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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PoLAR imposes radial structure on latent actions in hyperbolic space to factorize extent and mode, improving robot policy performance over baselines.
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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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PoLAR: Factorizing Extent and Mode in Latent Actions for Robot Policy Learning
PoLAR imposes radial structure on latent actions in hyperbolic space to factorize extent and mode, improving robot policy performance over baselines.