The shape of the reasoning matters more than its length.
Chain-of-thought: linear. Tree-of-thought: branching. Network-of-thought: a directed graph with typed nodes and edges, where intermediate results can merge and evidence from multiple sources can integrate (arXiv:2603.20730).
The finding: CoT remains effective for sequential tasks (where the answer follows from a single chain of deductions). Tree-of-thought helps for search tasks (where branching explores alternatives). But for multi-hop reasoning — where the answer requires combining evidence from multiple independent sources — NoT outperforms both. The topology matches the structure of the problem.
Self-generated controller heuristics proved more effective than fixed strategies for logical reasoning. The model generates its own traversal policy rather than following a predetermined schedule. The topology is adaptive — the graph structure changes based on the problem, not imposed in advance.
An additional finding: evaluation methodology significantly impacts method comparisons. String-matching underestimates performance on open-ended QA tasks. Methods that look worse under string matching look better under semantic evaluation. The benchmark topology — how you measure — is as consequential as the reasoning topology — how you think.
The structural principle: reasoning has geometry. A linear chain is the wrong shape for a problem that requires integrating independent evidence (it forces serialization of parallel reasoning). A tree is the wrong shape for a problem that requires merging (branches diverge but never reconverge). A graph is the general case — chains and trees are special graphs with restricted connectivity. The right reasoning topology is isomorphic to the problem's dependency structure.