Agent Systems: Reasoning and Representation Change

Problem

Some tasks fail because the chosen representation hides the next obstruction, not because the model needs a longer response.

Intent and structure

current representation → transform or decompose → candidate reasoning → check

The system may use linear decomposition, multiple candidate paths, program-aided reasoning, abstraction, analogy, or example generation. The output should be an artifact or proof obligation, not an unbounded private monologue.

Mathematical representation changes

• prose → definitions, claims, and hypotheses;
• geometric picture → invariant, diagram, or coordinate model;
• conjecture → examples and counterexample tests;
• proof idea → lemmas and dependency graph;
• symbolic expression → computer algebra or formal code.

Forces and failure modes

More search can improve coverage but increases cost and distracts from the obstruction. Tree-style exploration can explode; linear reasoning can miss a branch. Use a budget, a verifier, and a criterion for changing representation.

Design test

Which representation makes the next mathematical obstruction visible, and what independent check can reject the resulting candidate?

Figure

Figure: a candidate representation is transformed, evaluated, and revised.