A large deviation view of \emph{stationarized} fully lifted blirp interpolation
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912446425333760 |
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| author | Stojnic, Mihailo |
| author_facet | Stojnic, Mihailo |
| contents | We consider \emph{bilinearly indexed random processes} (blirp) and study their interpolating comparative mechanisms. Generic introduction of the \emph{fully lifted} (fl) blirp interpolation in [105] was followed by a corresponding stationarization counterpart in [103]. A \emph{large deviation} upgrade of [105] introduced in companion paper [106] is complemented here with the corresponding one of [103]. Similarly to [106], the mechanism that we introduce extends the range of [103]'s applicability so that it encompasses random structures \emph{atypical} features. Among others these include the \emph{local entropies} (LE) which explain atypical solutions clusterings in hard random optimization problems believed to be directly responsible for the presumable existence of the so-called \emph{computational gaps}. Moreover (and similar to [105]), despite on occasion somewhat involved technical considerations, the final forms of the uncovered fundamental interpolating parameters relations are rather elegant and as such provide a valuable tool readily available for further use. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19273 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A large deviation view of \emph{stationarized} fully lifted blirp interpolation Stojnic, Mihailo Probability Information Theory Machine Learning We consider \emph{bilinearly indexed random processes} (blirp) and study their interpolating comparative mechanisms. Generic introduction of the \emph{fully lifted} (fl) blirp interpolation in [105] was followed by a corresponding stationarization counterpart in [103]. A \emph{large deviation} upgrade of [105] introduced in companion paper [106] is complemented here with the corresponding one of [103]. Similarly to [106], the mechanism that we introduce extends the range of [103]'s applicability so that it encompasses random structures \emph{atypical} features. Among others these include the \emph{local entropies} (LE) which explain atypical solutions clusterings in hard random optimization problems believed to be directly responsible for the presumable existence of the so-called \emph{computational gaps}. Moreover (and similar to [105]), despite on occasion somewhat involved technical considerations, the final forms of the uncovered fundamental interpolating parameters relations are rather elegant and as such provide a valuable tool readily available for further use. |
| title | A large deviation view of \emph{stationarized} fully lifted blirp interpolation |
| topic | Probability Information Theory Machine Learning |
| url | https://arxiv.org/abs/2506.19273 |