Use this when revising prose and mathematics for COLT. The style target is a paper a learning theorist can referee efficiently: the model is unambiguous by page 3, the main theorem is quotable in one breath, and the proof overview convinces the reader the technique is new before the appendix is opened.
State important results twice — an informal version in the introduction and the formal version after the setup — and keep them visibly consistent:
% Introduction:
\begin{theorem}[informal; see Theorem~\ref{thm:main}]
Any proper learner needs $\Omega(d/\epsilon)$ samples in this model,
and an improper learner achieves $O(\log(d)/\epsilon)$.
\end{theorem}
% After the setup:
\begin{theorem}\label{thm:main}
Let $\mathcal{H}$ satisfy Assumption~\ref{ass:vc}. For every proper learner $A$
there is a distribution $D$ with ... . Moreover, Algorithm~\ref{alg:improper}
outputs $h$ with $\mathrm{err}_D(h) \le \epsilon$ using
$m = O(\epsilon^{-1}\log d)$ samples, with probability $1-\delta$.
\end{theorem}
The informal statement is a promise; reviewers check that the formal statement redeems it without weasel adjustments (an extra assumption appearing only in the formal version is a credibility leak).
| Draft habit | COLT-grade replacement |
|---|---|
| "It is easy to see that..." | "By Jensen's inequality applied to (7)," — name the tool |
| "For simplicity assume..." (silently binding) | "Assumption 3 (stated formally in Section 2); we discuss removing it in Remark 4" |
| "significantly improves prior work" | "improves the dependence on $d$ from $d^2$ to $d\log d$ (Table 1)" |
| "standard concentration arguments give" | "Bernstein's inequality with variance bound (12) gives" |
| "we believe the bound is tight" | "we conjecture the $\log$ factor is necessary; Section 5 gives partial evidence" |
| "our novel technique" | Describe the technique; let the reviewer call it novel |
The 2026 CFP allowed 12 PMLR-formatted body pages (references and appendix free, checked 2026-07-08). A working allocation for a two-theorem paper:
If the spine does not fit, cut a secondary theorem to the appendix wholesale rather than thinning every proof overview into mush.
Five sentences carry a COLT abstract: (1) the model and the question, in field vocabulary; (2) the best known bounds; (3) your result with explicit rates or the separation named; (4) the technique in one clause; (5) an optional consequence or open question. Numbers belong in the abstract at this venue — an abstract without a rate reads as an abstract without a result. Delete from drafts: application motivation beyond one clause, "extensive experiments," and any sentence beginning "Recently, there has been growing interest."
Write self-references in third person ("extending the reduction of [14]") and strip
acknowledgements for review — the 2026 template's anon option handles the author
block, but prose leaks are on you. See colt-submission for the full sweep.
[Style verdict] referee-efficient / setup-deficient / overclaimed / disorganized
[First-pages arc] <which of the five steps is missing or out of order>
[Statement hygiene] <quantifier / constant / probability-mode fixes>
[Technique paragraph] present and honest / absent / vague
[12-page plan] <sections over budget and the cut>