Home / Concepts /Cognitive Function × Execution Topology

Cognitive Function × Execution Topology

Two orthogonal axes. What the agent is doing, and what shape the work takes. Crossed, they form a coordinate system from which 28 named patterns are read.

Definition

An agent design is the intersection of two axes. Cognitive function names what the agent is trying to do — perception, memory, reasoning, action, reflection, collaboration, governance (7 categories). Execution topology names what shape the work takes — chain, route, parallel, loop, hierarchy, orchestrate (6 archetypes). Crossed, they form a 7×6 = 42-cell matrix; 28 cells are populated with named patterns, 14 are intentionally empty.

The problem it names

[TODO: 咖哥 voice — 为什么 "flat list of patterns" 不够。 工程团队拿到 ReAct / Reflection / Multi-Agent / Tree of Thoughts 一长串名字之后, 还是不知道自己问题在哪一格。坐标系给的是"我的失败属于哪条轴"这个能问出的问题。]

How it changes design decisions

Pattern selection becomes coordinate selection. "We need a Reflection pattern" is under-specified; "we need Reflection × Loop with a deterministic exit signal" is a design. Two engineers saying "we use Plan-and-Execute" can mean two different cells — Action × Chain (linear plan) or Action × Orchestrate (dynamic replanning) — and the choice carries real architectural consequences. The coordinates make those choices visible before they show up as production bugs.

Lineage

• Christopher Alexander — patterns as orthogonal generative axes, not as a list
• GoF (1994) — pattern matrix structure with creational / structural / behavioral × class / object
• Cloud architecture catalogs — Microsoft / AWS reference architectures organized by scenario × topology

What it is NOT

• Not a taxonomy of frameworks. LangChain / AutoGen / CrewAI are mechanisms; the matrix is about designs you compose using those mechanisms.
• Not a flat list of 28 patterns. The list is a flattening of the matrix; the matrix is the source.
• Not a maturity scoreboard. Cells are not ranked. A simpler cell is not less serious than a harder one.

Where it's developed further

• Position paper: arXiv:2605.13850 — full formal treatment with the empirical pattern-selection laws
• Book treatment: Designing AI Agents (Manning, 2026) — the matrix is the spine of the entire book
• Full catalog: adpsagent.com/patterns/ — 33 enterprise white papers, one per cell
• Interactive matrix: /research/dual-axis/

Cite as: Huang, J. (2026). Cognitive Function × Execution Topology. kage-ai.com/concepts/cognitive-function-x-execution-topology/