Layer-Parallel Training of Residual Networks with Auxiliary-Variable Networks

The paper defines the per-epoch speedup ratio ρ exactly as in Eq. (27) and notes that if Tf+Tb exceeds tψ+t_f^(λ)+t_b^(λ), then a sufficiently large K gives speedup; it also states the finite-K upper bound (Td+Tf+Tb)/(Td+tψ+t_f^(λ)+t_b^(λ)) . The model reproduces Eq. (27) algebraically, gives an explicit K0 threshold for ρ>1 under the same assumption, proves the stated bound, shows the K→∞ limit equals that bound, and establishes monotonicity in K—all consistent with and extending the paper’s sketch. No substantive conflict was found.