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REVIEW 3 major objections 4 minor 111 references

Conv4Rec: A 1-by-1 Convolutional AutoEncoder for User Profiling through Joint Analysis of Implicit and Explicit Feedbacks

T0 review · 3 major / 4 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read A single 1-by-1 convolutional autoencoder with six-class cross-entropy can predict both which items a user will interact with and what rating they would give, and provably recovers the sampling distribution over interactions.

desk verdict The six-class joint-feedback autoencoder is a real idea and Theorems 1–2 look like real work, but the TV guarantee in Theorem 3 is proved for a loss that is not the trained loss, so the headline recovery claim does not currently follow. read the letter →

arxiv 2509.07499 v1 pith:RWJ4L2OM submitted 2025-09-09 cs.LG

Antoine Ledent , Petr Kasalický , Rodrigo Alves , Hady W. Lauw This is my paper · ORCID
classification cs.LG
keywords recommendersystemscollaborativefilteringimplicitfeedbackexplicitconvolutionalautoencodergeneralizationboundssamplingdistributionrecoveryserendipitousrecommendations
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Conv4Rec aims to establish that a single recommender model can handle the two tasks the field usually separates: predicting which items a user will interact with (implicit feedback) and predicting what rating they would give if they did (explicit feedback). The paper's central claim is that encoding each user's row as a six-class one-hot matrix—ratings 1–5 plus an 'unobserved' class—and training a 1-by-1 convolutional autoencoder with six-class cross-entropy yields calibrated probabilities for both the interaction event and each possible rating. Under a realizability condition, minimizing this loss provably recovers the sampling distribution over interactions up to a small total-variation error, and in the noiseless case the same training controls test mean-squared error. On five real datasets, the same single model reports state-of-the-art or competitive RMSE for ratings and Recall@50/100 for interactions, and its separate probability outputs let it flag serendipitous items users are unlikely to encounter but likely to enjoy. The payoff is that platforms no longer have to assume that a highly ranked item is one the user will consume; the model separates the two questions.

What carries the argument

The key object is the six-class one-hot user-item input matrix U_i and the 1-by-1 convolutional autoencoder that reconstructs it. Each filter is a vector of k+1 weights applied to every item row, so associations like '4 or 5' or 'unseen or 1' are learned once with shared weights; this sharing makes sample complexity scale with parameter count rather than with m·n. The six-class cross-entropy loss over ratings plus 'no interaction' has Bayes optimum G_Bayes: probability N·p_{i,j,κ} for an observed rating and 1 − N·p_{i,j,.} for an unobserved cell, where N is the dataset size and p is the sampling distribution. This identity links explicit rating probabilities to the implicit sampling distribu

What would settle it

Generate synthetic data from a known interaction-and-rating distribution that satisfies the theorem's representability condition, train the model with the six-class cross-entropy loss on samples of increasing size N, and measure the total variation between the model's normalized probability output and the true distribution. If the error does not shrink toward zero at the predicted rate—or if, on real datasets, the predicted 'no interaction' probabilities systematically miss observed interaction rates within the bound—the central recovery guarantee would be falsified.

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Extended reading notes

Core claim

One 1-by-1 convolutional autoencoder can represent the full interaction distribution for every user-item pair: the input is a row of one-hot vectors with six classes, and the output is a per-item softmax that separates the probability of any interaction from the conditional probability of each rating. Because the first encoder and last decoder layers share weights across items, associations among rating categories are learned once and transfer across the whole matrix. The proof shows that if the true sampling distribution is realizable by this architecture, minimizing the six-class cross-entropy loss recovers that distribution in total variation up to a shrinking error, with a test-MSE bound

Load-bearing premise

The central guarantee only holds when the true pattern of interactions and ratings can be represented perfectly by the constrained architecture; the paper gives no evidence that any real rating dataset satisfies that realizability condition.

Editorial extensions

If this is right

  • A single Conv4Rec model can act as both a ranking engine (order items by 1 − G_{i,j,0}) and a rating predictor (expected value of the conditional rating distribution), removing the need for separate implicit and explicit models.
  • The six-class output makes serendipity explicit: items with low interaction probability but high expected rating conditional on interaction can be surfaced, something single-matrix baselines like CoRating and WADMF cannot do by construction.
  • The generalization bounds imply that sample efficiency grows roughly like the decoder's parameter count plus the per-user embedding dimension, so the weight sharing of 1-by-1 convolutions is a statistical advantage, not just a parameter-saving trick.
  • Under the theorem's realizability condition, one loss function (six-class cross-entropy) simultaneously controls the recovered sampling distribution in total variation and, in the noiseless case, the rating error.
  • Per-user λ analysis indicates that how much to weight implicit versus explicit signals differs by user and dataset, with larger sparser catalogs leaning more on implicit feedback, so retrieval can be tuned per user rather than globally.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The calibration identity G_{i,j,0} ≈ 1 − N·p_{i,j,.} could be used as a diagnostic: a systematic mismatch between predicted 'no interaction' probabilities and observed interaction rates would signal distribution shift or failure of the realizability assumption; the paper does not run this check.
  • Because the convolutional filters are item-agnostic, the learned rating-category associations should transfer to new items and users once embeddings are available, suggesting a cold-start extension the paper leaves untested.
  • The same joint distribution output could feed exploration/exploitation or active-learning objectives directly, where the separation of interaction probability from conditional rating is the quantity of interest; the paper only gestures at this possibility.
  • The theory bounds the gap for a constrained function class; comparing the size of the bound to actual generalization errors on real datasets would show how much slack the guarantees carry, a quantitative test the paper leaves open.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper proposes Conv4Rec, a 1-by-1 convolutional autoencoder that takes a user's one-hot encoded row over items and rating classes and reconstructs it as six-class probabilities: five rating classes plus a 'no interaction' class. The authors argue that this joint modelling yields separate predictions for implicit and explicit feedback, gives generalization bounds for the explicit-feedback square loss, and provides a total-variation recovery guarantee for the interaction sampling distribution when the ground-truth Bayes predictor is realizable. Experiments on Douban, MovieLens 100K/25M, Amazon Electronics, and Amazon Games are reported for both RMSE and Recall@50/100.

Significance. The distributional-output idea is attractive and the architecture is simple and interpretable. The parameter-counting and norm-based bounds (Theorems 1 and 2) are substantial and appear to be derived in detail from first principles. If the total-variation recovery guarantee were valid for the loss actually optimized, it would be a valuable contribution. However, as printed, the TV theorem is proved for a weighted objective that is not equivalent to the training loss used in experiments, and the empirical support for the implicit-feedback claims is inconsistent with the reported tables.

major comments (3)
  1. [Appendix D, Eqs. (D.1)-(D.2); Eq. (4); Theorem 3] The claimed equivalence between the theoretical loss (D.1) and the actual training loss (4) is algebraically false. With no duplicates and K=1/N, (D.1) expands to L_D1 = (1/N)Σ_Ω log G_{i,j,r} - (2/N)Σ_Ω log G_{i,j,0} - (1/N)Σ_U log G_{i,j,0}, whereas Eq. (4) is L = -(1/(mn))Σ_Ω log G_{i,j,r} - (1/(mn))Σ_U log G_{i,j,0}. The coefficients are not proportional: observed cells affect L only through the rating log-probability, while L_D1 also penalizes log G_{i,j,0} on observed cells, and the weights on the log G_r terms differ by a factor of mn/N. Consequently the minimizers differ even in the unconstrained case, so the excess-risk bound in Theorem D.1 and the TV guarantee in Theorem 3/Cor. D.2 do not apply to the loss optimized by the model. The abstract's statement that 'optimizing our loss function guarantees the recovery of the exact sampling distribution' is therefore unsupported for t
  2. [Theorem 3, Eqs. (D.9)-(D.13)] Even if the loss mismatch is repaired, the TV and MSE guarantees are conditional on realizability: the theorem assumes g* = G_Bayes with G_Bayes_{i,j,κ} = N p_{i,j,κ}, together with the norm constraints in Eq. (D.10) and the condition (D.8) on per-cell probabilities. No argument or evidence is given that real rating datasets satisfy these conditions, or that the proposed architecture can represent G_Bayes under the stated constraints. The abstract and introduction state the recovery conclusion without these qualifications. Please make the conditional nature explicit and discuss (or test) when the realizability assumption is plausible.
  3. [Experiments, Table I and 'Results for the Implicit Feedback'] The text says Conv4Rec 'particularly excels in MovieLens 25M and Amazon Electronics', and the abstract claims state-of-the-art implicit performance. In Table I, for Amazon Electronics Conv4Rec has Recall@50 = 0.0998 and Recall@100 = 0.1437, below NCF (0.2154/0.2900), LightGCN (0.2803/0.3781), XSimGCL (0.2540/0.3417), and CoRating (0.1974/0.2425). Additionally, the Amazon Games block contains only the Conv4Rec row, so the state-of-the-art claim cannot be checked there. The text and table need to be reconciled, and the missing baseline rows for Amazon Games need to be supplied.
minor comments (4)
  1. [Abstract and Introduction] The recovery guarantee should be qualified from the start as conditional on realizability and on the specific weighted loss of Appendix D; the current wording overstates the theorem.
  2. [Table I] The dataset labels are unclear: the first block has no dataset name, and the placement of 'Douban' between a baseline block and the Conv4Rec row is confusing. Please restructure the table so each dataset has a clear header row.
  3. [Appendix D] The symbol K in Eq. (D.1) is later fixed to 1/N, but this is not stated where the loss is first introduced. State the value of K directly in the theorem setup.
  4. [Throughout] There are several typos, e.g., 'likelyhood', 'interatction', 'Froebenius', and 'Chroenecker'. A careful proofreading pass is needed.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the total-variation recovery proof is a substantive excess-risk argument; the D.1-vs-Eq.(4) bridge is a correctness gap, not a circular reduction.

full rationale

The derivation chain is not circular. The paper defines a population loss L1 whose unconstrained minimizer is G_Bayes = Np (Appendix D.2, Eqs. D.6-D.9), then proves a Rademacher/covering-number excess-risk bound for the constrained empirical minimizer (Theorem D.1) and applies Pinsker's inequality to convert KL to TV (Corollary D.2). This is a genuine consistency argument: the conclusion that the normalized output approaches p is contingent on the explicit realizability assumption g* = G_Bayes and on norm constraints; it is not an identity in the definitions. The generalization bounds are derived from Lipschitz and covering-number lemmas (Propositions B.1, B.5, C.4). The cited [76] propositions are general compositional-covering lemmas used to bound one secondary norm-based result, and their author overlap does not make the recommender-system TV conclusion a restatement of that citation. The main caveat is non-circular: the paper asserts that loss (D.1) equals the training loss Eq. (4) up to a constant when Ω has no duplicates and K=1/N (main text before Thm 3; Appendix D), but algebraically the coefficient patterns differ (D.1 has -2/N log G0 on observed cells and -1/N log G0 on unobserved cells, while Eq. 4 has -1/(mn) log G0 on both, and different G_r coefficients). Thus the TV guarantee is proved for a surrogate weighted objective rather than the exact optimized loss. This is a theorem-scope/correctness gap, not a circularity: the loss is not defined in terms of the predicted output, and no fitted parameter is renamed as a prediction. Consequently, the circularity score is 0; correctness risk should be assessed separately.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the i.i.d. sampling model, the treatment of unobserved entries as negative class 0, and the realizability of the Bayes predictor. These are explicit assumptions, not fully checked against real data. The model hyperparameters r, L, K2 are selected by validation, contributing free capacity. No novel physical or conceptual entities are introduced.

free parameters (3)
  • embedding dimension r = 8 to 128 per dataset
    Tuned on validation sets to optimize RMSE/Recall@50; controls the capacity of the bottleneck.
  • decoder depth L = 2, 3, 5, 9
    Validated per dataset; the paper reports trying these values.
  • first convolutional filter width K2 = 6, 12, 16
    Validated per dataset; channel width at the first convolutional stage of the decoder.
assumptions (4)
  • domain assumption Observed entries are sampled i.i.d. from a fixed distribution D over (user, item, rating) triples.
    All generalization bounds rely on this sampling model; the paper acknowledges in Appendix D that real datasets are not literally i.i.d. because duplicates are removed.
  • domain assumption All unobserved entries are treated as class 'no interaction' in the cross-entropy loss, and G_{i,j,0} is interpreted as the probability that an N-sample dataset does not contain (i,j).
    This turns missing data into a negative signal, assuming that the pattern of observed ratings is informative about user preference. This is standard in implicit feedback but not validated in the paper.
  • domain assumption The ground truth distribution is realizable by the Conv4Rec architecture under norm constraints on weights and embeddings (g* = G_Bayes).
    Theorem 3 and Corollaries D.2-D.3 are conditional on this realizability; the paper does not verify it for any dataset.
  • standard math Standard Rademacher complexity, covering number, Talagrand contraction, and Pinsker inequality tools.
    Used in Appendices B-E to derive the bounds; these are well-established results from the cited literature.

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Cite this review

Pith. "Pith review of Conv4Rec: A 1-by-1 Convolutional AutoEncoder for User Profiling through Joint Analysis of Implicit and Explicit Feedbacks." pith.science (2026). https://pith.science/paper/RWJ4L2OM

@misc{pith2026250907499,
  author       = {Pith},
  title        = {Pith review of: Conv4Rec: A 1-by-1 Convolutional AutoEncoder for User Profiling through Joint Analysis of Implicit and Explicit Feedbacks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RWJ4L2OM}},
  note         = {Machine review of arXiv:2509.07499}
}
read the original abstract

We introduce a new convolutional AutoEncoder architecture for user modelling and recommendation tasks with several improvements over the state of the art. Firstly, our model has the flexibility to learn a set of associations and combinations between different interaction types in a way that carries over to each user and item. Secondly, our model is able to learn jointly from both the explicit ratings and the implicit information in the sampling pattern (which we refer to as `implicit feedback'). It can also make separate predictions for the probability of consuming content and the likelihood of granting it a high rating if observed. This not only allows the model to make predictions for both the implicit and explicit feedback, but also increases the informativeness of the predictions: in particular, our model can identify items which users would not have been likely to consume naturally, but would be likely to enjoy if exposed to them. Finally, we provide several generalization bounds for our model, which to the best of our knowledge, are among the first generalization bounds for auto-encoders in a Recommender Systems setting; we also show that optimizing our loss function guarantees the recovery of the exact sampling distribution over interactions up to a small error in total variation. In experiments on several real-life datasets, we achieve state-of-the-art performance on both the implicit and explicit feedback prediction tasks despite relying on a single model for both, and benefiting from additional interpretability in the form of individual predictions for the probabilities of each possible rating.

Figures

Figures reproduced from arXiv: 2509.07499 by the authors.

Figure 1
Figure 1. Illustration of our architecture. The input and output represented correspond to a single user, but the weights are [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Illustration of the information that can be extracted from our model’s output. The four graphs on the left represent output probabilities (Gri,j,κ for 0 ď κ ď 5) for four user-item combinations sampled from the Douban dataset’s test set. The four graphs on the right illustrate the output probabilities G˜ i,j,κ for 1 ď κ ď k and the probability of an interaction between the corresponding user i and item j, in compari… view at source ↗
Figure 3
Figure 3. Density of indication λ across the datasets. Further explanation in the main text. ‚ WADMF: The model from [13] one of the very few existing works which perform predictions for both ex￾plicit and implicit feedbacks. Both predictions are based on a single matrix Φ which is learnt with a two-stage matrix factorization approach using both implicit and explicit feedback datasets. The implicit feedback dataset used in pr… view at source ↗

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Reference graph

Works this paper leans on

111 extracted references · 74 canonical work pages

  1. [1]

    Matrix factorization techniques for recommender systems,

    Y . Koren, R. M. Bell, and C. V olinsky, “Matrix factorization techniques for recommender systems,”IEEE Computer, vol. 42, no. 8, pp. 30–37, 2009

    2009

  2. [2]

    Spectral regularization algorithms for learning large incomplete matrices,

    R. Mazumder, T. Hastie, and R. Tibshirani, “Spectral regularization algorithms for learning large incomplete matrices,”J. Mach. Learn. Res., vol. 11, p. 2287–2322, Aug. 2010

    2010

  3. [3]

    Neural collab- orative filtering,

    X. He, L. Liao, H. Zhang, L. Nie, X. Hu, and T. Chua, “Neural collab- orative filtering,” inProceedings of the 26th International Conference on World Wide Web, WWW 2017, Perth, Australia, April 3-7, 2017, pp. 173–182, 2017

    2017

  4. [4]

    Autorec: Au- toencoders meet collaborative filtering,

    S. Sedhain, A. K. Menon, S. Sanner, and L. Xie, “Autorec: Au- toencoders meet collaborative filtering,” inProceedings of the 24th international conference on World Wide Web, pp. 111–112, 2015

    2015

  5. [5]

    Collaborative filtering for implicit feedback datasets,

    Y . Hu, Y . Koren, and C. V olinsky, “Collaborative filtering for implicit feedback datasets,” in2008 Eighth IEEE international conference on data mining, pp. 263–272, Ieee, 2008

    2008

  6. [6]

    Scalable linear shallow autoencoder for collaborative filtering,

    V . Van ˇcura, R. Alves, P. Kasalick `y, and P. Kordík, “Scalable linear shallow autoencoder for collaborative filtering,” inProceedings of the 16th ACM Conference on Recommender Systems, pp. 604–609, 2022

    2022

  7. [7]

    Unifying explicit and implicit feedback for collaborative filtering,

    N. N. Liu, E. W. Xiang, M. Zhao, and Q. Yang, “Unifying explicit and implicit feedback for collaborative filtering,” inProceedings of the 19th ACM International Conference on Information and Knowledge Management, CIKM ’10, (New York, NY , USA), p. 1445–1448, Association for Computing Machinery, 2010

    2010

  8. [8]

    Unifying explicit and implicit feedback for rating prediction and ranking recommendation tasks,

    A. H. Jadidinejad, C. Macdonald, and I. Ounis, “Unifying explicit and implicit feedback for rating prediction and ranking recommendation tasks,” inProceedings of the 2019 ACM SIGIR International Confer- ence on Theory of Information Retrieval, ICTIR ’19, (New York, NY , USA), p. 149–156, Association for Computing Machinery, 2019

    2019

Show all 111 references
  1. [9]

    Lightgcn: Simplifying and powering graph convolution network for recommenda- tion,

    X. He, K. Deng, X. Wang, Y . Li, Y . Zhang, and M. Wang, “Lightgcn: Simplifying and powering graph convolution network for recommenda- tion,” inProceedings of the 43rd International ACM SIGIR conference on research and development in Information Retrieval, pp. 639–648, 2020

    2020

  2. [10]

    Neural graph collaborative filtering,

    X. Wang, X. He, M. Wang, F. Feng, and T.-S. Chua, “Neural graph collaborative filtering,” inProceedings of the 42nd international ACM SIGIR conference on Research and development in Information Re- trieval, pp. 165–174, 2019

    2019

  3. [11]

    Inductive matrix completion based on graph neural networks,

    M. Zhang and Y . Chen, “Inductive matrix completion based on graph neural networks,” inInternational Conference on Learning Represent- ations, 2020

    2020

  4. [12]

    Explicit feedbacks meet with implicit feedbacks: A combined approach for recommendation system,

    S. Mandal and A. Maiti, “Explicit feedbacks meet with implicit feedbacks: A combined approach for recommendation system,” in Proceedings of the 7th International Conference on Complex Networks and Their Applications, p. 12, Springer, 2018

    2018

  5. [13]

    Unifying explicit and implicit feedback for rating prediction and ranking recommendation tasks,

    A. H. Jadidinejad, C. Macdonald, and I. Ounis, “Unifying explicit and implicit feedback for rating prediction and ranking recommendation tasks,” inProceedings of the 2019 ACM SIGIR International Confer- ence, pp. 123–132, 2019

    2019

  6. [14]

    Probabilistic matrix factoriza- tion,

    A. Mnih and R. R. Salakhutdinov, “Probabilistic matrix factoriza- tion,” inAdvances in Neural Information Processing Systems, vol. 20, pp. 1257–1264, Curran Associates, Inc., 2007

    2007

  7. [15]

    Providing reliability in recommender systems through bernoulli matrix factorization,

    F. Ortega, R. Lara-Cabrera, Ángel González-Prieto, and J. Bobadilla, “Providing reliability in recommender systems through bernoulli matrix factorization,”Information Sciences, vol. 553, pp. 110–128, 2021

    2021

  8. [16]

    Generalized probabilistic matrix factor- izations for collaborative filtering,

    H. Shan and A. Banerjee, “Generalized probabilistic matrix factor- izations for collaborative filtering,” inICDM 2010, The 10th IEEE International Conference on Data Mining, Sydney, Australia, 14-17 December 2010, pp. 1025–1030, 2010

    2010

  9. [17]

    Scalable recommendation with hierarchical poisson factorization,

    P. Gopalan, J. M. Hofman, and D. M. Blei, “Scalable recommendation with hierarchical poisson factorization,” inProceedings of the Thirty- First Conference on Uncertainty in Artificial Intelligence, UAI 2015, July 12-16, 2015, Amsterdam, The Netherlands, pp. 326–335, 2015

    2015

  10. [18]

    BPR: bayesian personalized ranking from implicit feedback,

    S. Rendle, C. Freudenthaler, Z. Gantner, and L. Schmidt-Thieme, “BPR: bayesian personalized ranking from implicit feedback,” inUAI 2009, Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence, Montreal, QC, Canada, June 18-21, 2009, pp. 452–461, 2009

    2009

  11. [19]

    Neural network matrix factorization,

    G. K. Dziugaite and D. M. Roy, “Neural network matrix factorization,” arXiv preprint arXiv:1511.06443, 2015

    2015 arXiv

  12. [20]

    Comparative convolu- tional dynamic multi-attention recommendation model,

    J. Ni, Z. Huang, C. Yu, D. Lv, and C. Wang, “Comparative convolu- tional dynamic multi-attention recommendation model,”IEEE Trans- actions on Neural Networks and Learning Systems, vol. 33, no. 8, pp. 3510–3521, 2022

    2022

  13. [21]

    Kernelized deep learning for matrix factorization recommendation system using explicit and implicit information,

    X. Zheng, Z. Ni, X. Zhong, and Y . Luo, “Kernelized deep learning for matrix factorization recommendation system using explicit and implicit information,”IEEE Transactions on Neural Networks and Learning Systems, vol. 35, no. 1, pp. 1205–1216, 2024

    2024

  14. [22]

    Collaborative denoising auto-encoders for top-n recommender systems,

    Y . Wu, C. DuBois, A. X. Zheng, and M. Ester, “Collaborative denoising auto-encoders for top-n recommender systems,” inProceedings of the Ninth ACM International Conference on Web Search and Data Mining, San Francisco, CA, USA, February 22-25, 2016, pp. 153–162, 2016

    2016

  15. [23]

    Variational autoencoders for collaborative filtering,

    D. Liang, R. G. Krishnan, M. D. Hoffman, and T. Jebara, “Variational autoencoders for collaborative filtering,” inProceedings of the 2018 World Wide Web Conference on World Wide Web, WWW 2018, Lyon, France, April 23-27, 2018, pp. 689–698, 2018

    2018

  16. [24]

    Bilateral variational au- toencoder for collaborative filtering,

    Q.-T. Truong, A. Salah, and H. W. Lauw, “Bilateral variational au- toencoder for collaborative filtering,” inProceedings of the 14th ACM International Conference on Web Search and Data Mining, pp. 292– 300, 2021

    2021

  17. [25]

    Representation learn- ing: serial-autoencoder for personalized recommendation,

    Y . Zhu, Y . Geng, Y . Li, J. Qiang, and X. Wu, “Representation learn- ing: serial-autoencoder for personalized recommendation,”Frontiers of Computer Science, vol. 18, no. 4, p. 184316, 2024

    2024

  18. [26]

    Convolutional mat- rix factorization for document context-aware recommendation,

    D. Kim, C. Park, J. Oh, S. Lee, and H. Yu, “Convolutional mat- rix factorization for document context-aware recommendation,” in 14 Proceedings of the 10th ACM conference on recommender systems, pp. 233–240, 2016

    2016

  19. [27]

    Collaborative deep learning for recommender systems,

    H. Wang, N. Wang, and D.-Y . Yeung, “Collaborative deep learning for recommender systems,” inProceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining, pp. 1235–1244, 2015

    2015

  20. [28]

    Exploring user retrieval integration towards large language models for cross-domain sequential recommendation,

    T. Shen, H. Wang, J. Zhang, S. Zhao, L. Li, Z. Chen, D. Lian, and E. Chen, “Exploring user retrieval integration towards large language models for cross-domain sequential recommendation,”arXiv preprint arXiv:2406.03085, 2024

    2024 arXiv

  21. [29]

    Knowledge graphs and pretrained language models enhanced representation learning for conversational recommender systems,

    Z. Qiu, Y . Tao, S. Pan, and A. W.-C. Liew, “Knowledge graphs and pretrained language models enhanced representation learning for conversational recommender systems,”IEEE Transactions on Neural Networks and Learning Systems, 2024

    2024

  22. [30]

    Vbpr: Visual bayesian personalized ranking from implicit feedback.,

    R. He and J. McAuley, “Vbpr: Visual bayesian personalized ranking from implicit feedback.,” inAAAI, pp. 144–150, 2016

    2016

  23. [31]

    Graph convolution network based recommender systems: Learning guarantee and item mixture powered strategy,

    L. Deng, D. Lian, C. Wu, and E. Chen, “Graph convolution network based recommender systems: Learning guarantee and item mixture powered strategy,”Advances in Neural Information Processing Systems, vol. 35, pp. 3900–3912, 2022

    2022

  24. [32]

    Graph convolutional adversarial networks for spatiotemporal anomaly detection,

    L. Deng, D. Lian, Z. Huang, and E. Chen, “Graph convolutional adversarial networks for spatiotemporal anomaly detection,”IEEE Transactions on Neural Networks and Learning Systems, vol. 33, no. 6, pp. 2416–2428, 2022

    2022

  25. [33]

    Rethinking and accelerating graph condensation: A training- free approach with class partition,

    X. Gao, T. Chen, W. Zhang, J. Yu, G. Ye, Q. V . H. Nguyen, and H. Yin, “Rethinking and accelerating graph condensation: A training- free approach with class partition,”arXiv preprint arXiv:2405.13707, 2024

    2024 arXiv

  26. [34]

    Multi-behavior graph neural networks for recommender system,

    L. Xia, C. Huang, Y . Xu, P. Dai, and L. Bo, “Multi-behavior graph neural networks for recommender system,”IEEE Transactions on Neural Networks and Learning Systems, vol. 35, no. 4, pp. 5473–5487, 2022

    2022

  27. [35]

    Siren: Sign-aware recommendation using graph neural networks,

    C. Seo, K.-J. Jeong, S. Lim, and W.-Y . Shin, “Siren: Sign-aware recommendation using graph neural networks,”IEEE Transactions on Neural Networks and Learning Systems, vol. 35, no. 4, pp. 4729–4743, 2022

    2022

  28. [36]

    Diversify- ing collaborative filtering via graph spreading network and selective sampling,

    Y . Fang, H. Wu, Y . Zhao, L. Zhang, S. Qin, and X. Wang, “Diversify- ing collaborative filtering via graph spreading network and selective sampling,”IEEE Transactions on Neural Networks and Learning Systems, 2023

    2023

  29. [37]

    Trustgnn: Graph neural network-based trust evaluation via learnable propagative and composable nature,

    C. Huo, D. He, C. Liang, D. Jin, T. Qiu, and L. Wu, “Trustgnn: Graph neural network-based trust evaluation via learnable propagative and composable nature,”IEEE Transactions on Neural Networks and Learning Systems, 2023

    2023

  30. [38]

    On deep learning for trust-aware recommendations in social networks,

    S. Deng, L. Huang, G. Xu, X. Wu, and Z. Wu, “On deep learning for trust-aware recommendations in social networks,”IEEE transactions on neural networks and learning systems, vol. 28, no. 5, pp. 1164– 1177, 2016

    2016

  31. [39]

    Rethink- ing missing data: Aleatoric uncertainty-aware recommendation,

    C. Wang, F. Feng, Y . Zhang, Q. Wang, X. Hu, and X. He, “Rethink- ing missing data: Aleatoric uncertainty-aware recommendation,”IEEE Transactions on Big Data, 2023

    2023

  32. [40]

    Uncertainty-adjusted recommend- ation via matrix factorization with weighted losses,

    R. Alves, A. Ledent, and M. Kloft, “Uncertainty-adjusted recommend- ation via matrix factorization with weighted losses,”IEEE Transactions on Neural Networks and Learning Systems, 2023

    2023

  33. [41]

    Federated learning enabled graph convolutional autoencoder and factorization machine for po- tential friendship prediction in social networks,

    H.-x. Hu, C. Cao, Q. Hu, and Y . Zhang, “Federated learning enabled graph convolutional autoencoder and factorization machine for po- tential friendship prediction in social networks,”Information Fusion, vol. 102, p. 102042, 2024

    2024

  34. [42]

    Multi- view enhanced graph attention network for session-based music re- commendation,

    D. Wang, X. Zhang, Y . Yin, D. Yu, G. Xu, and S. Deng, “Multi- view enhanced graph attention network for session-based music re- commendation,”ACM Transactions on Information Systems, vol. 42, no. 1, pp. 1–30, 2023

    2023

  35. [43]

    Intent-aware graph neural network for point-of-interest embedding and recommendation,

    X. Wang, D. Wang, D. Yu, R. Wu, Q. Yang, S. Deng, and G. Xu, “Intent-aware graph neural network for point-of-interest embedding and recommendation,”Neurocomputing, vol. 557, p. 126734, 2023

    2023

  36. [44]

    Multi-granularity interest retrieval and refinement net- work for long-term user behavior modeling in ctr prediction,

    X. Xu, H. Wang, W. Guo, L. Zhang, W. Yang, R. Yu, Y . Liu, D. Lian, and E. Chen, “Multi-granularity interest retrieval and refinement net- work for long-term user behavior modeling in ctr prediction,”arXiv preprint arXiv:2411.15005, 2024

    2024 arXiv

  37. [45]

    Multi-knowledge enhanced graph convolution for learning resource recommendation,

    Y . Dong, Y . Liu, Y . Dong, Y . Wang, and M. Chen, “Multi-knowledge enhanced graph convolution for learning resource recommendation,” Knowledge-Based Systems, vol. 291, p. 111521, 2024

    2024

  38. [46]

    Fuxi-alpha: Scaling recommendation model with feature interaction enhanced transformer,

    Y . Ye, W. Guo, J. Y . Chin, H. Wang, H. Zhu, X. Lin, Y . Ye, Y . Liu, R. Tang, D. Lian,et al., “Fuxi-alpha: Scaling recommendation model with feature interaction enhanced transformer,”arXiv preprint arXiv:2502.03036, 2025

    2025 arXiv

  39. [47]

    Knowledge-guided article embedding refinement for session-based news recommendation,

    H.-S. Sheu, Z. Chu, D. Qi, and S. Li, “Knowledge-guided article embedding refinement for session-based news recommendation,”IEEE Transactions on Neural Networks and Learning Systems, vol. 33, no. 12, pp. 7921–7927, 2022

    2022

  40. [48]

    Music recommendation via hypergraph embedding,

    V . L. Gatta, V . Moscato, M. Pennone, M. Postiglione, and G. Sperlí, “Music recommendation via hypergraph embedding,”IEEE Transac- tions on Neural Networks and Learning Systems, vol. 34, no. 10, pp. 7887–7899, 2023

    2023

  41. [49]

    Modeling self-representation label correlations for textual aspects and emojis recommendation,

    T. Wei, T. W. S. Chow, and J. Ma, “Modeling self-representation label correlations for textual aspects and emojis recommendation,” IEEE Transactions on Neural Networks and Learning Systems, vol. 34, no. 12, pp. 10762–10774, 2023

    2023

  42. [50]

    Category-aware self- supervised graph neural network for session-based recommendation,

    X. Wang, X. Zhang, X. He, and T.-S. Chua, “Category-aware self- supervised graph neural network for session-based recommendation,” World Wide Web, vol. 27, pp. 1055–1074, 2024

    2024

  43. [51]

    Dynamically expandable graph convolution for streaming recommendation,

    Y . Liu, L. Zhang, P. Li, S. Zhang, and C. Wu, “Dynamically expandable graph convolution for streaming recommendation,”Expert Systems with Applications, vol. 213, p. 122773, 2023

    2023

  44. [52]

    A survey on reinforcement learning for recommender systems,

    Y . Lin, Y . Liu, F. Lin, L. Zou, P. Wu, W. Zeng, H. Chen, and C. Miao, “A survey on reinforcement learning for recommender systems,”IEEE Transactions on Neural Networks and Learning Systems, vol. 35, no. 10, pp. 13164–13184, 2024

    2024

  45. [53]

    Plug-and-play model-agnostic counterfactual policy synthesis for deep reinforcement learning-based recommendation,

    S. Wang, X. Chen, J. McAuley, S. Cripps, and L. Yao, “Plug-and-play model-agnostic counterfactual policy synthesis for deep reinforcement learning-based recommendation,”IEEE Transactions on Neural Net- works and Learning Systems, vol. 36, no. 1, pp. 1044–1055, 2025

    2025

  46. [54]

    Dynamic and static representation learning network for recommendation,

    T. Liu, S. Lou, J. Liao, and H. Feng, “Dynamic and static representation learning network for recommendation,”IEEE Transactions on Neural Networks and Learning Systems, vol. 35, no. 1, pp. 831–841, 2024

    2024

  47. [55]

    Time interval- enhanced graph neural network for shared-account cross-domain se- quential recommendation,

    L. Guo, J. Zhang, L. Tang, T. Chen, L. Zhu, and H. Yin, “Time interval- enhanced graph neural network for shared-account cross-domain se- quential recommendation,”IEEE Transactions on Neural Networks and Learning Systems, vol. 35, no. 3, pp. 4002–4016, 2024

    2024

  48. [56]

    Tea: A sequential recommendation framework via temporally evolving aggregations,

    Z. Li, R. Cai, F. Wu, S. Zhang, H. Gu, Y . Hao, and Y . Yan, “Tea: A sequential recommendation framework via temporally evolving aggregations,”IEEE Transactions on Neural Networks and Learning Systems, vol. 35, no. 2, pp. 2628–2639, 2024

    2024

  49. [57]

    A survey on federated recommendation systems,

    Z. Sun, Y . Xu, Y . Liu, W. He, L. Kong, F. Wu, Y . Jiang, and L. Cui, “A survey on federated recommendation systems,”IEEE Transactions on Neural Networks and Learning Systems, vol. 36, no. 1, pp. 6–20, 2025

    2025

  50. [58]

    Privfr: Privacy-enhanced feder- ated recommendation with shared hash embedding,

    H. Zhang, X. Zhou, Z. Shen, and Y . Li, “Privfr: Privacy-enhanced feder- ated recommendation with shared hash embedding,”IEEE Transactions on Neural Networks and Learning Systems, vol. 36, no. 1, pp. 32–46, 2025

    2025

  51. [59]

    Estimating and evaluating the uncertainty of rating predictions and top-n recommendations in recommender systems,

    V . Coscrato and D. Bridge, “Estimating and evaluating the uncertainty of rating predictions and top-n recommendations in recommender systems,”ACM Transactions on Recommender Systems, vol. 1, no. 2, pp. 7:1–7:34, 2023

    2023

  52. [60]

    Ordrec: An ordinal model for predicting personalized item rating distributions,

    Y . Koren and J. Sill, “Ordrec: An ordinal model for predicting personalized item rating distributions,” inProceedings of the 5th ACM Conference on Recommender Systems, pp. 117–124, 2011

    2011

  53. [61]

    Modeling user rating profiles for collaborative filter- ing,

    B. M. Marlin, “Modeling user rating profiles for collaborative filter- ing,” inProceedings of the 16th International Conference on Neural Information Processing Systems, pp. 627–634, 2003

    2003

  54. [62]

    An introduction to matrix factorization and factorization machines in recommendation system, and beyond,

    Y . Zhang, “An introduction to matrix factorization and factorization machines in recommendation system, and beyond,”arXiv preprint arXiv:2203.11026, 2022

    2022 arXiv

  55. [63]

    Explainable recommendation via interpretable feature mapping and evaluation of explainability,

    D. Pan, X. Li, X. Li, and D. Zhu, “Explainable recommendation via interpretable feature mapping and evaluation of explainability,” inProceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence (IJCAI-20), pp. 2690–2696, 2020

    2020

  56. [64]

    The you- tube video recommendation system,

    J. Davidson, B. Liebald, J. Liu, P. Nandy, T. V . Vleet, U. Gargi, S. Gupta, Y . He, M. Lambert, B. Livingston, and et al., “The you- tube video recommendation system,” inProceedings of the 4th ACM conference on Recommender systems, pp. 293–296, ACM, 2010

    2010

  57. [65]

    Explainable recommendation: A survey and new perspectives,

    Y . Zhang and X. Chen, “Explainable recommendation: A survey and new perspectives,”Foundations and Trends® in Information Retrieval, vol. 14, no. 1, pp. 1–101, 2020

    2020

  58. [66]

    Matrix completion with the trace norm: Learning, bounding, and transducing,

    O. Shamir and S. Shalev-Shwartz, “Matrix completion with the trace norm: Learning, bounding, and transducing,”Journal of Machine Learning Research, vol. 15, pp. 3401–3423, 2014

    2014

  59. [67]

    Speedup matrix completion with side information: Application to multi-label learning,

    M. Xu, R. Jin, and Z.-H. Zhou, “Speedup matrix completion with side information: Application to multi-label learning,” inProceedings of the 26th International Conference on Neural Information Processing Systems - Volume 2, NIPS’13, (Red Hook, NY , USA), p. 2301–2309, Curran As...

    2013

  60. [68]

    A pac-bayesian approach to generalization bounds for graph neural networks,

    R. Liao, R. Urtasun, and R. Zemel, “A pac-bayesian approach to generalization bounds for graph neural networks,”arXiv, 2020

    2020

  61. [69]

    Stability and generalization of graph convolutional neural networks,

    S. Verma and Z.-L. Zhang, “Stability and generalization of graph convolutional neural networks,” inProceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp. 1539–1548, 2019

    2019

  62. [70]

    Generalization bounds for graph convolutional neural networks via rademacher complexity,

    S. Lv, “Generalization bounds for graph convolutional neural networks via rademacher complexity,”arXiv preprint arXiv:2102.10234, 2021

    2021 arXiv

  63. [71]

    Learning the- ory can (sometimes) explain generalisation in graph neural networks,

    P. Esser, L. Chennuru Vankadara, and D. Ghoshdastidar, “Learning the- ory can (sometimes) explain generalisation in graph neural networks,” Advances in Neural Information Processing Systems, 2021

    2021

  64. [72]

    Foundations and frontiers of graph learning theory,

    Y . Huang, M. Zhou, M. Yang, Z. Wang, M. Zhang, J. Wang, H. Xie, H. Wang, D. Lian, and E. Chen, “Foundations and frontiers of graph learning theory,”arXiv preprint arXiv:2407.03125, 2024

    2024 arXiv

  65. [73]

    Spectrally-normalized margin bounds for neural networks,

    P. L. Bartlett, D. J. Foster, and M. J. Telgarsky, “Spectrally-normalized margin bounds for neural networks,”Advances in Neural Information Processing Systems, vol. 30, pp. 6240–6249, 2017

    2017

  66. [74]

    Size-free generalization bounds for con- volutional neural networks,

    P. M. Long and H. Sedghi, “Size-free generalization bounds for con- volutional neural networks,” inInternational Conference on Learning Representations, 2020

    2020

  67. [75]

    On measuring excess capacity in neural networks,

    F. Graf, S. Zeng, B. Rieck, M. Niethammer, and R. Kwitt, “On measuring excess capacity in neural networks,” 2022

    2022

  68. [76]

    Norm-based general- isation bounds for deep multi-class convolutional neural networks,

    A. Ledent, W. Mustafa, Y . Lei, and M. Kloft, “Norm-based general- isation bounds for deep multi-class convolutional neural networks,” in Proceedings of the AAAI Conference on Artificial Intelligence, 2021

    2021

  69. [77]

    Neural tangent kernel: Conver- gence and generalization in neural networks,

    A. Jacot, F. Gabriel, and C. Hongler, “Neural tangent kernel: Conver- gence and generalization in neural networks,” inAdvances in Neural Information Processing Systems, vol. 31, Curran Associates, Inc., 2018

    2018

  70. [78]

    Fine-grained analysis of optimization and generalization for overparameterized two-layer neural networks,

    S. Arora, S. Du, W. Hu, Z. Li, and R. Wang, “Fine-grained analysis of optimization and generalization for overparameterized two-layer neural networks,” inICML, 2019

    2019

  71. [79]

    Gradient descent prov- ably optimizes over-parameterized neural networks,

    S. S. Du, X. Zhai, B. Poczos, and A. Singh, “Gradient descent prov- ably optimizes over-parameterized neural networks,” inInternational Conference on Learning Representations, 2019

    2019

  72. [80]

    Generalization bounds for unsupervised and semi-supervised learning with autoencoders,

    B. Epstein and R. Meir, “Generalization bounds for unsupervised and semi-supervised learning with autoencoders,” 2019

    2019

  73. [81]

    Lp-norm Sauer–Shelah lemma for margin multi- category classifiers,

    Y . Guermeur, “Lp-norm Sauer–Shelah lemma for margin multi- category classifiers,”Journal of Computer and System Sciences, 2017

    2017

  74. [82]

    Rademacher complexity and generalization performance of multi-category margin classifiers,

    K. Musayeva, F. Lauer, and Y . Guermeur, “Rademacher complexity and generalization performance of multi-category margin classifiers,” Neurocomputing, vol. 342, pp. 6 – 15, 2019. Advances in artificial neural networks, machine learning and computational intelligence

    2019

  75. [83]

    Vc theory of large margin multi-category classifiers.,

    Y . Guermeur, “Vc theory of large margin multi-category classifiers.,” Journal of Machine Learning Research, vol. 8, pp. 2551–2594, 11 2007

    2007

  76. [84]

    Implicit bias of large depth networks: a notion of rank for nonlinear functions,

    A. Jacot, “Implicit bias of large depth networks: a notion of rank for nonlinear functions,” 2022

    2022

  77. [85]

    Generalization analysis of deep non-linear matrix completion,

    A. Ledent and R. Alves, “Generalization analysis of deep non-linear matrix completion,” inProceedings of the 41st International Con- ference on Machine Learning, vol. 235 ofProceedings of Machine Learning Research, pp. 26290–26360, PMLR, 21–27 Jul 2024

    2024

  78. [86]

    Implicit bias of sgd inl_2-regularized linear dnns: One-way jumps from high to low rank,

    Z. Wang and A. Jacot, “Implicit bias of sgd inl_2-regularized linear dnns: One-way jumps from high to low rank,” inThe Twelfth Interna- tional Conference on Learning Representations (ICLR), 2023

    2023

  79. [87]

    Multi-class svms: From tighter data-dependent generalization bounds to novel algorithms,

    Y . Lei, Ürün Dogan, A. Binder, and M. Kloft, “Multi-class svms: From tighter data-dependent generalization bounds to novel algorithms,” in Advances in Neural Information Processing Systems, 2015

    2015

  80. [88]

    Fine-grained generalization analysis of vector-valued learning,

    L. Wu, A. Ledent, Y . Lei, and M. Kloft, “Fine-grained generalization analysis of vector-valued learning,” inProceedings of the AAAI Con- ference on Artificial Intelligence, vol. 35, pp. 10338–10346, 2021

    2021

  81. [89]

    Fine-grained gener- alization analysis of structured output prediction,

    W. Mustafa, Y . Lei, A. Ledent, and M. Kloft, “Fine-grained gener- alization analysis of structured output prediction,” inProceedings of the Thirtieth International Joint Conference on Artificial Intelligence, IJCAI-21(Z.-H. Zhou, ed.), pp. 2841–2847, International Joint Con- ...

    2021

  82. [90]

    Matrix completion and low-rank svd via fast alternating least squares,

    T. Hastie, R. Mazumder, J. D. Lee, and R. Zadeh, “Matrix completion and low-rank svd via fast alternating least squares,”Journal of Machine Learning Research, vol. 16, no. 104, pp. 3367–3402, 2015

    2015

  83. [91]

    Orthogonal inductive matrix completion,

    A. Ledent, R. Alves, and M. Kloft, “Orthogonal inductive matrix completion,”IEEE Transactions on Neural Networks and Learning Systems, pp. 1–12, 2021

    2021

  84. [92]

    Xsimgcl: Towards extremely simple graph contrastive learning for recommenda- tion,

    J. Yu, X. Xia, T. Chen, L. Cui, N. Q. V . Hung, and H. Yin, “Xsimgcl: Towards extremely simple graph contrastive learning for recommenda- tion,”IEEE Transactions on Knowledge and Data Engineering, vol. 36, no. 2, pp. 913–926, 2023

    2023

  85. [93]

    Dtcdr: A framework for dual-target cross-domain recommendation,

    F. Zhu, C. Chen, Y . Wang, G. Liu, and X. Zheng, “Dtcdr: A framework for dual-target cross-domain recommendation,” inProceedings of the 28th ACM International Conference on Information and Knowledge Management, pp. 1533–1542, 2019

    2019

  86. [94]

    Justifying recommendations using distantly-labeled reviews and fine-grained aspects,

    J. Ni, J. Li, and J. McAuley, “Justifying recommendations using distantly-labeled reviews and fine-grained aspects,” inProceedings of the 2019 conference on empirical methods in natural language pro- cessing and the 9th international joint conference on natural language proces...

    2019

  87. [95]

    High-dimensional probability,

    R. Vershynin, “High-dimensional probability,” 2019

    2019

  88. [96]

    Covering number bounds of certain regularized linear function classes,

    T. Zhang, “Covering number bounds of certain regularized linear function classes,”J. Mach. Learn. Res., vol. 2, pp. 527–550, Mar. 2002

    2002

  89. [97]

    Collaborative filtering with the trace norm: Learning, bounding, and transducing,

    O. Shamir and S. Shalev-Shwartz, “Collaborative filtering with the trace norm: Learning, bounding, and transducing,” inProceedings of the 24th Annual Conference on Learning Theory, vol. 19 ofProceedings of Machine Learning Research, pp. 661–678, PMLR, 2011

    2011

  90. [98]

    Matrix reconstruction with the local max norm,

    R. Foygel, N. Srebro, and R. R. Salakhutdinov, “Matrix reconstruction with the local max norm,” inAdvances in Neural Information Pro- cessing Systems(F. Pereira, C. J. C. Burges, L. Bottou, and K. Q. Weinberger, eds.), vol. 25, Curran Associates, Inc., 2012

    2012

  91. [99]

    Learning with the weighted trace-norm under arbitrary sampling distributions,

    R. Foygel, O. Shamir, N. Srebro, and R. R. Salakhutdinov, “Learning with the weighted trace-norm under arbitrary sampling distributions,” Advances in neural information processing systems, vol. 24, 2011

    2011

  92. [100]

    Using side information to reliably learn low-rank matrices from missing and corrupted obser- vations,

    K.-Y . Chiang, I. S. Dhillon, and C.-J. Hsieh, “Using side information to reliably learn low-rank matrices from missing and corrupted obser- vations,”J. Mach. Learn. Res., 2018

    2018

  93. [101]

    Matrix completion with noisy side information,

    K.-Y . Chiang, C.-J. Hsieh, and I. S. Dhillon, “Matrix completion with noisy side information,” inAdvances in Neural Information Processing Systems(C. Cortes, N. Lawrence, D. Lee, M. Sugiyama, and R. Garnett, eds.), vol. 28, Curran Associates, Inc., 2015

    2015

  94. [102]

    Fine-grained gener- alization analysis of inductive matrix completion,

    A. Ledent, R. Alves, Y . Lei, and M. Kloft, “Fine-grained gener- alization analysis of inductive matrix completion,” inAdvances in Neural Information Processing Systems(M. Ranzato, A. Beygelzimer, Y . Dauphin, P. Liang, and J. W. Vaughan, eds.), vol. 34, pp. 25540– 25552, Curr...

    2021

  95. [103]

    Rademacher complexity,

    C. Scott, “Rademacher complexity,”Lecture Notes, vol. Statistical Learning Theory, 2014

    2014

  96. [104]

    Ledoux and M

    M. Ledoux and M. Talagrand,Probability in Banach Spaces: isoperi- metry and processes, vol. 23. Springer Science & Business Media, 1991

    1991

  97. [105]

    Generalization error bounds for bayesian mixture algorithms,

    R. Meir and T. Zhang, “Generalization error bounds for bayesian mixture algorithms,”Journal of Machine Learning Research, vol. 4, no. Oct, pp. 839–860, 2003. 16 Notation Meaning }.} Spectral Norm }.}F r Froebenius Norm m(resp.n) Height (resp. width) of Ground Truth Matrix rms(...

    2003

  98. [106]

    For allAPB ℓ,F ℓ Ap.q:V ℓ´1 ÑV ℓ iss ℓ-Lipschitz with respect to the norms| .|ℓ´1 and| .|ℓ onV ℓ´1 and Vℓ respectively

  99. [107]

    1ifℓďL 0´1,U“nifL 0 ďℓďL,} .}ℓ,σ “ }.} (forℓďL´1),} .}ℓ,σ“} .J}2,8 (forℓ“L), with| .|ℓ being our layer specific norm} .}ℓ (cf. beginning of Section B) and withC ϵ,ℓ,n“256 log

    For allℓPt1,2, . . . , Lu, allbą0, allZ 1, Z2, . . . , ZN P Vℓ´1 such that|Z i|ℓ´1 ďb@iand allϵą0, there exists a subsetC ℓpb, Z, ϵqĂBℓ such that logp#pC ℓ,ϵ,npb, Z, ϵqqqďCℓ,ϵ,na2 l b2 ϵ2 ,(C.1) whereC ℓ,ϵ,n is some function ofℓ, ϵ, n(anda., b.) and, for allAPB ℓ, there exists...

  100. [108]

    For allθ 2PW a. ,s. there exists a sθ2PW a. ,s. such that for any¯xPC 1, we have ˇˇgθ2p¯xqj,k´f g¯θ2p¯xqj,k ˇˇďϵ 2.@k

  101. [109]

    1 s2 ℓ ff« Lÿ ℓ“1 ˆ aℓ sℓ ˙ 2 3 ff3 ˆ log ˆ D2n „ 16amaxS ϵ2 `7 ȷ„ 6χ ϵ1 `1 ȷ˙ . Now, define the following cover ofB m χ ˆW a. ,s. : sC:“C ˆm 0 ˆC 1. This induces a

    The cardinality of the coverC 0 is bounded by logp|C1|qď4χ 2C˚ ϵ2,n « Lź ℓ“1 s2 ℓ ff« Lÿ ℓ“1 ˆ aℓ sℓϵ ˙ 2 3 ff3 ď4χ 2C˚ ϵ2,n L2 ϵ2 2 « Lź ℓ“1 s2 ℓ ff Lÿ ℓ“1 ˆ aℓ sℓ ˙2 .(C.7) where, writinga max formaxpa 1, . . . ,Lq, C˚ ϵ2,n :“max ℓďL Cℓ,ϵ2 ď256 log „ˆ 16amaxS ϵ2 `7 ˙ rN D2n ...

  102. [110]

    With probability greater than1´δover the draw of the training setΩ, for every set of parametersθ 1, θ2 satisfying the following conditions: }W ℓ}ℓďs ℓ @ℓďL››› ` W ℓ´M ℓ˘J››› 2,1 ďa ℓ @ℓďL´1 ››› ` W L´M L˘J››› Fr ďa L max iďm }ϕθ1pUiq}ďχ, 26 we have: |PPopulation´P Empirical| ď...

  103. [111]

    This implies that training with our cross entropy loss provably allows the model to recover the precise sampling distribution, and to make accurate implicit feedback prediction. Interestingly, it also applies that training with our cross entropy loss also guarantees good perfo...

Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.