Automatic Model Selection Based on Task Complexity

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Which solver should handle a given task — with which tools, how much verification, and what opportunity to escalate? Every AI application answers that question, and most answer it implicitly. Defaulting to a large language model spends reasoning on work that never needed it. Choosing a small model on price alone does not remove the cost; it relocates the cost into errors and rework. This paper sets out an Adaptive Intelligence Router that chooses among deterministic programs, retrieval and service interfaces, small language models, more capable language models, and accountable human review. A task’s demands are carried by a complexity profile in which every component has a defined role: three dimensions generate the admissible set, one fixes the reliability floor and the mandatory oversight level, and the rest are predictive features and nothing more. Selection then becomes a constrained sequential decision problem spanning routing, verification, retries and handoffs. I distinguish the pre-execution success probability that chooses an action from the post-verification probability that licenses accepting its output, and show that only the second supports a bound on residual error among accepted work. An analytical illustration then parameterises a two-stage cascade by verifier recall and false-flag rate instead of escalation fraction. Doing so exposes a cost-quality frontier whose cheapest point is also its least accurate. The evaluation protocol proposed here compares static routing, fixed cascades, learned routing, decomposition, and a non-routing caching baseline under quality, latency and residual-risk constraints, and it counts the cost of certifying the router itself. The paper reports a design and a protocol; no router was trained and no benchmark results are given.