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.
Proceedings of the 33rd International Conference on International Conference on Machine Learning - Volume 48 , pages =
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LLMs disperse meaning-preserving prompts internally instead of clustering them, which produces an excessively high upper bound on output log-probability differences via Taylor expansion and Cauchy-Schwarz.
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Understanding the Prompt Sensitivity
LLMs disperse meaning-preserving prompts internally instead of clustering them, which produces an excessively high upper bound on output log-probability differences via Taylor expansion and Cauchy-Schwarz.