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Can Recommender Systems Teach Themselves? A Recursive Self-Improving Framework with Fidelity Control

Luankang Zhang, Hao Wang, Zhongzhou Liu, Mingjia Yin, Yonghao Huang, Jiaqi Li, Wei Guo, Yong Liu, Huifeng Guo, Defu Lian, Enhong Chen

arXiv:2602.15659v2cs.IR

TL;DR

Extreme interaction sparsity limits recommendation models’ training signals and is associated with rugged optimization landscapes and poor generalization. RSIR recursively generates synthetic interaction sequences, filters them for fidelity, and trains successor models on the enriched data. The paper reports consistent gains across benchmarks and architectures, including benefits from weak-to-strong transfer.

  • Problem

    Extreme sparsity in user interactions leaves recommenders with limited training signals and is associated with rugged optimization landscapes and poor generalization.

    Source: §1 · p. 1

  • Method

    RSIR iteratively uses a current recommender to generate plausible interaction sequences, applies fidelity-based quality control, and trains a successor model on the enriched dataset.

    Source: §1 · pp. 1–2

  • Results

    Across benchmarks and architectures, RSIR yields consistent, cumulative gains; it improves HSTU Recall@10 by 7.71% on Sports.

    Source: §1 · p. 2, §5.2 · p. 6

  • Takeaways & Limitations

    The authors conclude that recursive self-improvement can let even weak models generate training curricula that enhance stronger models.

    Source: §1 · p. 2, §6 · p. 9

Abstract

from arXiv · show

The scarcity of high-quality training data presents a fundamental bottleneck to scaling machine learning models. This challenge is particularly acute in recommendation systems, where extreme sparsity in user interactions leads to rugged optimization landscapes and poor generalization. We propose the Recursive Self-Improving Recommendation (RSIR) framework, a paradigm in which a model bootstraps its own performance without reliance on external data or teacher models. RSIR operates in a closed loop: the current model generates plausible user interaction sequences, a fidelity-based quality control mechanism filters them for consistency with user's approximate preference manifold, and a successor model is augmented on the enriched dataset. Our theoretical analysis shows that RSIR acts as a data-driven implicit regularizer, smoothing the optimization landscape and guiding models toward more robust solutions. Empirically, RSIR yields consistent, cumulative gains across multiple benchmarks and architectures. Notably, even smaller models benefit, and weak models can generate effective training curricula for stronger ones. These results demonstrate that recursive self-improvement is a general, model-agnostic approach to overcoming data sparsity, suggesting a scalable path forward for recommender systems and beyond. Our anonymized code is available at https://github.com/USTC-StarTeam/RSIR.

1. Introduction

Extreme interaction sparsity leaves recommendation models with rugged optimization landscapes and brittle generalization, while existing augmentation approaches rely on costly external data or teachers or only perturb existing interactions. RSIR instead recursively generates and filters synthetic histories to train successor models, with fidelity control intended to limit error amplification.

1. Introduction

  • Extreme user-interaction sparsity creates rugged optimization landscapes where recommendation models can converge to sharp, brittle minima that generalize poorly.Users interact with only a tiny fraction of a platform’s catalog.Source: §1 · p. 1
  • Curated side information is costly and domain-specific, teacher models can introduce dependencies and distributional mismatch, and heuristic augmentations do not create novel high-fidelity sequences.Masking and cropping provide alternative views of existing data rather than densifying user trajectories with new interaction sequences.Source: §1 · p. 1
  • RSIR recursively uses a current recommender to generate plausible user histories and trains a successor model on the enriched dataset.The proposed loop uses the model’s predictive capabilities to bootstrap its own training data.Source: §1 · p. 1
  • Fidelity-based quality control constrains synthetic sequences to remain faithful to users’ approximate preference manifold, limiting error amplification in the closed loop.The authors warn that an uncontrolled loop can pollute training data and cause performance collapse.Source: §1 · p. 2
  • RSIR combines synthetic-sequence generation, fidelity filtering, and successor-model training, and is presented as an implicit regularizer that improves performance across benchmarks and architectures.The authors also report that weaker models can generate training data that enhances stronger models.Source: §1 · p. 2

2. Related Works

Related work spans model-centric sequential recommendation, data-centric methods for improving data quality and utility, and self-improvement approaches developed in language, vision, and other domains. The section distinguishes heuristic augmentation from methods that synthesize new interaction records.

Sequential Recommendation

  • Deep learning methods have traditionally dominated sequential recommendation, while recent work divides into model-centric and data-centric approaches.Model-centric work increasingly explores generative architectures, particularly transformer decoders for interaction sequences.Source: §2 · p. 2
  • Data augmentation introduces perturbations or auxiliary signals into existing interactions, whereas data-generation methods learn distributions to synthesize new interaction records.The cited works frame both approaches as ways to enrich sparse data, with augmentation also aimed at robustness.Source: §2 · p. 2

Self-Improving AI

  • Self-improving language-model approaches use model outputs to refine the model, including STaR (Zelikman et al., 2022; Huang et al., 2025), reinforced self-training (Gulcehre et al., 2023; Zhang et al., 2024b), and self-rewarding (Yuan et al., 2024; Wang et al., 2024b).These approaches use large language models to identify potential directions for improvement within generated data.Source: §2 · pp. 2–3
  • Self-improvement has also been applied beyond text: RSIDiff (Zhang et al., 2025c) recursively trains diffusion models on self-generated data, while STEP produces reasoning-rich fine-tuning data from raw videos.The cited examples apply the paradigm to text-to-image generation and video-based reasoning data, respectively.Source: §2 · p. 3

3. Methodology

RSIR repeatedly trains a recommender, uses it to generate synthetic interaction sequences, filters those sequences for fidelity, and adds accepted sequences to the data for the next model. Generation balances reuse of a user’s history with exploration of the global item set, while complexity depends on training, sequence-generation, and item-scoring costs.

3.1. The Iterative Self-Improvement Loop

  • At iteration k, RSIR trains on Dk, generates synthetic sequences D′k+1 with the trained model, merges accepted sequences into Dk+1, and trains a successor model.The initial model is trained on D0 using a standard next-item prediction objective.Source: §3.1 · p. 3

3.2. Principled Synthetic Sequence Generation

  • Generation extends randomly chosen prefixes of user histories using a hybrid candidate pool drawn from the user’s interactions with probability p and the global item set with probability 1 − p.The historical pool supports recombination of observed items; the global pool permits exploration beyond observed interactions.Source: §3.2 · p. 3
  • After a candidate item provisionally extends a sequence, the fidelity check accepts it only when an item from the user’s remaining logged interactions is still ranked highly; otherwise generation stops for that sequence.Accepted sequences are collected after duplicate and minimum-length filtering.Source: §3.2 · pp. 3–4

3.3. Computational Complexity Analysis

  • The method’s cost includes training on Nk sequences for E epochs and m generation trials per sequence, with generation also requiring per-step item scoring.Cached autoregressive decoding costs depend on effective generated length Le, and the Break mechanism can make Le much smaller than the maximum length L.Source: §3.3 · p. 4

4. Discussion and Theoretical Analysis

The analysis frames RSIR as bounded exploration around known user trajectories, with fidelity checks selecting synthetic data that favors stable solutions. It characterizes the resulting regularization as manifold-aligned smoothing and gives a recursive error bound whose noise term makes strict fidelity control important.

4. Discussion and Theoretical Analysis

  • RSIR addresses sparse, fragmented recommendation signals through bounded exploration that densifies data around known user trajectories while constraining generation with fidelity control.The authors connect sparsity with overfitting to spurious correlations and convergence to sharp, brittle minima.Source: §4 · p. 4

4.1. Implicit Regularization and Landscape Smoothing

  • Fidelity filtering admits generated sequences only when the current model is robust in their vicinity, yielding a generated-data loss surface described as smooth and low-curvature near the current solution.The analysis interprets the generated-data loss as approximately equivalent to regularized optimization on the original landscape.Source: §4.1 · p. 4
  • RSIR acts as an implicit regularizer that penalizes sharpness and smooths along the user-preference manifold, encouraging flatter minima aligned with valid preference trajectories.The paper characterizes this as a Manifold Tangential Gradient Penalty rather than indiscriminate suppression of parameter updates.Source: §4.1 · pp. 4–5

4.2. Error Analysis and Stability Guarantee

  • The recursive generalization-error bound contracts prior error subject to hallucination noise, and convergence is guaranteed only when fidelity leakage remains below a threshold.Nonzero leakage creates an irreducible noise floor that may cause a plateau or slight degradation in later iterations.Source: §4.2 · p. 5
  • The paper argues that recursive regularization makes self-improvement accessible across model architectures rather than only to large models.It presents self-generated curricula as a way for a model to bootstrap its own performance without relying on a powerful external teacher.Source: §4.2 · p. 5

5. Experiments

Across sparse recommendation benchmarks and several model families, the experiments find that RSIR improves performance in one iteration and can add further gains through recursion. Ablations and generated-data analyses highlight the roles of fidelity control and balanced exploration.

5.1. Experimental Settings

  • Evaluation spans four sparse benchmarks and three model families, comparing RSIR with heuristic and learnable data-augmentation baselines.The datasets are Beauty, Sports, Toys, and Yelp; the backbones are SASRec, CL4SRec, and HSTU.Source: §5.1 · p. 5

5.2. Main Results: Efficacy of RSIR

  • On Sports, HSTU Recall@10 improves from 8.02% initially to 13.92% after three RSIR iterations.Performance eventually saturates, which the authors attribute to systemic biases accumulating until they outweigh data-densification benefits.Source: Figure 3 · p. 6, §5.2 · p. 6

5.3. Ablation and Analysis

  • Performance peaks around p = 0.5: pure exploitation limits novel-interest discovery, while pure exploration risks irrelevant sequences and inefficient generation.Fidelity thresholds also trade off diversity against data fidelity: thresholds that are too strict or too permissive degrade performance.Source: §5.3 · p. 6

5.2. Main Results: Efficacy of RSIR

  • RSIR yields significant gains across three backbones and four datasets; HSTU Recall@10 rises 7.71% on Sports and 7.14% on Yelp, outperforming heuristic augmentation.Gains appear with both RSIR-FT fine-tuning and RSIR retraining from a new random initialization.Source: §5.2 · p. 6, Table 1 · p. 7

5.3. Ablation and Analysis

  • Removing fidelity control yields marginal first-iteration gains but catastrophic collapse in subsequent iterations as errors and biases pollute training data.The ablation compares RSIR across iterations with and without fidelity control on Amazon-Sport.Source: §5.3 · p. 6, Table 2 · p. 7

5.4. Can Weaker Models Teach Stronger Models?

  • Stronger teachers provide better curricula, yet even a weak teacher gives a strong student a +1.95% performance lift.The authors note that a computationally inexpensive model could generate a training curriculum for a large-scale production model, balancing gains with resource constraints.Source: §5.4 · pp. 7–8, Figure 4 · p. 8

5.5. Analysis of Generated Data

  • +342.14% training-data density after eight iterations accompanies rising ApEn; unlike RSIR, Insertion increases density while lowering ApEn.The authors interpret rising ApEn as evidence that generated sequences add information-rich, novel patterns.Source: Figure 5 · p. 8, §5.5 · p. 8

5.6. Empirical Runtime Analysis

  • On Amazon-Toys, RSIR generation is fast and retraining cost is comparable to the base model, with slightly faster convergence despite added data.The comparison is reported under the same hardware setting.Source: Table 3 · p. 8, §5.6 · p. 8

6. Conclusion

RSIR addresses recommendation data sparsity by iteratively generating and refining training data, with fidelity control intended to prevent error amplification. The paper concludes that this framework yields cumulative gains and that even weak models can produce useful curricula for stronger ones.

6. Conclusion

  • RSIR uses fidelity-based quality control to keep synthetic interactions faithful to user preferences and stabilize recursive self-improvement.The conclusion attributes cumulative gains to the framework and identifies fidelity control as critical.Source: §6 · pp. 8–9

A. Pseudo Code for RSIR Framework

  • At each iteration, the framework trains a model, generates and checks synthetic sequences, then expands the training set with the accepted data.The pseudocode describes the training, quality-control generation, and data-expansion phases.Source: A. Pseudo Code for RSIR Framework · p. 13

B.1. Backbones

  • The evaluated recommendation backbones are SASRec, CL4SRec, and HSTU.They are described respectively as Transformer-based, contrastive-learning-enhanced, and generative recommendation models.Source: §B.1 · p. 13

B.2. Baselines

  • The comparison baselines include heuristic Reordering and Insertion, plus learnable generators ASREP, DiffuASR, and DR4SR.The methods represent sequence shuffling, item addition, sequence extension, diffusion generation, and sequence regeneration.Source: §B.2 · pp. 13–14

B.3. Dataset Statistics

The appendix describes benchmark dataset statistics, the scale and sparsity of datasets after one generation iteration, and performance comparisons against data-centric augmentation methods. The supplied passages specify comparison scopes but do not provide the underlying table values.

C.1. Generated dataset statistics

  • Table 5 compares original and one-iteration generated dataset scale and sparsity across four datasets and different generative backbones.Average sequence length is defined as the average number of interactions per user in the benchmark statistics.Source: §C.1 · p. 14, Table 5 · p. 14, §B.3 · p. 14
  • Table 6 compares three backbone models using @20 metrics and reports relative improvement over the best baseline.The caption identifies RSIR-FT as fine-tuning and RSIR as retraining; it also notes p-value < 0.05.Source: Table 6 · p. 15

C.2. Performance Comparison with Data-Centric Methods

  • The data-centric comparison covers four datasets, different backbone models, NDCG@20 and Recall@20, with RSIR run for one iteration.The reported ‘Improv’ row is defined as relative improvement over augmentation baselines.Source: §C.2 · p. 15

C.3. Evaluation on Comprehensive Metrics

RSIR is evaluated across comprehensive metrics, recursive iterations, hyperparameter settings, and compatibility with semantic-ID models. The appendix also analyzes computational costs and describes early termination and approximate retrieval as ways to reduce generation overhead.

C.3. Evaluation on Comprehensive Metrics

  • RSIR shows consistent, significant improvements across all five metrics on all datasets in the comprehensive evaluation.Examples reported are Precision@10 rising from 0.0080 to 0.0087 on Amazon-Toys and MRR improving 11.1% on Yelp, from 0.0126 to 0.0140.Source: §C.3 · pp. 15–16, Table 7 · p. 16

C.4. Recursive self-improving performance

  • Table 6 presents RSI performance on Amazon-Sport and Yelp across 8 iterations, including relative improvement compared with the previous round; Figures 6a and 6b show data quality evolving over iterations.Figures 6a and 6b use iteration count on the horizontal axis and NDCG@20 and Recall@20 on the vertical axis.Source: §C.4 · p. 16

C.5. Hyperparameter analysis

  • The hyperparameter analysis reports Amazon-Sport performance for different rank thresholds τ and exploitation probabilities p using four NDCG and Recall metrics.Tables 9 and 10 cover τ and p, respectively.Source: §C.5 · p. 17, Table 9 · p. 17, Table 10 · p. 17

C.6. Compatibility with External Knowledge-enhanced Models

  • RSIR further improves a Semantic ID-based model on Amazon-Toys, indicating compatibility with models that use external content hierarchies.The Semantic ID baseline reports NDCG@10 = 0.0507, compared with SASRec’s NDCG@10 = 0.0477.Source: §C.6 · pp. 17–18, Table 11 · p. 18

D.1. Notations and Preliminaries

  • The complexity analysis models training and generation costs using dataset size, sequence lengths, vocabulary size, generation trials, epochs, and iteration count.It leaves item-scoring costs symbolic to account for differing retrieval implementations.Source: §D.1 · p. 18

D.2. Complexity Derivation

  • For small K and bounded expansion rate α, the analysis estimates overall runtime as approximately linear in the initial dataset size, up to a small geometric factor.Generation includes incremental decoding and a per-step fidelity-check cost; cached decoding cost depends on effective generation length.Source: §D.2 · p. 19

D.3. Optimization and Scalability

  • Early termination can shorten effective generation length, while approximate MIPS/ANN retrieval can make fidelity checks sub-linear in vocabulary size in practice.The worst-case generation bound still allows effective length up to L; the retrieval-cost notation avoids asserting a universal worst-case bound.Source: §D.3 · p. 20

D.4. Empirical Runtime Analysis

The runtime analysis reports faster generation than the compared generative baselines and retraining time comparable to the base model. A clustering-based approximate retrieval strategy is also evaluated for scaling fidelity checks, while the theoretical appendix characterizes RSIR’s manifold-directed regularization.

D.4. Empirical Runtime Analysis

  • RSIR generation is approximately 18× faster than DR4SR (3m vs. 68m) and 5× faster than ASReP on the reported runtime comparison.RSIR retraining takes 2m16s, compared with 2m34s for the Base model, despite increased data volume.Source: §D.4 · p. 20, Table 13 · p. 21

D.5. Scalability Optimization via Clustering-based Retrieval

  • Clustering-based approximate retrieval reduces fidelity-check complexity from linear to sub-linear, and RSIR-Cluster remains close to exact RSIR, with a reported < 1.7% Recall@10 drop on Amazon-Sport.The strategy narrows search by selecting relevant clusters; the comparison also reports a marginal NDCG@10 advantage on Yelp in some cases.Source: §D.5 · p. 21, Table 12 · p. 21

E. Theoretical Analysis and Proofs

  • The theoretical appendix derives RSIR’s implicit regularizer and recursive error bound and convergence conditions.The cited proof overview identifies these as its two derivation goals.Source: E. Theoretical Analysis and Proofs · p. 22

E.1. Proof of Manifold Tangential Gradient Penalty

  • Under the stated manifold and local-consistency assumptions, the implicit regularizer minimizes the gradient norm projected onto the preference manifold.The proof frames the effect as consistency between predictions on a real context and a generated local neighbor.Source: §E.1 · p. 22

E.2. Recursive Error Bound and Convergence Analysis

RSIR’s error bound models each iteration as a mixture of original-data error and generated-data error, yielding a lower limiting error when valid-data contraction dominates leakage. Nonzero leakage creates a persistent noise floor that can eventually erase the diminishing gains from contraction.

E.2. Recursive Error Bound and Convergence Analysis

  • The recursive bound combines the original-data error, bounded by E0, with generated-data error from valid sequences and off-manifold leakage.Valid sequences contract error by a factor ρ; invalid sequences have error bounded by Emax, with leakage rate p̃k.Source: §E.2 · pp. 22–23
  • Self-improvement requires leakage p̃k to remain below the breakdown threshold; overly loose fidelity control can cause error divergence.A strict τ keeps p̃k approximately zero and leads to monotonic convergence.Source: §E.2 · p. 23
  • When leakage is negligible, error converges to a fixed limit E* below the baseline E0, while the marginal gain from each iteration diminishes near that limit.The analysis assumes strict fidelity control to make the noise term negligible.Source: §E.2 · p. 23
  • Because leakage is never exactly zero, its persistent noise penalty can outweigh the shrinking contraction benefit as error falls, producing a plateau or slight late-iteration degradation.The analysis identifies fidelity-based quality control as the mechanism for suppressing leakage and keeping the noise floor below contraction gains.Source: §E.2 · p. 23

F. Robustness Analysis under Data Noise

In controlled experiments with random interaction noise, RSIR remains above the Base model across the tested noise range, and its relative Recall@10 gains tend to grow as noise increases. The discussion attributes robustness to fidelity filtering of random, off-manifold interactions.

F. Robustness Analysis under Data Noise

  • The experiment injects random items from the global item set into user sequences at noise ratios η ∈ [0, 0.8] and compares RSIR with the Base model on two datasets.The datasets are Amazon-Sport and Yelp.Source: F. Robustness Analysis under Data Noise · p. 23
  • RSIR stays above the Base model from 0% to 80% noise on Amazon-Sport and Yelp, while both methods’ absolute performance declines as noise increases.Figure 7 presents the performance trends for Amazon-Sport and Yelp.Source: F. Robustness Analysis under Data Noise · pp. 23–24, Figure 7 · p. 24
  • On Amazon-Sport, Recall@10 improvement is 8.02% at noise ratio η = 0 and 14.93% at η = 0.8; on Yelp, it rises from 7.55% to 16.42% under the same noise conditions.Source: F. Robustness Analysis under Data Noise · p. 23
  • The discussion says fidelity control filters random, low-probability interactions, allowing valid on-manifold trajectories to be densified even when original signals are heavily corrupted.The authors characterize RSIR as a denoising filter for learning robust preferences.Source: F. Robustness Analysis under Data Noise · p. 24

G. Quantitative Evaluation of Generated Data

The paper evaluates generated sequences using a reciprocal Approximate Entropy measure and describes the sequential recommendation setup used in its experiments. That setup models next-item probabilities from historical interaction prefixes and trains with sampled softmax loss.

G. Quantitative Evaluation of Generated Data

  • Beyond recommendation-performance metrics Hit Rate (HR) and Normalized Discounted Cumulative Gain (NDCG), evaluation uses Approximate Entropy (ApEn) to assess sequence regularity, unpredictability, complexity, and diversity in generated data.The implementation sets r = 0 because similar item IDs may represent entirely different products, and uses ApEn′ = 1/ApEn to align the measure with conventional diversity. Higher ApEn reflects greater complexity and information density in a user’s interaction sequence.Source: G. Quantitative Evaluation of… · pp. 24–25
  • Approximate Entropy is computed from length-m subsequences by measuring their similarity under tolerance r and averaging logarithmic similarity across subsequences.The sequence is represented by m-dimensional subsequence vectors, with distances measured using Chebyshev distance.Source: G. Quantitative Evaluation of… · p. 24

H. Sequential recommendation paradigm

  • Sequential recommendation predicts the next item from the historical prefix, mapping it to embeddings and a context representation before scoring candidate items and applying softmax.At inference, the model outputs the item with the highest predicted probability.Source: H. Sequential recommendation paradigm · p. 25
  • The experiments train sequential models with sampled softmax cross-entropy, summing or averaging losses across positions; SASRec is one instantiation using self-attention.Other sequential encoders and loss functions are possible, but the experiments use sampled softmax to match the method design.Source: H. Sequential recommendation paradigm · p. 25

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