Competitive and Complementary Tools

What the math gives to ML

The paper gives a coupled dynamical system in which competence and tool reliance reinforce one another, producing bistability and hysteresis rather than a single smoothly optimal operating point. This is transferable to tool-augmented neural agents: a router can maintain an explicit competence state and use different thresholds for increasing versus decreasing tool use, preventing a model from permanently outsourcing solvable subtasks. The main asset is the positive-feedback state dynamics and the prediction that identical current tool access can yield opposite behaviors depending on training history. A practical first deployment is a competence-aware calculator or retrieval gate evaluated under tool ablation and recovery protocols.