Source-linked AI summary
RecSoup: Efficient Model Merging Approach for Controllable Multi-Objective Recommendation
Zidong Jia, Guofu Xie, Xiao Zhang
TL;DR
Dynamic objective preferences make controllable recommendation useful, but reranking restricts trade-offs and parameter generation adds cost; direct model merging also faces interference and incompatible task-vector geometry. RecSoup combines conflict-aware pruning with preference-conditioned merging, and experiments report higher Hypervolume than strong merging baselines across evaluated settings.
Problem
CMOR must accommodate changing objective preferences at inference time, while reranking restricts trade-offs and parameter-generation approaches add training and inference costs.
Source: §1 · p. 1Method
RecSoup prunes task vectors using objective-specific importance and cross-objective relevance, then learns a preference-to-coefficient mapping for adaptive parameter merging.
Source: §1 · p. 2, §4.2 · p. 4, §4.3 · p. 5Results
Across three backbones and datasets, RecSoup consistently exceeds Soup and TATR in Hypervolume; on MovieLens-1M, Hypervolume gains reach 8.5% on SASRec and 7.3% on TiSASRec.
Source: §6.2 · p. 8Takeaways & Limitations
The paper concludes that model merging offers a more efficient and effective paradigm than parameter generation for controllable multi-objective recommendation.
Source: §7 · p. 10The theoretical analysis assumes two conflicting objectives and defines the Pareto-optimal set as the convex hull of two expert models.
Source: §5.1 · p. 6
Abstract
from arXiv · showhide
Recommender systems often need to balance multiple conflicting objectives. Controllable Multi-Objective Recommendation (CMOR) enables dynamic adjustment of objective trade-offs at inference time without retraining, adapting to shifting user or system requirements. Existing CMOR approaches typically rely on output-level reranking or parameter-generating modules, which either limit the scope of feasible trade-offs or incur substantial training and inference cost. Model merging provides a promising alternative by reusing multiple objective-specific models via parameter combination. However, its direct application to recommender systems is challenging due to the lack of a shared linear regime and cross-objective interference. To address these issues, we propose RecSoup, a lightweight two-stage approach for effective CMOR via specialized model merging. RecSoup first mitigates parameter interference across objectives through a pruning strategy that jointly considers objective-specific importance and cross-objective relevance. It then performs adaptive parameter merging via a learnable preference-to-coefficient mapping, allowing dynamic trade-off control at inference time without joint retraining or additional generative modules. Theoretically, we prove that RecSoup outperforms the parameter generation paradigm in effectiveness and efficiency, as it can fully navigate the Pareto front without smoothness constraints. Extensive experiments on multiple benchmarks demonstrate that RecSoup achieves improved Pareto front quality and effective controllability while delivers 165--228x faster inference-time latency than parameter generation approaches. Code is available at https://github.com/35798642/RECSOUP.git.
1 Introduction
Controllable multi-objective recommendation (CMOR) addresses changing objective preferences at inference time, but existing approaches either constrain trade-offs or add training and inference costs. RecSoup reuses objective-specialized models through pruning and adaptive parameter merging.
1 Introduction
- CMOR enables inference-time adjustment to changing preferences, whereas reranking is constrained by its fixed candidate set and parameter generation incurs additional costs.Parameter-generation methods can also suffer optimization instability.Source: §1 · p. 1
- Model merging can reuse objective-specialized checkpoints already found in recommendation pipelines instead of discarding them or generating new parameters.A preference-to-coefficient merger combines specialist parameters to produce recommendations from users’ historical interactions.Source: §1 · pp. 1–2
- Recommendation task vectors lack the shared linear regime assumed by many merging methods, making naive interpolation ineffective and prone to cross-objective interference.Accuracy and diversity can drive heterogeneous parameter updates.Source: §1 · p. 2
- RecSoup introduces a two-stage CMOR framework that prunes parameters using objective-specific importance and cross-objective relevance, then learns preference-conditioned merging coefficients.The framework adjusts trade-offs in parameter space without joint multi-objective retraining.Source: §1 · p. 2
2 Related Work
Prior model-merging work addresses task interference or determines merging coefficients, while parameter-generation methods use preference-conditioned modules to produce objective-specific weights. RecSoup draws on these approaches while targeting dynamic trade-offs in recommendation.
2 Related Work
- Model-merging methods mitigate task-vector conflicts through pruning or projection, or determine coefficients, but many produce a single fixed model unsuitable for changing preferences.RecSoup adapts these ideas with recommendation-specific pruning and preference-conditioned coefficient generation.Source: §2 · p. 2
- Conflict-mitigation criteria in existing merging methods do not account for recommendation objectives’ specific contributions and cross-objective relevance.These gaps motivate RecSoup’s pruning criterion.Source: §2 · p. 2
- Parameter-generation approaches map preferences to weights using hypernetworks or diffusion models, but face architectural complexity and training-stability challenges.Recommendation examples include reranking parameters and objective-conditioned adapters.Source: §2 · p. 2
3 Problem Formulation and Analyses
The section formulates preference-conditioned model merging and examines why task-vector merging may not fit sequential recommendation. Its analyses motivate pruning and adaptive merging to handle heterogeneous parameter updates and trade-offs.
3.2 Problem Analyses
- PC1 explains 25.66%–26.23% of variance, and the top two components capture less than 45%, as accuracy- and diversity-optimized TiSASRec task vectors remain dispersed.The PCA projection plots task vectors on PC1 and PC2, which explain 25.7% and 15.8% of variance, respectively.Source: Figure 2 · p. 3, §3.2 · p. 3
3.1 Problem Formulation
- The formulation uses objective-specialized task vectors, defined as flattened expert-model parameters minus flattened base-model parameters, for N list-wise objectives.U and I denote users and items; objective metrics evaluate ranked recommendation lists.Source: §3.1 · pp. 2–3
- A preference vector maps to merging coefficients that need not equal the preference weights, defining a family of merged models.The family is intended to approximate the Pareto front in expectation while metrics respond consistently and monotonically to their corresponding preference weights.Source: §3.1 · p. 3
3.2 Problem Analyses
- Approximately 30% of parameters can be removed without severe degradation, but accuracy-oriented updates are more pruning-sensitive than diversity-oriented updates.This asymmetry motivates preserving task-critical parameters while reducing interference.Source: Figure 3 · p. 3, §3.2 · p. 4
- The linear-regime hypothesis assumes task-specific updates lie in a shared composable subspace, where fine-tuning outputs can be approximated by a first-order Taylor expansion.The section uses this assumption to explain why linear task-vector merging can work in other settings.Source: §3.2 · p. 3
- The dispersed task vectors indicate heterogeneous parameter directions across objectives, with parameter changes distributed through high-dimensional space rather than a compact linear subspace.The section concludes these updates cannot be mutually explained through linear combinations.Source: §3.2 · p. 4
4 RecSoup: The Proposed Approach
RecSoup separates parameter selection from coefficient determination: it prunes task vectors to mitigate interference, then learns preference-conditioned coefficients for merging.
4.1 Approach Overview
- A gating network maps each preference vector to merging coefficients in one forward pass, controlling competing metrics without retraining.The overview describes accuracy and diversity as example metrics.Source: §4.1 · p. 4
4.2 Conflict Mitigation via Pruning
- Pruning scores parameters using objective-specific importance and cross-objective relevance, then retains top-ranked entries until a norm-retention threshold is met.Cross-objective relevance uses interaction magnitude, preserving parameters even when task updates conflict in direction.Source: §4.2 · p. 5
4.3 Adaptive Model Merging with Learnable Coefficients
- The model merger maps user preferences to coefficients for combining pruned task vectors; training updates only the gating network, leaving those vectors and base weights fixed.The weighted task vectors are added to the base model parameters to recover the merged model.Source: §4.3 · p. 5
5 Discussion
The analysis gives a condition under which parameter generation cannot cover the full Pareto set achievable by model merging, and compares their inference-time complexity.
5.1 Theoretical Analysis
- When L < L0, parameter generation cannot cover every point in the convex-hull Pareto set reachable by model merging.The result compares two expert models and defines the Pareto set as their convex hull.Source: §5.1 · p. 6
5.2 Time Complexity Analysis
- Adapter-only merging costs O(N·d^2) plus O(N^2) gating; full-parameter merging costs O(N·P), versus generation costs O(P·H) or O(T·P·d).Full-parameter merging can be dominated by item embeddings when |I| ≫ d^2, but remains substantially more efficient than diffusion-based generation.Source: §5.2 · p. 6
6 Experiments
Across three backbones and datasets, RecSoup balances Pareto efficiency and controllability; analyses find that adaptive merging supports stable control, while pruning is most useful under stronger interference or noisy updates.
6.1.1 Dataset.
- Experiments cover MovieLens-1M and two Amazon Review categories, compare reranking, parameter-generation, and merging baselines, and report Hypervolume, Pareto-front length, and controllability.The evaluated backbones are SASRec, GRU4Rec, and TiSASRec; controllability measures alignment with user preferences.Source: §6.1.1 · p. 6, §6.1.2 · pp. 6–7
6.2 Experiment Results
- RecSoup improves MovieLens-1M Hypervolume over Soup by up to 8.5% on SASRec and 7.3% on TiSASRec, with controllability near 1.0.Across three backbones and datasets, it produces longer Pareto fronts; on challenging Amazon settings it exceeds parameter-generation methods by around 20–50% in Hypervolume while maintaining controllability above 0.89.Source: Table 1 · p. 7, §6.2 · p. 8
- Removing the coefficient learner consistently reduces Hypervolume, while pruning mainly improves robustness when task vectors contain stronger interference or noisy updates.Without pruning, performance can be comparable or better when task vectors are compatible or sparsification removes useful updates.Source: §6.2 · p. 8
6.3 Analyses
- Pruning reduces task-vector overlap and increases support concentration while preserving the singular spectrum and main directions, accompanying an expanded Pareto front.The analysis attributes the cleaner merging basis to reduced cross-objective interference and more focused objective-specific updates.Source: §6.3.1 · p. 8, Figure 5 · p. 8
- With merging coefficients and procedures held identical, RecSoup exceeds TIES in MovieLens-1M Hypervolume by 4.95% on SASRec, 2.71% on GRU4Rec, and 1.78% on TiSASRec.The comparison isolates the contribution of cross-objective relevance, which helps retain parameters important to multiple objectives.Source: §6.3.2 · p. 9, Figure 7 · p. 9
- RecSoup has lower parameter-construction latency than hypernetwork generation, while diffusion generation takes about 87.79 seconds per preference with 10,000 denoising steps.The latency comparison averages parameter construction over 11 preferences; merging reuses fixed task vectors.Source: §6.3.3 · p. 9, Table 2 · p. 9
- For Accuracy-Fairness on MovieLens-1M with SASRec, RecSoup achieves the highest Hypervolume among compared controllable baselines; Paragon is excluded because it collapses to one solution.Removing the coefficient learner or pruning reduces performance in this setting.Source: §6.3.4 · p. 9, Table 3 · p. 9
- For Accuracy, Diversity, and Fairness, RecSoup achieves the best Hypervolume and overall controllability among baselines, despite Soup producing slightly more Pareto solutions.Soup’s lower Hypervolume indicates inferior frontier quality; Table 4 reports average controllability across objective pairs.Source: §6.3.4 · pp. 9–10, Table 4 · p. 10
7 Conclusions
Task-vector merging does not directly transfer to multi-objective sequential recommendation because a shared linear regime is absent. RecSoup mitigates interference through pruning and controls trade-offs with a lightweight gating network.
7 Conclusions
- RecSoup combines pruning to mitigate parameter interference with a lightweight gating network for controllable trade-offs, addressing the absence of a shared linear regime in multi-objective sequential recommendation.The work concludes that model merging is more efficient and effective than parameter generation for this task.Source: §7 · p. 10
A Proof of Theorem 5.1
The proof argues that a Lipschitz parameter-generation mapping cannot cover the full Pareto-optimal set under the stated condition L < L0. It derives a contradiction from the mapping’s endpoint behavior and the existence of a Pareto point outside its image.
A Proof of Theorem 5.1
- The proof considers the half-weighted combination (1/2)θ1 + (1/2)θ2 ∈ P and aims to show θ* ∉ g([0, 1]) by contradiction, assuming θ* = g(λ*) for λ* ∈ [0, 1].Source: A Proof of Theorem 5.1 · p. 10
- Lipschitz continuity bounds the distances from θ* to g(1) and g(0), whose sum is at most L.The endpoint values are identified with θ1 and θ2, respectively, under the proof’s practical-utility argument.Source: A Proof of Theorem 5.1 · p. 10
- Since the proof gives L0 ≤ L, contradicting L < L0, θ* is not in g([0, 1]) and g cannot generate every element of P.Source: A Proof of Theorem 5.1 · p. 10
B Additional Implementation Details
The appendix specifies MMR’s candidate-pool and preference-vector evaluation settings, and the coefficient learner’s architecture and training setup.
B Additional Implementation Details
- MMR reranks each user’s top-100 candidate pool into a final top-100 list and evaluates 11 accuracy-diversity preference vectors.The accuracy and diversity weights sum to 1, with accuracy weight from 0.0 to 1.0 in increments of 0.1.Source: B Additional Implementation Details · p. 10
- The coefficient learner is a single-layer linear router; backbone and expert task vectors remain frozen while routing parameters are trained.The router uses Adam with learning rate 0.001 and batch size 512.Source: B Additional Implementation Details · p. 10
C Additional Experimental Results
Across backbone-dataset configurations in the Accuracy-Diversity setting, RecSoup leads the pruning-based merging baselines on average Pareto-front quality and ranking.
C Additional Experimental Results
- RecSoup achieves the highest average hypervolume, controllability, and Pareto-front coverage, with the best average ranking among all methods.The comparison covers all backbone-dataset configurations under the Accuracy-Diversity setting.Source: C Additional Experimental Results · p. 10
- RecSoup consistently outperforms DARE in every evaluated setting.Source: C Additional Experimental Results · p. 10
- RecSoup demonstrates stronger overall Pareto efficiency than CABS and LwPTV.The passage links this result to incorporating cross-objective relevance into pruning for more robust controllable model merging.Source: C Additional Experimental Results · p. 10