cs.IRFeb 18, 2026

The Diversity Paradox revisited: Systemic Effects of Feedback Loops in Recommender Systems

Authors: Gabriele Barlacchi, Margherita Lalli, Emanuele Ferragina, Fosca Giannotti, Dino Pedreschi, Luca Pappalardo

Organizations: Scuola Normale Superiore and Università di Pisa · Scuola Normale Superiore · Sciences Po · Università di Pisa · 

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Abstract

Recommender systems shape individual choices through feedback loops in which user behavior and algorithmic recommendations coevolve over time. The systemic effects of these loops remain poorly understood, in part due to unrealistic assumptions in existing simulation studies. We propose a feedback-loop model that captures implicit feedback, periodic retraining, probabilistic adoption of recommendations, and heterogeneous recommender systems. We apply the framework on online retail and music streaming data and analyze systemic effects of the feedback loop. We find that increasing recommender adoption may lead to a progressive diversification of individual consumption, while collective demand is redistributed in model- and domain-dependent ways, often amplifying popularity concentration. Temporal analyses further reveal that apparent increases in individual diversity observed in static evaluations are illusory: when adoption is fixed and time unfolds, individual diversity consistently decreases across all models. Our results highlight the need to move beyond static evaluations and explicitly account for feedback-loop dynamics when designing recommender systems.

Figures & tables

Figure 1: Variation of the average individual Gini (a, b) and the collective Gini (c, d) as a function of the adoption rate η\eta , for the Amazon dataset (a, c) and the Last.fm dataset (b, d), across all benchmark recommender systems.
Figure 2: (a,b) Item-level distribution, illustrating how total consumption volume is allocated across items. (c,d) User-level distribution, indicating how broadly user attention is spread across the catalog. Results for the Amazon and Last.fm datasets and for ItemKNN and SpectralCF.
Figure 3: Item co-purchase networks under η=0.2\eta{=}0.2 and η=0.8\eta{=}0.8 for SpectralCF. Networks are extracted at the end of the simulation and focus on items with high, medium, and low popularity. In panel (b), edge colors indicate increases (green) or decreases (orange) in interaction volume, which is also showed through node size variation.
Figure 4: Average user similarity J‾(U)\overline{J}(\mathcal{U}) as a function of the adoption rate η\eta , for different recommender systems, on the Amazon (a) and Last.fm (b) datasets.
Figure 5: Evolution of the average individual Gini (a-b), collective Gini (c-d), and average individual similarity (e–f) over the 24 simulation epochs, for the Amazon and Last.fm datasets. Each curve corresponds to a different adoption rate η\eta , averaged across recommender systems.
Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 6: Evolution of the average individual Gini at different adoption rates. (a-b) η=0.2\eta=0.2 . (c-d) η=0.8\eta=0.8 .
Figure 7: Evolution of the average individual item coverage at different adoption rates. (a-b) η=0.2\eta=0.2 . (c-d) η=0.8\eta=0.8 .
Figure 8: Evolution of the Jaccard similarity at different adoption rates.
 AmazonLast.fm
ModelN@10P@10R@10ItemCovN@10P@10R@10ItemCov
SGL0.35970.15140.27940.70530.37860.37860.7120.7120.12920.12920.18650.1865
Neu MF0.29870.29870.15020.15020.28910.28910.40510.40510.73910.73910.72330.72330.12620.12620.15290.1529
BPR0.24960.24960.11010.11010.23650.23650.07450.07450.75820.73270.12250.1405
NGCF0.23030.23030.11210.11210.23320.23320.38990.38990.6660.6660.63940.63940.09760.09760.1640.164
SPECTRAL CF0.19960.19960.09510.09510.20290.20290.01730.01730.16590.16590.08730.08730.19340.19340.57210.5721
Appendix
Table 1: Performance comparison of recommendation systems across datasets. Best results within each dataset are in bold .
ModelTrainingModel-specific hyperparameters
CF-KNN (item)E=1E{=}1k=100k{=}100 , shrink =0.0=0.0
BPRE=50E{=}50 , lr =0.001=0.001–
NeuMFE=50E{=}50 , lr =0.004=0.004dropout =0.2=0.2 , MLP =[64,32,16]=[64,32,16]
NGCFE=50E{=}50 , lr =0.02=0.02dim =32=32 , layers =[64,64,64]=[64,64,64] , node-drop =0.2=0.2 , msg-drop =0.01=0.01 , λ=0.002\lambda{=}0.002
SGLE=50E{=}50 , lr =0.03=0.03dim =128=128 , L=3L{=}3 , λ=0.002\lambda{=}0.002 , τ=0.12\tau{=}0.12 , α=0.03\alpha{=}0.03 , drop-ratio =0.2=0.2 , aug=ND
SpectralCFE=50E{=}50 , lr =0.0045=0.0045L=3L{=}3 , λ=0.0005\lambda{=}0.0005
Appendix
Table 2: Best hyperparameters used in our experiments for the Amazon dataset
ModelTrainingModel-specific hyperparameters
CF-KNN (item)E=1E{=}1k=150k{=}150 , shrink =0.0=0.0
BPRE=50E{=}50 , lr =0.0001=0.0001–
NeuMFE=50E{=}50 , lr =0.004=0.004dropout =0.1=0.1 , MLP =[64,64,64]=[64,64,64]
NGCFE=50E{=}50 , lr =0.0002=0.0002dim =32=32 , layers =[64,64,64]=[64,64,64] , node-drop =0.2=0.2 , msg-drop =0.01=0.01 , λ=0.002\lambda{=}0.002
SGLE=50E{=}50 , lr =0.003=0.003dim =64=64 , L=3L{=}3 , λ=0.002\lambda{=}0.002 , τ=0.12\tau{=}0.12 , α=0.03\alpha{=}0.03 , drop-ratio =0.2=0.2 , aug=ND
SpectralCFE=50E{=}50 , lr =0.006=0.006L=3L{=}3 , λ=0.0005\lambda{=}0.0005
Appendix
Table 3: Best hyperparameters used in our experiments for the Last.fm dataset
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