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This work unifies prior approaches through the framework of priority sampling, designing algorithms that establish a smooth tradeoff between the number of MIPS indices and number of retrieved keys and designing algorithms that outperform top-$k and sampling approaches used in prior work and yield attention approximatio...
The main contribution is giving an essentially matching lower bound on the space complexity of diameter estimation for a set of points in Euclidean space in the dynamic (turnstile) streaming model.
It is proved that without distributional assumptions, finding the optimal balanced halfspace is NP-hard, and an efficient improper learning algorithm is designed that outputs a balanced polynomial threshold function of degree 1 that cuts at most an $O(\sqrt{\alpha+\varepsilon})$ fraction.
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