Graph Of Thought

Overview & Purpose

Graph of Thought (GoT) extends beyond tree structures by representing thoughts as vertices in a Directed Acyclic Graph (DAG). This allows operations like combining multiple independent lines of reasoning (aggregation), refining existing thoughts, and forming feedback loops or complex dependencies between distinct ideas.

When to Use

• Non-linear Problems: Complex dependency networks, multi-perspective synthesis, or system integrations.
• Thought Aggregation: Combining outputs from 2+ distinct sub-analyses into a unified synthesis node.
• Iterative Refinement Graphs: When an idea needs feedback or inputs from multiple prior stages simultaneously.

Execution Workflow

1. Define Graph Vertices (Nodes):

   • Identify discrete units of reasoning or hypotheses as nodes ($V_1, V_2, \dots, V_n$).

2. Establish Directed Edges (Dependencies):

   • Connect nodes with directional edges indicating dependencies ($V_i \to V_j$).

3. Perform Graph Transformations:

   • Aggregation: Merge insights from $V_a$ and $V_b$ into $V_{combined}$.
   • Refinement: Pass $V_i$ through a critique node to produce $V_{improved}$.
   • Branching: Split $V_i$ into sub-hypotheses $V_{i1}$ and $V_{i2}$.

4. Evaluate Topological Order:

   • Process nodes according to topological dependencies to synthesize final conclusions.

Expected Output Contract

### Graph of Thought Representation
- **Nodes**:
  - `Node A`: [Premise / Initial Finding]
  - `Node B`: [Independent Finding]
  - `Node C (Aggregated)`: [Merged insight from A + B]
- **Edges**: `A -> C`, `B -> C`
- **Graph State**: [Topological Execution / Synthesis Summary]

Scripts

• scripts/graph_of_thought.py - Deterministic evaluation, state validation, and CLI tool for graph-of-thought.