Source-linked AI summary
Bezier-Guided Adaptive Flow for Cross-domain Sequential Recommendation
Ziang Lu, Yu Zhang, Xinzhe Jiang, Lei Sang, Yiwen Zhang
TL;DR
Cross-domain sequential recommendation transfers preferences across domains, but users differ in how consistent those preferences are and existing methods often rely on global alignment or coarse transfer strategies. BGAFlow combines a personalized transfer horizon with state-adaptive residual flow, and the paper reports that it outperforms state-of-the-art baselines on real-world datasets.
Problem
Users have varying cross-domain preference consistency, while many existing methods rely on global alignment or coarse transfer strategies with limited flexibility for adapting transfer to individual users.
Source: §1 · pp. 1–2Method
BGAFlow uses unified dual-domain pretraining and LLM-inferred profiles, estimates a personalized transfer horizon from latent interest overlap, and learns residual flow along a conditional Bézier reference using intermediate preference feedback.
Source: §1 · p. 3Results
BGAFlow outperforms state-of-the-art baselines on real-world cross-domain recommendation datasets, and the paper reports analyses validating its key components.
Source: §1 · p. 3Takeaways & Limitations
The reported findings support combining personalized transfer control with state-adaptive semantic evolution for cross-domain sequential recommendation.
Source: §1 · p. 3The studied setting assumes two domains with disjoint item sets and considers users overlapping across the domains.
Source: §3.1 · p. 5
Abstract
from arXiv · showhide
Cross-domain sequential recommendation aims to alleviate data sparsity and cold-start problems by transferring useful preference knowledge across domains. However, users exhibit varying degrees of preference consistency across domains, while existing methods often rely on global alignment objectives or coarse-grained transfer strategies. Such approaches may introduce irrelevant information and provide limited flexibility in adapting semantic representations to individual user preferences. To address these challenges, we propose BGAFlow, a personalized framework that combines state-adaptive semantic evolution with user-specific transfer control. BGAFlow first establishes a shared semantic space through unified dual-domain pretraining with user profiles inferred by a large language model (LLM). Based on latent interest overlap, it then estimates a personalized horizon to determine the appropriate transfer extent for each user. To enable semantic adaptation, BGAFlow constructs a conditional Bezier curve as a geometric reference and learns a residual flow that progressively refines the trajectory based on intermediate preference states. The learned flow incorporates dynamic preference feedback to adjust transfer directions, while recommendation supervision and trajectory regularization encourage effective and smooth adaptation. Extensive experiments on real-world datasets demonstrate that BGAFlow consistently outperforms state-of-the-art baselines, validating the benefits of personalized transfer control and state-adaptive semantic evolution.
1 Introduction
BGAFlow addresses the mismatch between users’ cross-domain preference consistency and the uniform or coarse transfer strategies used by many existing methods. It combines personalized transfer control with state-adaptive semantic evolution, and the reported experiments show improvements over state-of-the-art baselines.
1 Introduction
- Users differ in cross-domain preference consistency, while many existing methods use global alignment or coarse transfer strategies that may introduce irrelevant information.Such methods offer limited flexibility to adapt transfer to individual users.Source: §1 · pp. 1–2
- On Sport-Cloth, BGAFlow’s alignment strength varies more across user groups than InfoNCE and adversarial alignment, with stronger alignment for users whose interests are more similar.LLM-inferred user interests show substantial variation in cross-domain similarity.Source: Figure 2 · p. 2, §1 · p. 3
- Cross-domain adaptation must progressively refine representations in response to intermediate semantic states while maintaining a coherent, smooth trajectory.This contrasts with relying only on one-step fusion or direct mapping.Source: §1 · p. 3
- BGAFlow uses latent interest overlap to estimate each user’s transfer horizon, then learns a residual flow that refines a conditional Bézier reference using intermediate preference states.Dynamic preference feedback adjusts transfer directions; task-guided supervision and trajectory regularization support recommendation-aware, smooth adaptation.Source: §1 · p. 3
- BGAFlow outperforms state-of-the-art baselines on real-world cross-domain recommendation datasets and its key components are validated through comprehensive analyses.The introduction reports effectiveness without specifying metric values.Source: §1 · p. 3
2 Related Work
Prior cross-domain recommendation work uses architectural sharing, representation alignment, and transfer-control strategies; LLM-based work adds semantic knowledge and profiles. Flow-based recommendation models preference dynamics, while BGAFlow applies these ideas to personalized cross-domain semantic adaptation.
2.1 Cross-domain Recommendation
- Architectural sharing methods connect domain-specific networks, while alignment methods learn transferable representations; recent cooperative strategies also estimate transferability, but personalized transfer strength and intermediate semantic adaptation are not always modeled together.Examples include CoNet and π-Net, C2DSR and Tri-CDR, and approaches such as RecGURU, DIIT, ABXI, and cooperative transfer methods,,,.Source: §2.1 · p. 4
2.2 LLM-based Recommendation
- LLM-based recommendation uses language-model knowledge to augment interaction graphs, integrate semantic embeddings, or create cross-domain profiles; BGAFlow uses LLM-inferred profiles to guide personalized transfer.Prior cross-domain examples include LeCDSR, LLM4CDSR, LLMCDSR, and X-Cross,,.Source: §2.2 · p. 4
2.3 Flow Matching
- Flow-based recommenders model preference trajectories or user-conditioned dynamics, but their primary objectives differ from personalized cross-domain semantic adaptation.Examples include FlowCF, FMRec, FlowRec, PDFlow, and ConFM, [20],.Source: §2.3 · pp. 4–5
3 Methodology
BGAFlow addresses cross-domain sequential recommendation by first building comparable semantic representations, then transferring preference information through a user-specific, state-adaptive process. Its methodology combines unified dual-domain pretraining with a Bézier-guided residual flow.
3.1 Problem Formulation
- For overlapping users with time-ordered sequences in domains with disjoint item sets, the goal is to improve recommendations in one domain using useful preferences from the other.Source: §3.1 · p. 5
3.2 System Overview
- BGAFlow combines unified dual-domain pretraining with Bézier-guided state-adaptive flow, then combines adapted semantic representations with collaborative information for recommendation.Source: §3.2 · pp. 5–6, Figure 3 · p. 6
3.3 Unified Dual-Domain Pretraining
- LLM-inferred domain profiles, a shared text tower, a domain-specific ID tower, and profile, item-semantic, and CORAL objectives establish comparable semantic representations for transfer.Source: §3.2 · p. 5, §3.3 · p. 7, §3.3.1 · p. 7
3.4 Bézier-guided State-Adaptive Flow
- A profile-conditioned Bézier reference is refined by residual flow with current-state prototype feedback; prototype-overlap and geometric similarity set each user’s horizon, while task-guided supervision and smoothstep scheduling regulate corrections.Source: §3.4 · p. 9, §3.4.1 · pp. 9–11, §3.4.3 · p. 11
4 Experiments
This section evaluates BGAFlow on two cross-domain sequential recommendation datasets against diverse baselines and examines its components and design choices. Analyses cover pretraining objectives, hyperparameters, personalized horizon estimation, alignment mechanisms, Bézier control points, transfer horizons, and residual-flow alternatives, including their relation to recommendation performance and user-specific alignment behavior.
4.1.1 Datasets and Evaluation Protocol.
- The datasets pair users’ recent interactions in Movie-Book or Sport-Cloth, retain ratings of at least 4, and require more than two interactions per user in each domain.Evaluation uses each domain’s last interacted item as ground truth and 999 sampled negatives; metrics are HR@N and NDCG@N at N=5.Source: §4.1.1 · p. 14
4.1.2 Baselines.
- The cited comparison names SASRec as a classic single-domain sequential recommendation model, π-Net for shared-account cross-domain recommendation, and DiffuRec as introducing diffusion modeling into sequential recommendation.Source: §4.1.2 · pp. 14–15
4.1.3 Implementation Details.
- Implementation uses 128-dimensional embeddings and hidden states, Adam with learning rate 1×10−4 and batch size 128, and a two-stage training procedure.The flow stage uses 128 prototypes and K=16 rollout steps, with early stopping based on validation performance.Source: §4.1.3 · pp. 15–16
4.2 Performance Comparisons
- BGAFlow achieves the best results across all domains and evaluation metrics, with relative improvements of 3.91%–16.62% over the strongest baselines (p<0.001).The evaluation covers Movie-Book and Sport-Cloth.Source: Table 2 · p. 16, §4.2 · p. 16
4.3 Further Analysis
- Component ablations show that removing pretraining or the Bézier reference lowers all eight metrics, dynamic feedback and task-guided matching lower every metric, while removing smoothness lowers seven and slightly improves Book NDCG@10.Without pretraining, Movie HR@10 falls from 0.5532 to 0.4643 and NDCG@10 from 0.4333 to 0.3559; without task-guided flow matching, Book HR@10 decreases from 0.4002 to 0.3992 and NDCG@10 from 0.2948 to 0.2945.Source: Table 3 · p. 17, §4.3.1 · p. 18
- Removing Lprofile, Litem, or Lcross degrades performance in most domains, with Lcross especially important on Book and Cloth.The ablation study associates these losses with profile-based preference supervision, user–item semantic alignment, and cross-domain distribution regularization, respectively.Source: §4.3.2 · p. 18, Figure 5 · p. 19
- BGAFlow generally performs best at K=16, except Sport HR@10 is slightly higher at K=4; np=128 performs best across all four domains.More integration steps do not consistently improve performance and add computational overhead; the authors use K=16 and np=128 by default.Source: §4.3.3 · pp. 18–19, Figure 6 · p. 19
- BGAFlow achieves the best HR@10 and NDCG@10 across all four domains among horizon-estimation variants.Its horizon combines prototype-level preference overlap and condition-related geometric similarities to control Bézier reference extent and residual correction scale.Source: §4.3.4 · p. 19, Figure 7 · p. 20
- Prototype-level preference overlap combined with condition-related geometric information provided more informative transfer-control signals than profile similarity, cosine similarity, or semantic prediction alone.Semantic prediction improved over simple cosine-based variants in several cases but remained inferior to BGAFlow.Source: §4.3.4 · p. 20
4.3.6 Analysis of Dynamic Alignment Behavior
- BGAFlow’s alignment strength generally increased with interest similarity, unlike the relatively stable or inconsistently varying patterns of InfoNCE, Adversarial alignment, Tri-CDR, SyNCRec, and ABXI.Movie-Book had a broad similarity distribution with a concentration of high-similarity users, while Sport-Cloth was concentrated in the middle-to-high range; stronger alignment alone does not ensure effective transfer for users with weak preference correspondence.Source: Figure 10 · p. 21, §4.3.4 · p. 22
4.3.5 Study on Bézier Trajectory Waypoint
- BGAFlow achieved the best HR@10 and NDCG@10 across all four domains, while Global, Random, Avg. profile, Src. only, and Tgt. only performed worse.The results support user-conditioned control points that jointly use both domains’ preference information to guide the Bézier reference and residual velocity field.Source: §4.3.4 · p. 21
4.3.6 Analysis of Dynamic Alignment Behavior
- HR@10 was 0.2701 on Sport, 0.2460 on Cloth, 0.5532 on Movie, and 0.4002 on Book; versus Diffusion, gains were 4.74%, 6.36%, 0.19%, and 2.54%.Diffusion was the strongest competing alignment variant; the Movie result was nearly comparable.Source: Figure 11 · p. 22, §4.3.4 · p. 22
4.3.7 Adaptive versus Fixed Transfer Horizons
- BGAFlow outperformed every evaluated fixed horizon across four domains and both metrics, while the best fixed horizon varied by domain and metric.Increasing the fixed horizon from zero generally helped, but further increases did not consistently improve performance; gaps were relatively small in some settings, such as Sport.Source: Figure 12 · p. 23, §4.3.7 · p. 23
4.3.8 Necessity of State-Adaptive Residual Flow
- Against Closed-form Bézier, BGAFlow improved HR@10 by up to 4.42% and NDCG@10 by up to 8.02%, and its NDCG@10 gains over Bézier Flow ranged from 1.04% to 3.76%.BGAFlow also surpassed Matched MLP across all domains; HR@10 gains over Bézier Flow were relatively modest in some domains.Source: §4.3.7 · pp. 23–24, Figure 13 · p. 24
4.3.9 Case Study of State-Adaptive Residual Refinement
- In the Sport case study, BGAFlow’s residual direction shifted by approximately 37° during migration, and the target item’s final rank improved from 13 to 8.The trajectory generally followed the Bézier reference while applying progressive corrections in the original 128-dimensional semantic space; its later-stage target-item score margin was higher than the reference’s.Source: Figure 14 · p. 24, §4.3.7 · p. 25
5 Conclusion
BGAFlow combines unified dual-domain pretraining with personalized transfer control and state-adaptive semantic refinement. Experiments on real-world cross-domain datasets show it consistently outperforms state-of-the-art baselines.
5 Conclusion
- BGAFlow consistently outperforms state-of-the-art baselines on real-world cross-domain datasets.The paper attributes this result to personalized transfer control and adaptive residual refinement.Source: §5 · p. 25
- Unified dual-domain pretraining preserves domain-specific collaborative information while learning comparable semantic representations.Source: §5 · p. 25
- A personalized horizon controls transfer extent, while a conditional Bézier reference and state-adaptive residual flow refine semantic representations according to evolving preference states.Task-guided flow matching and trajectory smoothness regularization encourage effective, gradual adaptation.Source: §5 · p. 25