Reasoning Structure Shapes Capability

The geometry of prompted reasoning determines what kinds of problems a model can solve.

Linear (Chain-of-Thought): Step-by-step reasoning. Works for problems with a single solution path. Fails when exploration or backtracking is required.

Branching (Tree-of-Thoughts): Explores multiple paths, evaluates progress, backtracks from dead ends. Enables look-ahead reasoning.

Graph (Graph-of-Thoughts): Non-linear connections, combines insights from different branches. Mirrors how humans actually think, jumping between ideas, making unexpected connections.

Each structural advance isn’t just an optimization, it enables qualitatively different reasoning. A chain can’t backtrack. A tree can’t combine insights from separate branches. Structure is capability.

Related: 05-molecule—chain-of-thought-prompting, 02-atom—format-shapes-cognition