Deterministic rounding worsens GD generalization from O(T/n) to O(T/sqrt(n)) with vacuous Omega(T) stability, while SGD retains O(T/n) or O(T^2/n) stability depending on dimension, and stochastic rounding can increase error with dimension.
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Uniform Stability and Generalization Error of GD and SGD on Fixed-Point Parameters
Deterministic rounding worsens GD generalization from O(T/n) to O(T/sqrt(n)) with vacuous Omega(T) stability, while SGD retains O(T/n) or O(T^2/n) stability depending on dimension, and stochastic rounding can increase error with dimension.