Fully lifted \emph{blirp} interpolation -- a large deviation view
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909658729414656 |
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| author | Stojnic, Mihailo |
| author_facet | Stojnic, Mihailo |
| contents | [104] introduced a powerful \emph{fully lifted} (fl) statistical interpolating mechanism. It established a nested connection between blirps (bilinearly indexed random processes) and their decoupled (linearly indexed) comparative counterparts. We here revisit the comparison from [104] and introduce its a \emph{large deviation} upgrade. The new machinery allows to substantially widen the [104]'s range of applicability. In addition to \emph{typical}, studying analytically much harder \emph{atypical} random structures features is now possible as well. To give a bit of a practical flavor, we show how the obtained results connect to the so-called \emph{local entropies} (LE) and their predicated role in understanding solutions clustering and associated \emph{computational gaps} in hard random optimization problems. As was the case in [104], even though the technical considerations often appear as fairly involved, the final interpolating forms admit elegant expressions thereby providing a relatively easy to use tool readily available for further studies. Moreover, as the considered models encompass all well known random structures discussed in [104], the obtained results automatically apply to them as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19272 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fully lifted \emph{blirp} interpolation -- a large deviation view Stojnic, Mihailo Probability Information Theory Machine Learning [104] introduced a powerful \emph{fully lifted} (fl) statistical interpolating mechanism. It established a nested connection between blirps (bilinearly indexed random processes) and their decoupled (linearly indexed) comparative counterparts. We here revisit the comparison from [104] and introduce its a \emph{large deviation} upgrade. The new machinery allows to substantially widen the [104]'s range of applicability. In addition to \emph{typical}, studying analytically much harder \emph{atypical} random structures features is now possible as well. To give a bit of a practical flavor, we show how the obtained results connect to the so-called \emph{local entropies} (LE) and their predicated role in understanding solutions clustering and associated \emph{computational gaps} in hard random optimization problems. As was the case in [104], even though the technical considerations often appear as fairly involved, the final interpolating forms admit elegant expressions thereby providing a relatively easy to use tool readily available for further studies. Moreover, as the considered models encompass all well known random structures discussed in [104], the obtained results automatically apply to them as well. |
| title | Fully lifted \emph{blirp} interpolation -- a large deviation view |
| topic | Probability Information Theory Machine Learning |
| url | https://arxiv.org/abs/2506.19272 |