6827**  | **0.4231**  | **0.6583**    | **0.4027**  | **0.6884**    | **0.4280**  | **0.8361**    | **0.5261** | **0.3252**    | **0.1832**  |\n| HPSERec-QSplit  |         | 0.6457  | 0.3940  | 0.6458    | 0.3910  | 0.6466    | 0.3947 | 0.8236    | 0.5139 | 0.2309    | 0.1146  |\n| HPSERec-DPPrune |         | 0.6585  | 0.4063  | 0.6542    | 0.3988  | 0.6594    | 0.4082 | 0.8282    | 0.5233 | 0.2629    | 0.1339  |\n| HPSERec         |  Beauty | **0.5281**  | **0.3665**  | **0.5799**    | **0.4148**  | **0.5163**    | **0.3557** | **0.7306**    | **0.5229** | **0.3203**    | **0.2060**  |\n| HPSERec-QSplit  |         | 0.4263  | 0.2673  | 0.4866    | 0.3229  | 0.4125    | 0.2546 | 0.7056    | 0.4556 | 0.1395    | 0.0741  |\n| HPSERec-DPPrune |         | 0.4509  | 0.2982  | 0.5181    | 0.3592  | 0.4356    | 0.2844 | 0.6967    | 0.4701 | 0.1986    | 0.1219  |\n\nAlthough the time complexity of these schemes is not as high as that of the method described in the text, the focus of this study is on accuracy, so we have abandoned the other methods."}, {"review_id": "tbVHAE8mf8", "reviewer": "Reviewer_hCvg", "summary": "The paper introduces HPSERec (Hierarchical Progressive Stepwise Enhancement for Long-Tail Recommendation), a novel framework designed to address the long-tail problem in sequential recommendation systems. HPSERec integrates hierarchical dynamic partitioning, progressive knowledge distillation, and optimal transport-based feedback alignment to improve the modeling of sparse and imbalanced user-item interactions. By leveraging a data-driven distribution balancing module and multi-level expert networks, the framework adapts to varying degrees of item popularity while avoiding negative transfer. Unlike LLM-enhanced approaches, HPSERec achieves robust performance without relying on large language models, making it more efficient and scalable for real-world deployment.", "questions": "1. The authors note in the appendix that the proposed method is only suitable for small-scale datasets, but fail to clarify its potential industrial application scenarios. Could the authors elaborate on how this approach might be adapted or scaled for real-world industrial deployment?\n\n2. Although the proposed alternating training strategy—optimizing downstream experts during the feedforward moduleand fine-tuning upstream experts in the feedback module—significantly improves model performance, does the backpropagation-based update of upstream expert parameters during the feedback module risk disrupting the already stabilized parameters learned in the feedforward module?", "limitations": "NA", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1. The work proposes a principled hierarchical decomposition of long-tail distributions, moving beyond simplistic head/tail dichotomy to provide a more granular and theoretically grounded approach to sparsity mitigation in recommendation systems.\n\n2. A novel optimal transport-assisted feedback alignment mechanism is introduced, which leverages Sinkhorn-based distribution matching to theoretically guarantee feature consistency across different hierarchical subsets, ensuring more robust knowledge transfer.\n\n3. Comprehensive experimental validation across multiple benchmark datasets demonstrates the framework's effectiveness, while rigorous ablation studies provide valuable insights into the contribution of individual components to the overall performance.\n\n4. Compared to LLM-dependent approaches like RLMRec, HPSERec achieves comparable performance while operating within traditional recommendation architectures, making it significantly more scalable and practical for real-world deployment.\n\nWeaknesses:\n\n1. The cascaded computation in the multi-layer MoE (Mixture of Experts) architecture increases both memory consumption and inference latency, which potentially impact the real-time responsiveness requirements of online recommendation services.\n\n2. The theoretical foundation of the optimal transport component assumes ideal uniform distributions, an assumption that does not fully align with real-world user behavior data that often exhibits strong clustering effects and complex distribution patterns.", "was_revised": true, "final_justification": "I have read the author's responses to my concerns in their rebuttal. Thank you for the efforts of the authors and the AC, which have helped me further reflect on the score evaluation.", "rebuttal": "Thank you. We've made responses (Res) to all Questions (Q):\n\n***Q1:** The authors note in the appendix that the proposed method is only suitable for small-scale datasets, but fail to clarify its potential industrial application scenarios. Could the authors elaborate on how this approach might be adapted or scaled for real-world industrial deployment?*\n\n\n**Res to Q1:** Thank you for raising this important question. This method can mainly be divided into two parts: dataset division and recommendation framework. Although the algorithm complexity of dataset division is relatively high, in the industrial field, it is acceptable for an item pool in the tens of millions. As for the recommendation framework part, although the training process involves multiple expert networks, in the inference stage, we only use the last expert network. In future research, we will combine it with incremental learning algorithms to further enhance the practicality of this method.\n\n\n***Q2:** Although thposed alternating training strategy—optimizing downstream experts during the feedforward moduleand fine-tuning upstream experts in the feedback module—significantly improves model performance, does the backpropagation-based update of upstream expert parameters during the feedback module risk disrupting the already stabilized parameters learned in the feedforward module?*\n\n**Res to Q2:** Thank you for the insightful question. While it is reasonable to be concerned that updating upstream experts via backpropagation may cause representation drift, our framework is specifically designed to mitigate this risk. The updates in the feedback module are guided by an optimal transport plan that ensures distribution-consistent fine-tuning rather than disruptive re-learning. Empirically, the feedback module consistently improves performance across head and tail users/items, indicating that it enhances rather than destabilizes upstream representations."}, {"review_id": "IFVKQwhxP2", "reviewer": "Reviewer_zHNT", "summary": "This paper proposes HPSERec, a method that splits items into balanced groups and uses stepwise knowledge transfer to better recommend rare (tail) items. It improves long-tail recommendation accuracy while keeping overall performance strong.", "questions": "Regarding the division of head and tail, it seems that for different data sets, a simpler strategy can be used to divide them through statistical information. The division method proposed by the author is reasonable, but is it necessary? Could the authors provide comparative experiments using simpler or naive grouping strategies to better demonstrate the necessity and effectiveness of their proposed partitioning approach?", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Pros:\n1. Clear motivation, focusing on a problem of practical significance.\n2. Good Writing.\n3. The method is reasonable and provides theoretical support.\n\nCons:\n1. Regarding the division of head and tail, it seems that for different data sets, a simpler strategy can be used to divide them through statistical information. The division method proposed by the author is reasonable, but the necessity needs further discussion.\n2. Regarding the grouping method, there is also a lack of comparative experiments with some naive strategy groupings.\n3. The author focuses on the long-tail problem, but in the selection of baselines, there are not enough methods that focus on the long-tail problem for comparison.\n4. The experiment in Figure 4 is difficult to understand, and the correspondence between the two axes and the figure should be more clearly stated. At the same time, it seems that the performance trends of different methods in different groups are consistent, which does not seem to clearly show the advantages of the author's method for long-tail problems.\n5. The method is relatively complex, and it is recommended to add experiments to demonstrate its scalability.", "was_revised": true, "final_justification": "The authors have addressed my concerns. I will raise my score of this paper to 4.", "rebuttal": "Thank you. We've made responses (Res) to all weaknesses (W) and Questions (Q):\n\n***W1, W2 & Q1:** Regarding the division of head and tail, it seems that for different data sets, a simpler strategy can be used to divide them through statistical information. The division method proposed by the author is reasonable, but is it necessary? Could the authors provide comparative experiments using simpler or naive grouping strategies to better demonstrate the necessity and effectiveness of their proposed partitioning approach?*\n\n**Response to W1, W2 & Q1:** We sincerely thank the reviewer for this insightful suggestion. While simpler partitioning strategies do exist, they tend to compromise overall model accuracy, which is the central focus of this work. In fact, we carefully considered multiple partitioning strategies during the design of our method, and experimental results consistently showed that these alternatives underperformed compared to our proposed approach. To further evaluate the necessity and effectiveness of our method, we conducted experiments with two additional variants: 1) HPSERec-QSplit adopts a simpler quantile-based partitioning strategy that statically divides items based on their interaction counts. This comparison helps evaluate whether the use of more complex partitioning algorithms is justified in practice. 2) HPSERec-DPPrune incorporates a pruning-based optimization into our original dynamic programming framework. While this variant does not guarantee finding the global optimum, it substantially improves computational efficiency.\n\nThe corresponding experimental results are presented below.\n\n|      Model      | Dataset | Overall |         | Head user |         | Tail user |        | Head item |        | Tail item |         |\n|:---------------:|:-------:|:-------:|:-------:|:---------:|:-------:|:---------:|:------:|-----------|--------|-----------|---------|\n|                 |         | HR@10      | NDCG@10    | HR@10        | NDCG@10    | HR@10        | NDCG@10   | HR@10        | NDCG@10  | HR@10        | NDCG@10    |\n| HPSERec         |  Music  | **0.6592**  | **0.4786**  | **0.7144**    | **0.5069**  | **0.6428**    | **0.4701** | **0.8989**    | **0.6806** | **0.4425**    | **0.2959**  |\n| HPSERec-QSplit  |         | 0.5847  | 0.4151  | 0.6717    | 0.4682  | 0.5588    | 0.3993 | 0.8442    | 0.6287 | 0.3501    | 0.2220   |\n| HPSERec-DPPrune |         | 0.6280   | 0.4423  | 0.7112    | 0.5028  | 0.6088    | 0.4311 | 0.8943    | 0.6798 | 0.3871    | 0.2407  |\n| HPSERec         |   Yelp  | **0.6827**  | **0.4231**  | **0.6583**    | **0.4027**  | **0.6884**    | **0.4280**  | **0.8361**    | **0.5261** | **0.3252**    | **0.1832**  |\n| HPSERec-QSplit  |         | 0.6457  | 0.3940  | 0.6458    | 0.3910  | 0.6466    | 0.3947 | 0.8236    | 0.5139 | 0.2309    | 0.1146  |\n| HPSERec-DPPrune |         | 0.6585  | 0.4063  | 0.6542    | 0.3988  | 0.6594    | 0.4082 | 0.8282    | 0.5233 | 0.2629    | 0.1339  |\n| HPSERec         |  Beauty | **0.5281**  | **0.3665**  | **0.5799**    | **0.4148**  | **0.5163**    | **0.3557** | **0.7306**    | **0.5229** | **0.3203**    | **0.2060**  |\n| HPSERec-QSplit  |         | 0.4263  | 0.2673  | 0.4866    | 0.3229  | 0.4125    | 0.2546 | 0.7056    | 0.4556 | 0.1395    | 0.0741  |\n| HPSERec-DPPrune |         | 0.4509  | 0.2982  | 0.5181    | 0.3592  | 0.4356    | 0.2844 | 0.6967    | 0.4701 | 0.1986    | 0.1219  |\n\n***W3:** The author focuses on the long-tail problem, but in the selection of baselines, there are not enough methods that focus on the long-tail problem for comparison.*\n\n**Res to W3:** Thank you for highlighting this limitation. Among the seven baselines we included in our current experiments, three methods, CITIES, MELT, and LLM-ESR, are specifically designed to address the long-tail recommendation problem. In the final version of the paper, we will further enrich the comparative evaluation by including additional long-tail-focused baselines, namely ASReP and INSERT, to provide a more comprehensive assessment.\n\nThe corresponding experimental results are presented below.\n\n|  Model  | Dataset | Overall |         | Head user |         | Tail user |         | Head item |        | Tail item |         |\n|:-------:|:-------:|:-------:|:-------:|:---------:|:-------:|:---------:|:-------:|-----------|--------|-----------|---------|\n|         |         | HR@10      | NDCG@10    | HR@10        | NDCG@10    | HR@10        | NDCG@10    | HR@10       | NDCG@10   | HR@10        | NDCG@10    |\n| HPSERec |  Music  | **0.6592**  | **0.4786**  | **0.7144**    | **0.5069**  | **0.6428**    | **0.4701**  | **0.8989**    | **0.6806** | **0.4425**    | **0.2959**  |\n| ASEeP   |         | 0.5448  | 0.3573  | 0.6573    | 0.4591  | 0.4943    | 0.3496  | 0.8254    | 0.6225 | 0.2637    | 0.1559  |\n| INSERT  |         | 0.4414  | 0.2774  | 0.4845    | 0.3103  | 0.4174    | 0.2607  | 0.8455    | 0.5385 | 0.0776    | 0.0310   |\n| HPSERec |   Yelp  | **0.6827**  | **0.4231**  | **0.6583**    | **0.4027**  | **0.6884**    | **0.4280**   | **0.8361**    | **0.5261** | **0.3252**    | **0.1832**  |\n| ASEeP   |         | 0.5307  | 0.3032  | 0.5141    | 0.2899  | 0.5277    | 0.2873  | 0.6821    | 0.3894 | 0.0161    | 0.0057  |\n| INSERT  |         | 0.4873  | 0.2746  | 0.4728    | 0.2543  | 0.4895    | 0.2774  | 0.6264    | 0.3418 | 0.0177    | 0.0059  |\n| HPSERec |  Beauty | **0.5281**  | **0.3665**  | **0.5799**    | **0.4148**  | **0.5163**    | **0.3557**  | **0.7306**    | **0.5229** | **0.3203**    | **0.2060**  |\n| ASEeP   |         | 0.4674  | 0.3108  | 0.5375    | 0.3766  | 0.4515    | 0.284   | 0.7531    | 0.5113 | 0.1764    | 0.0899  |\n| INSERT  |         | 0.4091  | 0.2682  | 0.4371    | 0.2672  | 0.4018    | 0.2470  | 0.7503    | 0.4511 | 0.0275    | 0.0101  |\n\n***W4:** The experiment in Figure 4 is difficult to understand, and the correspondence between the two axes and the figure should be more clearly stated. At the same time, it seems that the performance trends of different methods in different groups are consistent, which does not seem to clearly show the advantages of the author's method for long-tail problems.*\n\n**Res to W4:** Thank you for your valuable suggestion. We acknowledge that Figure 4 lacks a clear explanation in its current form. In this figure, we split users and items into seven groups based on sequence length and popularity, respectively. The bar chart represents the number of users or items in each group, while the line chart indicates the recommendation performance of each method within the corresponding group.\n\nIt is true that all methods exhibit a consistent performance trend, with weaker results on tail data and stronger results on head data, which is a common characteristic in long-tail recommendation scenarios. However, closer inspection reveals distinctive behaviors among the models: for instance, MELT performs well on head items but suffers significantly on tail items. In contrast, our proposed HPSERec achieves the best performance across all user groups, demonstrating its ability to provide consistent and high-quality recommendations for both head and tail users.\n\nIn the final version of the paper, we will offer a more precise explanation of both axes and the comparative insights it conveys, to ensure greater clarity and stronger support for our claims.\n\n\n***W5:** The method is relatively complex, and it is recommended to add experiments to demonstrate its scalability.*\n\n**Res to W5:** Thank you for your suggestion. We acknowledge that the current version of the paper lacks a thorough discussion of the scalability of our proposed method. In the present submission, we have evaluated the integration of our framework with SASRec. To address this concern, we will include additional experiments in the final version by incorporating our framework into FMLP, thereby providing a more comprehensive analysis of the method’s scalability and adaptability to different backbone architectures."}, {"review_id": "cx52E7fZku", "reviewer": "Reviewer_2hmm", "summary": "This paper presents HPSERec, a framework for long-tailed sequential recommendation that mitigates item popularity bias. It features: (1) hierarchical item partitioning via a dynamic imbalance metric; (2) stepwise expert training with knowledge distillation; and (3) a feedback module using Sinkhorn optimal transport for global alignment. Experiments on three datasets demonstrate superior tail-item performance over traditional and LLM-based baselines without sacrificing head-item accuracy.", "questions": "1. The proposed method trains user interests starting from tail interests in the feedforward module until complete user interests are learned. However, is the reverse approach more reasonable?\n2. Why does this paper not include comparisons with classical long-tail recommendation methods, such as LightGCN?\n3. Is there a potential error in the definition of data imbalance (Equation 5)? Could the authors clarify the meanings of the two exponential terms (α and 1/(1−α)) separately?\n4. While the paper primarily addresses the long-tail distribution of known items, how does the proposed method perform on entirely cold-start items?", "limitations": "yes", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "Strengths:\n1. This work proposes a hierarchical dynamic partitioning strategy that utilizes a data imbalance metric and dynamic programming algorithm to replace traditional fixed-ratio partitioning methods, demonstrating superior adaptability to varying skewed distributions across different datasets.\n2. The stepwise enhancement approach progressively improves tail item representations through a Mixture-of-Experts network architecture, combined with knowledge distillation, effectively mitigating the issue of negative transfer in representation learning.\n3. The study makes a theoretical contribution by being the first to decompose the long-tail problem into multi-level subtasks, presenting a comprehensive framework that integrates metric design, partitioning, distillation, and alignment.\n\nWeaknesses:\n1. The dynamic programming-based partitioning algorithm exhibit computational inefficiency when applied to extremely large-scale item sets, requiring further optimization or approximation methods for practical deployment.\n2. While the method indirectly improves performance for tail users through item representation enhancement, the lack of dedicated modules specifically addressing user-side sparsity could potentially limit its effectiveness for extreme cold-start user scenarios.\n3. The alternating training strategy significantly increases training complexity, potentially affecting the method's scalability and practical implementation efficiency.", "was_revised": true, "final_justification": "My concerns have been well addressed. I would like to keep my positive score.", "rebuttal": "Thank you. We've made responses (Res) to all Questions (Q):\n\n***Q1:** The proposed method trains user interests starting from tail interests in the feedforward module until complete user interests are learned. However, is the reverse approach more reasonable?*\n\n**Res to Q1:** Thank you for raising this insightful question. This issue was indeed considered during our experimental exploration. Our empirical results show that starting from tail interests achieves superior performance.\nThis observation can be interpreted as follows: In the feedforward module, beginning from head items allows the model to learn well-established knowledge, which is then propagated to the global user representation. While this seems plausible, it presents a limitation in the feedback stage. Since head interests are already well trained, using the global representation to supervise them yields marginal gains.\nIn contrast, our proposed approach begins with tail interests in the feedforward module and progressively transfers this knowledge upward. We hypothesize that this process implicitly assigns more importance to tail interests, encouraging the global user representation to better encode information from the long tail. Subsequently, in the feedback module, the global representation guides the refinement of tail interests, delivering additional supervision and significantly enhancing their accuracy. This targeted reinforcement helps to overcome the inherent sparsity and noise associated with tail data, leading to more robust overall performance.\n\n***Q2:** Why does this paper not include comparisons with classical long-tail recommendation methods, such as LightGCN?*\n\n**Res to Q2:** Thank you for raising this important question. As demonstrated in many related studies [2,6], the accuracy of several classical long-tail recommendation methods, such as LightGCN, is generally lower than that of the more advanced baselines we compared against in this paper. To further strengthen our experimental evaluation, we will include two recent long-tail recommendation methods, named ASReP and INSERT, in the comparative experiments in the final version of the paper.\n|  Model  | Dataset | Overall |         | Head user |         | Tail user |         | Head item |        | Tail item |         |\n|:-------:|:-------:|:-------:|:-------:|:---------:|:-------:|:---------:|:-------:|-----------|--------|-----------|---------|\n|         |         | HR@10      | NDCG@10    | HR@10        | NDCG@10    | HR@10        | NDCG@10    | HR@10       | NDCG@10   | HR@10        | NDCG@10    |\n| HPSERec |  Music  | 0.6592  | 0.4786  | 0.7144    | 0.5069  | 0.6428    | 0.4701  | 0.8989    | 0.6806 | 0.4425    | 0.2959  |\n| ASEeP   |         | 0.5448  | 0.3573  | 0.6573    | 0.4591  | 0.4943    | 0.3496  | 0.8254    | 0.6225 | 0.2637    | 0.1559  |\n| INSERT  |         | 0.4414  | 0.2774  | 0.4845    | 0.3103  | 0.4174    | 0.2607  | 0.8455    | 0.5385 | 0.0776    | 0.031   |\n| HPSERec |   Yelp  | 0.6827  | 0.4231  | 0.6583    | 0.4027  | 0.6884    | 0.428   | 0.8361    | 0.5261 | 0.3252    | 0.1832  |\n| ASEeP   |         | 0.5307  | 0.3032  | 0.5141    | 0.2899  | 0.5277    | 0.2873  | 0.6821    | 0.3894 | 0.0161    | 0.0057  |\n| INSERT  |         | 0.4873  | 0.2746  | 0.4728    | 0.2543  | 0.4895    | 0.2774  | 0.6264    | 0.3418 | 0.0177    | 0.0059  |\n| HPSERec |  Beauty | 0.5281  | 0.3665  | 0.5799    | 0.4148  | 0.5163    | 0.3557  | 0.7306    | 0.5229 | 0.3203    | 0.2060  |\n| ASEeP   |         | 0.4674  | 0.3108  | 0.5375    | 0.3766  | 0.4515    | 0.284   | 0.7531    | 0.5113 | 0.1764    | 0.0899  |\n| INSERT  |         | 0.4091  | 0.2682  | 0.4371    | 0.2672  | 0.4018    | 0.2470  | 0.7503    | 0.4511 | 0.0275    | 0.0101  |\n\n[2] K. Kim, D. Hyun, S. Yun, and C. Park, “Melt: Mutual enhancement of long-tailed user and\nitem for sequential recommendation,” in Proceedings of the 46th international ACM SIGIR\nconference on Research and development in information retrieval, 2023, pp. 68–77.\n\n[6]Z. Liu, Z. Fan, Y. Wang, and P. S. Yu, “Augmenting sequential recommendation with pseudoprior items via reversely pre-training transformer,” in Proceedings of the 44th international ACM SIGIR conference on Research and development in information retrieval, 2021, pp. 1608–1612.\n\n***Q3:** Is there a potential error in the definition of data imbalance (Equation 5)? Could the authors clarify the meanings of the two exponential terms (α and 1/(1−α)) separately?*\n\n**Res to Q3:** Thank you for raising this important question. The definition in Equation (5) is essentially derived from a variant of Rényi entropy, which is designed to quantify the unevenness of interaction frequency distributions within each subset. In our context, it serves as a measure of the “entropy-based imbalance” for each partitioned item group.\n\n1) The parameter α controls the sensitivity of the metric to the distribution of probabilities. When α -> 0, all items are treated nearly equally, resembling a measure of set cardinality. As α -> \\infty, the metric becomes increasingly dominated by the highest-frequency items, thus emphasizing head items in a long-tail distribution. A smaller α encourages more uniform subset splits, while a larger α highlights skewed distributions. In essence, α determines the smoothness and focus of the entropy measure.\n2) 1/1-α is not an independent parameter but a structural component of the Rényi entropy definition. It acts as a power transformation to normalize the scale of \\sum p_i^α across different values of α, ensuring that the resulting measure remains comparable across settings. Its purpose is to map the aggregated value back into the entropy space, where higher values indicate lower imbalance and greater distributional uniformity.\n\n***Q4:** While the paper primarily addresses the long-tail distribution of known items, how does the proposed method perform on entirely cold-start items?*\n\n**Res to Q4:** Thank you for raising this important question. The key issue addressed in this paper is the long-tail problem, which, although related to the cold-start problem, has a distinct definition and focus. The long-tail problem arises from the imbalance in user-item interactions, which results in suboptimal recommendations for users and limited exposure for less popular items. In contrast, the cold-start problem refers to the challenge of making recommendations when users or items have little to no historical interaction data. In our future work, we plan to explore how the proposed framework can be extended to effectively handle cold-start scenarios."}, {"review_id": "HNkCq6lAi7", "reviewer": "Reviewer_Cp2v", "summary": "This paper investigates the sequential recommendation problem for long-tail items and proposes a stepwise enhancement approach. Specifically, it improves recommendation performance for long-tail items by progressively transferring knowledge among experts trained on different item groups.", "questions": "1.\tWhat is the computational cost introduced by training experts? Could this be theoretically analyzed?\n2.\tDoes the entire training process guarantee convergence? How is convergence determined?\n3.\tDoes the stepwise data-increment method for training experts ensure diverse data distribution across different experts?\n4.\tWhich expert does the model rely on for its final output?", "limitations": "Limitations are not fully addressed. In order to improve the paper, some other ways to generate the sub-datasets to train different experts can be added.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1.\tThe proposed idea of stepwise training experts at different levels is innovative, and its training methodology has broad generalizability.\n2.\tThe appendix provides a theoretical proof for the feedback module.\n3.\tExperiments demonstrate significant performance improvements with the proposed method.\n\nWeaknesses:\n1.\tThe algorithm incurs higher computational costs. Beyond the notable cost of partitioning item groups, training experts also involves substantial overhead, which was not evaluated in the paper.\n2.\tThe paper’s clarity could be improved. Some formulas are ambiguously expressed, including undefined symbols and a lack of explanations (e.g., Appendix Formula 18). Additionally, Equation (14) mentioned in the main text is not visible.\n3.\tThe appendix (Section A.2) does not clearly explain the differences between the provided proof and the standard Sinkhorn algorithm.", "was_revised": false, "final_justification": "", "rebuttal": "Thank you. We've made responses (Res) to all Questions (Q):\n\n***Q1:** What is the computational cost introduced by training experts? Could this be theoretically analyzed?*\n\n**Res to Q1:** We sincerely thank you for raising this important question.\nIn the Feedforward stage, using SASRec as the base recommender architecture, the overall computational complexity of expert training can be expressed as:\n$\\mathcal{O}(E \\cdot T^2 \\cdot d \\cdot L_T)$\nwhere $T$ denotes the sequence length, $d$ is the embedding dimension, $L_T$ is the number of Transformer layers, and $E$ is the number of expert modules. This reflects the fact that each expert is trained independently on a subset of data in a staged manner.\nIn the Feedback stage, the cost is primarily associated with computing soft alignment between user representations via Sinkhorn optimal transport. Specifically,\nconstructing the pairwise similarity matrix has complexity $\\mathcal{O}(m^2 \\cdot d)$.\nThe Sinkhorn-Knopp algorithm, with t iterations, has complexity $\\mathcal{O}(t \\cdot m^2)$,\nresulting in an overall cost of \n$\\mathcal{O}(m^2 \\cdot (d + t))$, where $m$ is the batch size (typically 128 or 256), $d$ is the embedding dimension, and $t$ is the number of Sinkhorn iterations (usually between 10 and 20). Given the relatively small size of $m$, this cost remains manageable and GPU-friendly.\nFinally, in the inference stage, only the final expert is used for prediction. Hence, the inference complexity is $\\mathcal{O}(T^2 \\cdot d \\cdot L_T)$, which is equivalent to that of a standard SASRec model, ensuring no additional latency at test time.\n\nIn summary, the overall training complexity is $\\mathcal{O}(E \\cdot T^2 \\cdot d \\cdot L_T) + \\mathcal{O}(m^2 \\cdot (d + t)),$\nand the inference complexity is $\\mathcal{O}(T^2 \\cdot d \\cdot L_T)$.\n\n\n***Q2:** Does the entire training process guarantee convergence? How is convergence determined?*\n\n**Res to Q2:** Thank you for raising this important question. Due to the complexity of our model, which involves multiple expert networks, knowledge distillation, and the Sinkhorn optimal transport mechanism, we have not provided a formal theoretical proof of convergence in the paper. However, empirical evidence shows that the training process of HPSERec is stable and exhibits clear convergent behavior. For example, on the Music dataset, HPSERec typically converges within approximately 20 epochs, while on the Yelp dataset, convergence is generally achieved within around 15 epochs.\nWe employ the following combined strategies to determine model convergence:\n1. Validation metrics (e.g., HR@10, NDCG@10) are computed after each epoch. Early stopping is triggered if no improvement is observed for a consecutive number of epochs (default: 5).\n2. The overall training loss (encompassing both cross-entropy and feedback losses) consistently exhibits stable descent and eventual convergence across multiple experimental runs.\n\n***Q3:** Does the stepwise data-increment method for training experts ensure diverse data distribution across different experts?*\n\n**Res to Q3:** Thank you for your question. In our method, each expert receives a different subset of user interaction sequences and is assigned a distinct responsibility. Specifically, the first expert is trained only on long-tail items, the second expert on long-tail plus mid-tail items, and so on, with the final expert receiving all items. Accordingly, the first expert focuses on learning users’ long-tail interests, the second expert on mid-tail interests, and the final expert on users’ global preferences. This diversity in training data across experts inherently ensures that each expert captures a different aspect of the user-item distribution.\n\n\n***Q4:** Which expert does the model rely on for its final output?*\n\n**Res to Q4:** Thank you for raising this question. As explained in our response to the previous question, the final expert is responsible for learning the complete user interest representation. Therefore, the model relies on the output of the last expert for its final prediction."}]

Author rebuttal:

Meta-review: The paper proposes a recommendation algorithm, HPSERec, to address the long-tail problem in sequential recommendation. The approach leverages hierarchical partitioning based on a data imbalance metric, progressive knowledge distillation, and Sinkhorn optimal transport-based feedback.

Most reviewers recognized the following strengths:
* The proposed algorithm is novel, with well-integrated components.
* The method demonstrates consistent improvements over competitive baselines, including recent LLM-based approaches, across multiple datasets and scenarios (tail users/items and overall ranking). Ablation studies further validate the contribution of each module.

Reviewers also noted several weaknesses: the lack of baselines specifically designed for long-tail recommendation, the computational cost of the method, and the absence of modeling for temporal dynamics that are common in real-world recommendation scenarios. Some of these concerns were addressed in the rebuttal. The authors are encouraged to incorporate the additional results presented in the rebuttal, as well as to address the remaining issues where possible, in the final version of the paper.
Decision: Accept (poster)