A Unified Geometric Framework for Weighted Contrastive Learning
Authors: Raphael Vock, Edouard Duchesnay, Benoit Dufumier
Summary
arXiv:2605. 13943v1 Announce Type: new Abstract: Contrastive learning (CL) aims to preserve relational structure between samples by learning representations that reflect a similarity graph.
Relevance
Read next because A Unified Geometric Framework for Weighted Contrastive Learning overlaps with clean result "Leakage rate is a usable signal for recovering trigger-shaped phrases on Gaperon-1125-1B without knowing the hidden trigger itself (MODERATE confidence)", clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)", clean result "Only continuous soft prefixes hit both EM axes at once on Qwen-2.5-7B-Instruct: discrete prompt searches split between the alignment objective and the distributional objective, and both discretizations of the soft prefix collapse (MODERATE confidence)". Matching terms: class, under, soft, rate, symmetry. Source: arxiv cs.LG (Machine Learning).
Threat model
Potential threat/caveat for clean result "Leakage rate is a usable signal for recovering trigger-shaped phrases on Gaperon-1125-1B without knowing the hidden trigger itself (MODERATE confidence)": this item discusses failure.
Abstract
arXiv:2605.13943v1 Announce Type: new Abstract: Contrastive learning (CL) aims to preserve relational structure between samples by learning representations that reflect a similarity graph. Yet, the geometry of the resulting embeddings remains poorly understood. Here we show that weighted InfoNCE objectives can be interpreted as Distance Geometry Problems, where the weighting scheme specifies the target geometry to be realized by the representation. This viewpoint yields exact characterizations of the optimal embeddings for several supervised and weakly supervised objectives. In supervised classification, both SupCon and Soft SupCon (a dense relaxation of it where pairs from distinct classes have small non-zero similarity) collapse samples within each class to a single prototype. However, while balanced SupCon recovers the classical regular simplex geometry, class imbalance breaks this symmetry: SupCon induces non-uniform inter-class similarities depending on class sizes, whereas Soft SupCon preserves a regular simplex geometry regardless of class imbalance. In continuous-label settings, our framework reveals a different failure mode: y-Aware CL generally cannot attain its entropic optimum unless the labels lie on a hypersphere, exposing a mismatch between Euclidean label weights and spherical latent similarity. By contrast, geometrically consistent choices such as Euclidean-Euclidean weighting or X-CLR admit unique optimal embeddings. Our results show that the choice of weighting scheme determines whether contrastive learning is geometrically realizable, degenerate, or inconsistent, providing a principled framework for designing contrastive objectives.