Derives a novel two-point deterministic equivalence for random matrix resolvents to obtain unified asymptotics for SGD-trained linear regression, kernel regression, and random feature models.
Then, Fourier transforming in each variable separately and restricting to thet=t ′ diagonal yields: ˆF(t) = Z ω,ω ′ eit(ω+ω ′) ¯w⊤ ˆΣ( ˆΣ+iω) −1( ˆΣ+iω ′)−1 ¯w| {z } ˆF(ω,ω ′)
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Two-Point Deterministic Equivalence for Stochastic Gradient Dynamics in Linear Models
Derives a novel two-point deterministic equivalence for random matrix resolvents to obtain unified asymptotics for SGD-trained linear regression, kernel regression, and random feature models.