Agent System Design Pattern

The aim of this note is to give a brief introduction to the design patterns used in building agent systems. We divide the note into two parts: (1) the common design patterns for agent systems, and (2) a case study of the agent system I built for my own mathematical research.

An agent system is a way of trading determinism for flexibility. The design patterns are the tools for buying back as much determinism as the task requires.

Part I. Common Design Patterns

[I.0 Terminology]

[I.1 Prompt chaining pattern]

[I.2 Router pattern]

[I.3 Parallelization pattern]

[I.4 Reflection pattern]

[I.5 Tool use pattern]

[I.6 Multiple agent cooperation pattern]

[I.7 Plan pattern]

[I.8 Memory management pattern]

[I.9 Learning and adapdation pattern]

[I.10 Human in the loop pattern]

Part II. Agent Systems in Examples

In the second part of this note I case study the design of a concrete agent system: the one I built to support my own work in birational geometry. It runs over an Obsidian vault of roughly 11,600 mathematical notes, and it exists to do three things — keep my daily research schedule, turn papers into structured notes, and check mathematics I have written.

I will describe each component and identify which pattern from Part I it instantiates, including the places where I chose a pattern badly and had to change it.