Mixing Implicit and Explicit Deep Learning with Skip DEQs and Infinite Time Neural ODEs (Continuous DEQs)

The paper’s three focal claims are present and supported in the PDF: (A) average speedups are stated in Figure 1 (2.55x train, 3.349x predict) and reiterated in the conclusion (≈2.5x, 3.4x) with per-task tables (MNIST Dense/Conv., CIFAR‑10, SVHN) reporting the underlying timings used to form such ratios . (B) Robustness and convergence-depth improvements are described qualitatively and quantitatively (e.g., “best models have a 3.74x reduction in convergence depth”; continuous forms stabilize depth and improve convergence in MNIST Conv./SVHN) . (C) The continuous DEQ’s gradients use the same implicit differentiation as discrete DEQ, so no backpropagation through time is required, as explicitly stated in the Continuous DEQ section and consistent with the DEQ identity given earlier in the paper . By contrast, the candidate solution’s empirical check misreads CIFAR‑10 (using nonexistent “training time (s/batch)” and values that do not appear in Table 3), and it leaves the MNIST/SVHN aggregation unfinished despite the necessary numerals being available in the uploaded PDF. Its proof for (C) is correct, but its verification for (A) is numerically wrong and incomplete, and (B) is only argued theoretically without reconciling the precise reported figures.