Accuracy and Architecture Studies of Residual Neural Network solving Ordinary Differential Equations

The paper’s Theorem 1 proves the one-step error bound for a ResNet ODE solver by decomposing the error into training error plus the target’s local truncation error; the candidate solution uses the same triangle-inequality decomposition and the standard one-step local truncation expansion. Aside from minor notational slips in the paper (a redundant Lipschitz term in Lemma 1 and a slight ambiguity about whether “k-th order” refers to method order or the order of the local truncation term), the logical content agrees. The candidate adds a clear uniformity argument over a finite training set. Overall, the proofs are essentially the same and correct.