Principle:Diagram of thought Diagram of thought Convergence Assessment
| Knowledge Sources | |
|---|---|
| Domains | Reasoning, Convergence, Decision_Theory |
| Last Updated | 2026-02-14 |
| Implemented By | Implementation:Diagram_of_thought_Diagram_of_thought_Summarizer_Completeness_Check |
Overview
Convergence assessment is the decision procedure that determines when an iterative reasoning process has accumulated sufficient validated evidence to produce a coherent final answer.
Description
In the Diagram of Thought (DoT) framework, reasoning proceeds through repeated propose-critique cycles that build a directed acyclic graph (DAG) of propositions and critiques. The convergence assessment is the mechanism by which a reasoning agent determines whether this iterative process is complete.
The summarizer role is responsible for this determination. After each propose-critique cycle, the summarizer reviews the current state of the reasoning DAG and evaluates several conditions:
- Sufficiency of validated propositions: Are there enough validated reasoning steps to construct a coherent, well-supported answer to the original question?
- Absence of unresolved contradictions: Have all critiques been addressed? Are there invalidated propositions that undermine the current chain of reasoning?
- Coverage of the problem: Do the validated propositions collectively address all aspects of the problem, or are there gaps that require further exploration?
This assessment acts as the decision point that controls the iteration loop. If the summarizer determines that the reasoning is incomplete -- for example, because a validated proposition raises a new question that has not been explored, or because a key critique remains unaddressed -- the cycle continues with further proposer and critic contributions. If the summarizer determines that the validated evidence is sufficient, the framework proceeds to final synthesis.
The convergence assessment is inherently a judgment call rather than a mechanical check. The summarizer must weigh the quality and completeness of the accumulated reasoning holistically, balancing thoroughness against the diminishing returns of additional iteration.
Usage
Apply convergence assessment after each propose-critique cycle to decide whether to:
- Continue iteration: Return to the proposer for additional reasoning steps, incorporating feedback from the critic
- Proceed to synthesis: Move to the final summarization phase, where the validated propositions are organized into a coherent chain-of-thought leading to the answer
This pattern is particularly important in problems that require multi-step reasoning, where premature convergence would yield an incomplete answer and excessive iteration would waste resources without improving the result.
Theoretical Basis
In the category-theoretic framework described in the DoT paper, the reasoning DAG is modeled as a category where propositions are objects and edges represent logical dependencies. Convergence corresponds to the point where the available validated subobjects are sufficient to compute the colimit -- the universal synthesis that coherently integrates all validated reasoning paths.
More concretely, the validated propositions form a subgraph of the full DAG. The convergence assessment asks whether this validated subgraph contains enough information to determine a unique (up to equivalence) final answer. If the validated subgraph is sparse or disconnected -- meaning there are logical gaps or unresolved branches -- the colimit cannot be meaningfully computed, and further iteration is needed.
The convergence check can be expressed in pseudo-code as:
converged = summarizer.assess(dag.validated_nodes, dag.pending_critiques)
if converged:
proceed_to_synthesis()
else:
continue_iteration()
In practice, this assessment is performed by the LLM itself in the <summarizer> role, guided by the prompt instructions to review the DAG of propositions and critiques and determine if the reasoning is complete.
Related Pages
- Implementation:Diagram_of_thought_Diagram_of_thought_Summarizer_Completeness_Check - Concrete prompt-based pattern for implementing the convergence assessment using the summarizer role