--- name: colt-reproducibility description: Use when strengthening the reproducibility of a COLT (Conference on Learning Theory) paper, where reproducing means re-deriving — complete proofs, explicit assumptions, tracked constants, correctly invoked external results, self-contained notation — plus seeds and scripts for any numerical illustration the paper carries. --- # COLT Reproducibility At COLT, reproducibility means a competent reader can *re-derive* every claim from the PDF alone. There is no reproducibility checklist form in the COLT 2026 CFP (checked 2026-07-08) — the venue enforces the property the hard way, through referees who attempt the re-derivation during review. This skill is the pre-submission audit that makes that attempt succeed. ## The re-derivability standard A theorem is reproducible when all of the following hold: - Its statement is formally complete: every symbol quantified, every assumption named in the statement itself or cited by an explicit assumption label, the probability space and adversary model unambiguous. - Its proof exists in full inside the submitted PDF — COLT's unlimited appendix removes every excuse for "omitted for lack of space." - Each proof step is locally checkable: an expert reading line k needs only lines 1..k-1, cited external results, and standard background — never your unpublished intuition. - Constants and parameter regimes survive the chain: if Theorem 1 needs n ≥ C·d·log(1/δ), the reader can trace what C is or where it was declared absolute. ## Audit table: where re-derivation fails | Failure mode | Typical symptom in the PDF | Repair | |---|---|---| | Hypothesis smuggling | Proof uses independence never assumed | Add the assumption to the statement, or redo the step | | External-result misuse | "By [X], ..." where [X] needs bounded support you don't have | Check [X]'s hypotheses; find the right variant or prove a lemma | | Constant drift | C doubles silently between two displays | Number constants (C_1, C_2, ...) and track them in a ledger | | Case leakage | "The case d=1 is analogous" when it is not | Write the case or prove the reduction | | Notation overload | Same symbol for a filtration and a function class | One notation table, enforced globally | | Silent regime switch | Bound proved for T large, quoted for all T | State the threshold explicitly in the theorem | ## Assumption bookkeeping pattern Give assumptions their own numbered environment and cite them by label everywhere: ```latex \newtheorem{assumption}{Assumption} \begin{assumption}[Bounded losses]\label{ass:bounded} For all $t$, the loss $\ell_t$ maps to $[0,1]$. \end{assumption} \begin{theorem}\label{thm:regret} Under Assumptions~\ref{ass:bounded} and~\ref{ass:oblivious}, the algorithm's regret satisfies $R_T \le 4\sqrt{T \log K}$ for all $T \ge 1$. \end{theorem} ``` The payoff is auditable dependency: a reviewer can grep which theorems rely on obliviousness, and your rebuttal can answer "is Assumption 2 needed for Theorem 3?" with a pointer instead of an essay. ## Numerical illustrations, when present Some COLT papers plot a simulated regret curve or a phase transition to illustrate a bound. The theory community's floor for those figures: - Fixed seeds, stated replication counts, and error bars whose meaning the caption defines; a noisy single run "consistent with the theory" persuades no one here. - The simulated regime must be the theorem's regime — matching horizon, dimension, and noise assumptions — or the mismatch must be acknowledged as exploratory. - The generating script should be one dependency-light file, releasable after acceptance; during review, describe the procedure precisely in the appendix since no upload channel exists. - Never let an illustration silently extend the claim ("the bound appears to hold for heavy tails too") without labeling it as conjecture. ## Vignette: the spine of a lower-bound paper Consider a submission whose main result is a $\Omega(\sqrt{TK})$ lower bound via a new instance family. Its re-derivability spine, in the order a referee will attack it: - the instance family's construction, with every distribution parameter explicit and the randomization protocol (oblivious vs. adaptive) named; - the information-theoretic step (say, a KL-divergence calculation) with the exact divergence bound displayed, not cited as "standard"; - the reduction from learner performance to the divergence quantity, where hypothesis smuggling most often hides (does the argument secretly assume deterministic learners? say so or generalize); - the final optimization over instance parameters, with the maximizing choice written out — "choosing ε appropriately" is where constants go to die. A referee who can walk this spine without leaving the PDF marks correctness resolved; each externalized step converts into a review question, and three review questions into a reject. ## Pre-submission re-derivation drill 1. Print the numbered-statement list (all definitions, assumptions, lemmas, theorems). 2. For each, a non-author coauthor answers: can I state precisely what this claims, including quantifiers, without reading the proof? Rewrite until yes. 3. Verify proofs in dependency order, marking each line verified/unverified; the `colt-artifact-evaluation` skill's ledger format works here. 4. Re-check every external citation against the cited source's actual hypotheses — allocate real time; this is where careful papers die. 5. Reconcile body sketches against appendix proofs: a sketch that describes an older proof strategy than the appendix executes reads as a gap to a referee. ## Cycle-volatility warnings - If a future COLT cycle adds any checklist, code policy, or supplementary channel, the current CFP announces it; the 2026 cycle had none (待核实 in later cycles). - The 12-page body and single-PDF rules that shape where proofs live are the 2026 formulation; re-read the live CFP before restructuring a paper around them. - Formatting of assumptions and environments is a house-style choice, not a CFP rule; the CFP-level constraints remain the 12-page body and the single PDF. ## Output format ```text [Re-derivability verdict] re-derivable / gaps found [Statement completeness] [Constant ledger] tracked / drift at [External-results audit] [Illustration floor] seeds+replications stated / absent / no numerics in paper ```