Backpropagation on Dynamical Networks

Eugene Tan, Débora Corrêa, Thomas Stemler, Michael Small

wrongmedium confidenceCounterexample detected

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

Both derive the same expected one-step contraction and the same stability window 0 < dt^2 αLR E[g12^2] < 1/2 (main text Eq. 3.8 and Appendix B), and both rely on the same zero-mean, state-independent model-error assumption. However, the paper’s case breakdown for E[g12^2] contains algebraic slips: (i) in Case 1 it equates E[(X2−X1)^2] to Var(X1)+Var(X2) without stating the needed equal-means/centering assumption, and (ii) in Case 3 it omits the factor 2 in the cross term, writing Var(X1)+Var(X2)−E[X1X2] instead of Var(X1)+Var(X2)−2 Cov(X1,X2) under centered data. The candidate solution gives the correct derivation and highlights the missing factor of 2. See the paper’s Eq. (3.8) and Appendix B derivations and cases for comparison .

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The work adapts BPTT to infer both local dynamics and couplings and presents a useful two-node stability analysis. The core convergence window is correct and valuable for practice; empirical sections are coherent. However, Appendix B contains small but material algebra and sign slips in the decomposition of E[(X2−X1)\^2] and the displayed gradient, which should be fixed to avoid misleading guidance about the effect of synchronisation on admissible learning rates. These issues are straightforward to remedy without altering the main conclusions.