Unate distributions require θ̃(n^{3/2}) samples for uniformity testing and allow Õ(n^{3/2}) conditional samples for unateness testing in the subcube model.
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Inkheart SGD and M4 use bidirectional compression to achieve time complexities in distributed SGD that improve with worker count n and surpass prior lower bounds under a necessary structural assumption.
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Testing Unate Distributions
Unate distributions require θ̃(n^{3/2}) samples for uniformity testing and allow Õ(n^{3/2}) conditional samples for unateness testing in the subcube model.
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Scalable Distributed Stochastic Optimization via Bidirectional Compression: Beyond Pessimistic Limits
Inkheart SGD and M4 use bidirectional compression to achieve time complexities in distributed SGD that improve with worker count n and surpass prior lower bounds under a necessary structural assumption.