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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2 Pith papers cite this work. Polarity classification is still indexing.
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L¹ polynomial regression achieves Õ(n^{O(log(1/ε)/σ)}) for smoothed agnostic halfspace learning, with nearly matching SQ lower bound n^{Ω(log(1+σ/ε²)/σ)}.
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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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A Near-optimal SQ Lower Bound for Smoothed Agnostic Learning of Boolean Halfspaces
L¹ polynomial regression achieves Õ(n^{O(log(1/ε)/σ)}) for smoothed agnostic halfspace learning, with nearly matching SQ lower bound n^{Ω(log(1+σ/ε²)/σ)}.