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Does a Shared Temperature Imply a Shared Angular Scale in Probabilistic Contrastive Learning? — arXiv:2609.38784

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.38784
License (as archived): CC0-1.0
Archived: 2026-10-07T13:45:31.119Z
SHA-256 of the archived text: 6c8c093369ef30ca2aebe909deeeb06974a83e28526abb72a75ea629e268500e
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How to cite

Does a Shared Temperature Imply a Shared Angular Scale in Probabilistic Contrastive Learning? — arXiv:2609.38784 — arXiv (en), https://arxiv.org/abs/2609.38784 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_cc8aed1f024f (Metraipolis archive dc_cc8aed1f024f, sha256 6c8c093369ef30ca2aebe909deeeb06974a83e28526abb72a75ea629e268500e)

BibTeX

@misc{dccc8aed1f024f,
  title = {Does a Shared Temperature Imply a Shared Angular Scale in Probabilistic Contrastive Learning? — arXiv:2609.38784},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.38784},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_cc8aed1f024f; sha256 6c8c093369ef30ca2aebe909deeeb06974a83e28526abb72a75ea629e268500e},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.38784. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In probabilistic contrastive learning, a shared temperature is commonly interpreted as a shared similarity scale, but this interpretation does not hold for high-dimensional distributional class representations. We study the exact von Mises-Fisher (vMF) probabilistic score used by ProCo when representation dimension and class concentration grow jointly. We prove that the score retains a class-dependent leading angular gain $g_c=A_c/\tau$, where $A_c$ is the mean resultant length. This gain enters Softmax competition, pairwise decision boundaries, and feature gradients. On real CIFAR-LT, ImageNet-LT, and iNaturalist representations, the theory accurately predicts boundary movements and local gradient changes under the full vMF score. Classwise temperature adjustment also changes the cosine-zero intercept and finite-dimensional response. We construct intercept-preserving and Pure Angular controls to separate the leading gain from these accompanying changes. Complete gain equalization yields a shared-scale cosine prototype rule at leading order; a finite-dimensional margin condition guarantees agreement of the two classifiers. Across 16 frozen representation settings, prediction agreement is 98.43-99.99%, with disagreements concentrated at small cosine margins. In controlled contrastive-only training with the training-frequency prior, Pure Angular editing improves both learned representations at all tested CIFAR-10/100 imbalance factors and retains positive changes on ImageNet-LT. Thus vMF concentration not only describes class distributions, but also forms a decision and learning scale in high-dimensional probabilistic contrastive learning.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-10-01 in cs.LG).
Categorie arXiv: Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2609.38784 — 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 2026-10-07T13:18:10.255Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-10-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).