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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RAIC unifies uniform recovery of structured signals from nonlinear observations via PGD, yielding error rates comparable to nonuniform guarantees up to log factors in sparse and 1-bit settings.
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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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Robust Uniform Recovery of Structured Signals from Nonlinear Observations
RAIC unifies uniform recovery of structured signals from nonlinear observations via PGD, yielding error rates comparable to nonuniform guarantees up to log factors in sparse and 1-bit settings.