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Identifiable alignment of unpaired representations — arXiv:2611.11460

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.11460
License (as archived): CC0-1.0
Archived: 2026-11-10T18:43:24.751Z
SHA-256 of the archived text: 5de5fe58e98c6f12c4bfa428f6ad16c1af52e6ca1fdf70405b86368c8d739584
Stable URL of this page: https://metraipolis.com/documento/dc_f263dbddf727

How to cite

Identifiable alignment of unpaired representations — arXiv:2611.11460 — arXiv (en), https://arxiv.org/abs/2611.11460 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_f263dbddf727 (Metraipolis archive dc_f263dbddf727, sha256 5de5fe58e98c6f12c4bfa428f6ad16c1af52e6ca1fdf70405b86368c8d739584)

BibTeX

@misc{dcf263dbddf727,
  title = {Identifiable alignment of unpaired representations — arXiv:2611.11460},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.11460},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_f263dbddf727; sha256 5de5fe58e98c6f12c4bfa428f6ad16c1af52e6ca1fdf70405b86368c8d739584},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.11460. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Aligning two models without paired data requires a distance that both share, yet existing methods use Euclidean or spherical geometry. This is either an arbitrary choice or imposed by their loss function. We show that, under a precise form of the manifold hypothesis, the pullback of the data metric gives such a distance for any two models of one data-generating process. This holds whether the models are encoders, decoders or both, and whatever their architecture, loss, prior or training data. The alignment map preserves this distance and the distribution of representations, and is identifiable if and only if the data distribution breaks every symmetry of the data manifold. We show that this symmetry breaking holds generically. Identifiability makes the alignment coupling the unique optimum of Gromov--Wasserstein and of its weighted combinations with a linear program. The linear program alone has the same optimum if almost every data point has a distinct distribution of distances. The coupling, and with it the alignment map, is recovered exactly from permuted samples, even without identifiability, and consistently from independent ones. Our method, Neural Gromov--Monge Alignment (NGMA), uses no pairs or labels and outperforms every unpaired and label-informed baseline. It relies on pullback distances to align image models with different priors and single-cell models trained on disjoint cells, where Euclidean distances fail.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.AI, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (stat.ML) ; Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Methodology (stat.ME).
Pagina del lavoro: https://arxiv.org/abs/2611.11460 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-10T18:37:37.641Z dalla pagina https://arxiv.org/list/cs.AI/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).