--- name: colt-supplementary description: Use when structuring the appendix of a COLT (Conference on Learning Theory) submission — the unlimited-length proof appendix inside the single PDF — covering body/appendix splitting for a 12-page limit, theorem restatement discipline, lemma ordering, notation tables, and what referees expect to find where. --- # COLT Supplementary COLT's "supplementary material" is the appendix of the same PDF: the 2026 CFP (checked 2026-07-08) capped the main body at 12 PMLR-formatted pages excluding references and put **no page limit on references and appendices**, with the entire manuscript submitted as a single file. There is no separate upload, no later supplement deadline, and no distinction between "appendix" and "supplement" — which changes how you should architect the document compared to venues with detached supplements. ## Consequences of the single-PDF model - The appendix is unambiguously part of the reviewed record; referees are choosing to read it, not to download it. Lower the cost of that choice. - Nothing can be added after the deadline. A proof hole discovered post-submission cannot be patched by a supplement upload the way an artifact fix sometimes can elsewhere. - Length is free but attention is not: a 60-page appendix is normal at COLT, a disorganized one is a soft reject, because the referee's verification budget is the binding constraint. ## The 12-page split decision What must stay in the body: - Formal problem setup: the model, the interaction protocol, the adversary or distributional assumptions, and the performance measure — complete, not "see Appendix A for the model." - Every main theorem statement, with all hypotheses visible. - A proof overview per main theorem: the decomposition, the key lemma, and the step where prior techniques fail. This is what earns the referee's appendix time. - The comparison to nearest prior bounds (a small table often beats prose). What belongs in the appendix: full proofs, auxiliary lemmas, generalized statements, deferred case analyses, extended related work, and any numerical-illustration details. ## Appendix architecture that referees can verify | Appendix section | Contents | Referee use pattern | |---|---|---| | A. Notation and preliminaries | Symbol table, standard inequalities used | Consulted repeatedly; keep to 2-3 pages | | B. Proof of Theorem 1 | Restated theorem, roadmap paragraph, main lemmas, proof | Read linearly, checked line by line | | C. Proof of Theorem 2 | Same pattern | Read only if Theorem 2 matters to the referee | | D. Auxiliary lemmas | Technical facts shared across proofs | Jumped to via references | | E. Deferred discussion / numerics | Extensions, illustration details | Skimmed | Ordering rule: appendix sections mirror body theorem order, and each proof section is self-contained modulo Appendix A and D — a referee verifying Theorem 2 must never need to have read the proof of Theorem 1 unless the dependency is real and declared. ## Restatement discipline Restate every theorem and lemma before its appendix proof, with identical numbering, via a restatable environment rather than copy-paste (drift between two hand-maintained copies of a theorem is a notorious COLT embarrassment): ```latex \usepackage{thmtools, thm-restate} \declaretheorem[name=Theorem]{theorem} % In the body: \begin{restatable}{theorem}{mainregret}\label{thm:main} Under Assumptions 1--2, ALG attains $R_T = O(\sqrt{dT\log K})$. \end{restatable} % In Appendix B: \mainregret* % re-renders Theorem 1 verbatim, same number \begin{proof} We decompose the regret as ... (roadmap sentence first, then the argument). \end{proof} ``` ## Roadmap paragraphs are load-bearing Open each major appendix proof with 4-6 sentences: the decomposition, what each lemma contributes, where the novelty sits, and which steps are routine. Referees use the roadmap to allocate verification effort; proofs without one get either shallow reads (bad for credit) or suspicious reads (bad for scores). ## Vignette: splitting a two-theorem online-learning paper A draft proves an upper bound (algorithm + potential argument, 14 pages of proof) and a lower bound (instance family + information argument, 9 pages), plus one simulation. The COLT-shaped split: - Body: protocol and definitions (2 pp), both theorem statements with remarks (2.5 pp), upper-bound overview with the potential function displayed and one key lemma proved in full (3 pp), lower-bound overview with the instance family drawn as a figure (2 pp), related-work table and discussion (1.5 pp), simulation figure with a two-sentence reading (0.5 pp), intro (1.5 pp) — twelve and a half, so the second remark and one corollary move to the appendix to make twelve. - Appendix: A notation; B full upper-bound proof (restated theorem, roadmap, lemmas); C full lower-bound proof; D auxiliary facts; E simulation procedure. - The key-lemma-in-body choice is deliberate: proving one central lemma completely in the body demonstrates the paper's proof standard where every referee will read it. ## Common appendix defects at COLT - Lemma used before it is stated anywhere, forcing a forward hunt. - "By a standard argument" covering the one step that is actually new. - Notation redefined locally inside an appendix section, colliding with Appendix A. - Case analyses whose cases do not visibly exhaust the space. - Cross-references into the body by page number instead of by label (page numbers shift when the class file changes at camera-ready). - Illustration figures buried between proofs, breaking the verification flow — give numerics their own terminal section. ## Cycle-volatility warnings - The unlimited-appendix, single-PDF rule is the 2026 formulation; earlier cycles phrased limits differently and later ones may again (待核实 in each CFP). - If a cycle ever adds a separate supplement channel or reviewable-code slot, its CFP will say so; do not assume either from this file. ## Output format ```text [Split verdict] body self-contained / decision-critical material trapped in appendix [Appendix map]
theorem it serves> [Restatement check] restatable environments / copy-paste risk [Roadmaps] present for / major proofs [Top structural fix] ```