Defines empirical sensitivity and proves Ω(η + √(η d/n)) lower bound (tight up to logs) for any Gaussian mean estimator achieving optimal O(√(d/n)) ℓ₂ error.
Auto-Vectorizing TensorFlow Graphs: Jacobians, Auto-Batching And Beyond
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abstract
We propose a static loop vectorization optimization on top of high level dataflow IR used by frameworks like TensorFlow. A new statically vectorized parallel-for abstraction is provided on top of TensorFlow, and used for applications ranging from auto-batching and per-example gradients, to jacobian computation, optimized map functions and input pipeline optimization. We report huge speedups compared to both loop based implementations, as well as run-time batching adopted by the DyNet framework.
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Robust Statistical Estimators with Bounded Empirical Sensitivity
Defines empirical sensitivity and proves Ω(η + √(η d/n)) lower bound (tight up to logs) for any Gaussian mean estimator achieving optimal O(√(d/n)) ℓ₂ error.