What was already known
Earlier online bounds were O(log²(m)log(d)/ε⁴) and O(m/ε²). A prior offline bound has a different protocol setting.
AI involvement
The authors credit ChatGPT 5.6 Sol Pro with the main ideas and proof strategies. They studied, refined, checked and rewrote the final proofs.
The original authors assign the main ideas and central proof strategies to the model, with subsequent human refinement and verification.
Importance
The two protocols match classical adaptive-data-analysis rates up to constants within their stated online model.
Limitations
The four authors report checking both final protocols and proofs. No machine formalization or separate external check is documented.
Technical verification
The four human authors explicitly report careful verification of the central ideas and take responsibility for every final claim and proof. This is a source-reported complete human proof check, not a reproduced or machine check.
Formal checking
Careful study, refinement and verification of the model-generated ideas and final proofs
- Checker
- Sitan Chen, Ryan O'Donnell, Angelos Pelecanos and John Wright
- Scope
- Both online shadow-tomography protocols and their adaptive sample-complexity bounds
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The human authors explicitly state understanding and explain the excitation decomposition, charging argument and damage control for both protocol regimes.
Correction and publication history
The two protocols match classical adaptive-data-analysis rates up to constants within their stated online model.
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