What was already known
Earlier high-dimensional approximate leave-one-out theory handled smooth penalties or narrower nonsmooth cases, often with stronger tail or regularity assumptions. The proof bounds how many active groups change after one observation is deleted.
AI involvement
The paper states that Stellar Colosseum, a fully automated agent system built on Gemini 4, initially obtained the proof. The named human authors verified it and edited its presentation; other models later edited the text. This documents model-led proof development without establishing the project’s full task-only autonomy.
Importance
Extends a quantitative leave-one-out approximation guarantee to a broad class of block-sparse nonsmooth penalties.
Limitations
The theorem compares exact deleted fits with restricted-fit surrogates. Controlling the additional Newton approximation used in a fast implementation remains separate. Data-selected hyperparameters, growing block sizes and the usual stronger tail-uniform guarantees are not covered by this rate. A separate Lean main-theorem artifact is linked by the authors; its full contents were not assessed here.
Technical verification
The AI disclosure explicitly reports that the named authors verified the model-produced proof, with Sections 2–4 specifying its hypotheses and argument. This is an author-reported complete human check of the assessed restricted-fit theorem. The linked Lean claim is not counted as an inspected machine check.
Independent checking
The AI disclosure reports completed author verification of the initially model-generated proof; the theorem and proof are stated in Sections 2–4
- Checker
- Honghao Lin, Songbin Liu, Arian Maleki, Vahab Mirrokni, Chen Shang, David P. Woodruff, Hanbo Yang and Wenjin Zhang
- Scope
- Under Assumptions 2.1–2.5, the expected average absolute loss discrepancy between exact leave-one-out fits and each of the two restricted-fit approximations is O(log^(3/2)(en)/√n). The setting has bounded block sizes, a fixed block partition, Gaussian design with covariance eigenvalues comparable to 1/p, n/p bounded above and below, positive deterministic ridge and penalty parameters, smooth convex loss, finite third score moments and the stated one-sided likelihood-curvature condition.
- Basis
- Reported by the linked checker
Human understanding
Lin, Liu, Maleki, Mirrokni, Shang, Woodruff, Yang and Zhang verify and explain the active-group stability, proximal comparison and exceptional-event estimates. Their discussion separates the proved surrogate guarantee from the remaining Newton-error question.
Correction and publication history
Added a reviewed, scoped central-AI contribution with checking and attribution limits.
Read this published revision