Dimension d = O(m^{-2} log n) nearly achieves the optimal margin m^rd(+∞, A) for retrieval embeddings, with matching lower bounds showing d = O(k log(n/k)) suffices and is necessary for m = Θ(k^{-1/2}) on k-sparse query matrices.
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cs.LG 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
The paper proves statistical consistency of contrastive loss for retrieval via an AUC criterion and derives generalization bounds O(1/m + 1/sqrt(n)) supervised and O(1/sqrt(m) + 1/sqrt(n)) self-supervised that explain benefits of large negative sets.
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Is Dimensionality a Barrier for Retrieval Models?
Dimension d = O(m^{-2} log n) nearly achieves the optimal margin m^rd(+∞, A) for retrieval embeddings, with matching lower bounds showing d = O(k log(n/k)) suffices and is necessary for m = Θ(k^{-1/2}) on k-sparse query matrices.
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Statistical Consistency and Generalization of Contrastive Representation Learning
The paper proves statistical consistency of contrastive loss for retrieval via an AUC criterion and derives generalization bounds O(1/m + 1/sqrt(n)) supervised and O(1/sqrt(m) + 1/sqrt(n)) self-supervised that explain benefits of large negative sets.