Writing study: Generalization Bounds for Semi-supervised Matrix Completion with Distributional Side Information
← AAAI 2026 oral writing corpus
Antoine Ledent, Soo Mun Chong, Nong Minh Hieu · Official AAAI 2026 oral record
Figure, table and section ledger
Editorial contribution type: Theory & formal analysis (primary).
Layout extraction, not a required paper template. Counts are distinct caption labels; a multi-panel figure counts once. Section spans are estimated from heading positions, including floats and whitespace. Method and limitations.
- Canonical PDF
- 9 physical pages
- Before references / appendix
- ≈ 7.09 page-equivalents
- Main figures / tables
- 1 / 1
- Attached appendix figures / tables
- 0 / 0
- Attached appendix span
- No boundary detected; not assumed zero
Extraction notes: No attached appendix boundary detected. Zero means no recognized caption, not independently verified absence.
Source-bound correction: Checked 2026-10-25 against main-paper reading, physical-page rasters 5–7 and Poppler boxes. Main Results on p.3 is a top-level heading; the smaller Main Results on p.5 is a subsection and must not double-count the main section. Figure 1 is the p.6 diagnostic scatter and Table 1 the p.7 RMSE comparison. Algorithm 1 is not included in the two-kind figure/table count. No attached appendix.
Section-by-section lengths and source pages
The title/abstract/front matter precede the first numbered heading. A span ends at the next detected top-level heading, not at the last sentence; end-page whitespace is included. References and statements are listed separately. These are not measurements of text-only or artwork area.
All detected figure and table locations
Main text
Attached appendix
No recognized caption labels.
Argument and organization
- Introduction; Related Works
Separates plentiful unlabeled interaction pairs from scarce explicit ratings, then positions the learning setting against inductive completion, implicit feedback and distribution-dependent evaluation.
- Main Results: Learning Setting and Assumptions; Model; Main Results
Defines the shared low-rank setting and seven assumptions before the two-stage algorithm, generalization theorem, excess-risk corollary and interpretation of the two error sources. The repeated Main Results label is a subsection within the larger main section.
- Experiments: Synthetic Data Experiments; Real Data Experiments
Names two claims explicitly, tests the additive-error explanation in controlled synthetic data, then asks whether unlabeled interactions help rating prediction under label removal.
- Conclusion; Acknowledgements; References
Restates the conditional rate and the distinction between sampling information and rating labels, while identifying assumptions and the nonlinear implementation gap as future work.
Problem, claim and contribution
Frames a change in the information available to the learner, not simply a new recommender leaderboard result: interaction locations estimate shared row/column subspaces, while the smaller labeled sample fits ratings within them. Related work distinguishes in-distribution risk under the sampling distribution from other completion objectives. This makes the claimed sample-efficiency benefit intelligible before the bound is introduced.
Introduction and Related Works, physical pp.1–3; Learning Setting, p.3 · Main paper
Argument and section order
Lists seven assumptions before presenting the model and Algorithm 1. Theorem 1 retains several terms, and the corollary and following interpretation explain when the interaction term can be absorbed. A practical factorized/Lagrangian optimization is distinguished from the constrained theoretical formulation. This is an assumption-to-algorithm-to-guarantee outline, not an architecture-first outline.
Assumptions 1–7, pp.3–4; Equations 9–16, Algorithm 1, Theorem 1 and Corollary 1, p.5; interpretation, p.6 · Main paper
Figures, captions and visual explanation
The sole numbered figure is a diagnostic scatter plot, not a model diagram: each point is a labeled/unlabeled sample-size configuration, with measured generalization gap on one axis and a sum of two reference-condition gaps on the other. The caption identifies averaging over 30 independent runs. The plot tests whether the theoretical decomposition describes the experiment; its correlation alone is not a proof of independence, and no uncertainty intervals are displayed.
Equation 17, Synthetic Data Experiments and Figure 1, p.6 · Main paper
Tables, comparisons and evidence
The experiments are introduced as Claim 1 and Claim 2, so each visual has a named argumentative role. Table 1 groups three datasets and four methods over eight label-removal fractions, states RMSE direction, and retains cases where IGMC wins at the largest removal fraction. The real-data setup explicitly replaces the theoretical SVD stage with a nonlinear autoencoder; the table therefore illustrates the learning paradigm rather than directly verifying the unchanged theorem algorithm or establishing state-of-the-art recommendation.
Experiments opening and Claim 1–2, p.6; Table 1 and Real Data Experiments, p.7 · Main paper
Appendix and reproducibility
Keeps the assumptions, main guarantee, algorithm and two core tests in the proceedings body, while referring to an appendix for a subspace clarification and synthetic configuration. Those pointers make an evidence trail, but the published nine-page file does not contain the destination. A new paper should provide an explicit accessible version and precise appendix locator instead of assuming that an external pointer establishes reproducibility.
Remark on the shared subspace and synthetic setup pointer, p.6; proceedings ending, pp.8–9 · Main paper
Clarity and writing conventions
Repeatedly translates the bound into the roles of unlabeled and labeled samples, and explicitly says that the real-data experiment aims to demonstrate the learning setting rather than a state-of-the-art recommender. That scope-aware wording is worth adopting. The simplified headline rate must still travel with the assumptions and sample-size condition; it should not be recast as an unconditional dimension-free labeled-sample guarantee.
Corollary discussion, pp.5–6; Real Data Experiments and Conclusion, p.7 · Main paper
What to reuse—and what not to infer
Transferable lesson: For a theory-led paper, connect a named claim to each experiment: a controlled diagnostic for the proposed mechanism and a separately qualified practical test. A theorem, concise pseudocode, one purposeful diagnostic plot and one comparative table can tell a complete argument without an arbitrary architecture-figure quota.
Boundary: The shared-subspace, sampling, conditioning and bounded-loss assumptions are substantive. The concise rate hides constants and additional conditions; the main text also prints different forms of the alternative labeled-sample threshold in Equation 15 and the conclusion, which should not be silently reconciled without checking the proof. Real-data DAMC changes the SVD stage, and Table 1 does not report uncertainty or the synthetic experiment's 30-run protocol. No universal sample-complexity or recommender superiority claim is inferred here.
Apply this lesson using the argument and evidence worksheet.
Inspection record and sources
- Checked
- 2026-10-25
- Reading status
- Writing-focused manuscript scan + selected visuals inspected
- Main text
- Writing-oriented reading of the complete main argument on physical pp.1–7, including assumptions, theorem/corollary statements, algorithm, experiment protocols and conclusion; acknowledgements and reference boundary/continuation on pp.8–9 checked. Full-page rasters of pp.5, 6 and 7 inspected. This is not proof verification, a code audit or a reproduction of the results.
- Appendix / supplement
- The nine-page proceedings PDF has no attached appendix. Main-text pointers to the appendix for a subspace remark and synthetic experiment details were inspected. The author manuscript at arXiv:2511.13049 was identified but its PDF and appendix were not read for this study; no coverage of those proofs or settings is claimed.
- Visually inspected PDF pages
- 5, 6, 7
This is a writing-focused scan of the manuscript and the stated supplementary scope: framing, organization, visual explanation, evidence presentation and wording. It is not a line-by-line proof audit, reproduction of results or exhaustive scientific review.