Ouranalysishelps13 illustrate why this worst-case behavior does not attain in practice. The standard union bound does not take advantage of model similarity; the refinement in equation (3) is the24 basis for our calculations that highlight the beneficial effect of model similarity. Our bounds demonstrate a link between similarity and protection against overfitting in both the30 non-adaptiveandadaptivecase. We agree an important direction for future work is exploring the extent to which our findings transfer to other44 settings. A concrete next step is evaluating model similarity on data from Kaggle competitions, which includes45 adiversesetofsample sizes, model classes, anddata types.

In addition to solving (1), we also wish topreserve privacyfor the people who contributed to the dataset Z.

The Pentagon is moving to deploy frontier AI capabilities across all classification levels, an official who requested anonymity said. The Pentagon is pushing the top AI companies including OpenAI and Anthropic to make their artificial-intelligence tools available on classified networks without many of the standard restrictions that the companies apply to users. During a White House event on Tuesday, Pentagon Chief Technology Officer Emil Michael told tech executives that the military is aiming to make the AI models available on both unclassified and classified domains, according to two people familiar with the matter. The Pentagon is moving to deploy frontier AI capabilities across all classification levels, an official who requested anonymity said. In a time of both misinformation and too much information, quality journalism is more crucial than ever.

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Wethen define asurrogatelossLtoy(~P RD)foranetworkconfigurationP inthisweight11 space, which we choose to depend monotonically on theL2 distance to the nearestn-wedge. Together, these21 define locally ann-dimensional hyperplane of finite thickness in the remainingD nthin direction, i.e. acuboid.22 To go beyond classification, we also looked at CNN-based31 autoencoders. In all cases the results supported our landscape model and we will include them in the final version.32 R5: Radial tunnels = what low-dimensional cuts would show.

Some recent studies attempted to explore this problemindifferentcontexts.