2508.09808
Directed Cycles as Higher-Order Units of Information Processing in Complex Networks
Hardik Rajpal, Paul Expert, Vaiva Vasiliauskaitė
incompletemedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:57 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper presents clear and consistent empirical findings from simulations but does not provide formal proofs and contains a stability mis-specification (α = 1/λmax(A) asserted as a “stability condition”). The model’s candidate solution offers plausible theoretical mechanisms and inequalities that qualitatively explain all five reported phenomena, but several key steps are heuristic (e.g., exogenous-noise lower bound, preservation of ΦR ordering, and small-κ expansions without explicit error control). Hence, while the two agree on the phenomena and mechanisms, both arguments are incomplete: the paper for lack of rigor (and a technical stability error), the model for sketch-level derivations lacking full hypotheses and bounds.
Referee report (LaTeX)
\textbf{Recommendation:} major revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The manuscript identifies and systematically explores the distinct roles of feedforward and feedback cycles in directing information processing on networks, offering clear and interesting empirical trends. The study is timely and relevant to higher-order network science and information dynamics. However, there is a technical misstatement regarding stability (the use of α=1/λmax(A) as a “stability condition”) that conflicts with the claim of steady-state behavior, and the main claims rest entirely on simulations without formal derivations or error analysis. Addressing these issues—by correcting the stability specification, clarifying analytic assumptions, and adding at least partial theoretical bounds or ablations—would substantially strengthen the work.