One 8B model stops using a fixed reasoning template: AlgoPilot picks a paradigm and writes the formulation, lifting average accuracy from 38.4% to 72.9%

Faced with cross-domain problems, the language model no longer applies one reasoning template to every input; it first judges which kind of computational paradigm fits the problem, then decides whether extra structured formulation is needed. Earlier prompting methods rely on fixed reasoning templates or choose only between textual reasoning and code execution, and adaptive routing methods route over inference configurations, prompting strategies, models and external tools rather than over fundamentally different computational paradigms and their problem formulations. On a test set covering 5 problem categories, 13 benchmarks and 66 domains, AlgoPilot with Qwen3-8B as the execution model reaches 72.9% average accuracy, against 38.4% for the same model under direct prompting and 36.1% under reason-then-solve prompting, while the best large-model prompting baseline GLM-5 reaches 61.2%.

Three models divide the work: one selects the paradigm, one writes the formulation, and one executes. SteerLM is trained with supervised fine-tuning followed by GRPO reinforcement learning and outputs a ranked list of paradigm-mode candidates ordered by execution success; each paradigm has its own GuideLM, fine-tuned with supervision to produce that paradigm's structured formulation, such as decision variables, objective and constraints for optimization, or states, actions and transitions for planning. In ablations, learned paradigm selection without formulation guidance averages 45.7%, formulation guidance with the execution model choosing its own paradigm averages 45.3%, and the two together reach 72.9%; on 432 problems from 10 held-out domains, AlgoPilot reaches 73.3% instance-weighted accuracy, against 53.0% for direct prompting and 66.2% for reason-then-solve prompting.

The demonstrated scope is accuracy on 2,220 held-out test problems across 13 benchmarks and 66 domains, plus 432 problems from 10 held-out domains and three paraphrase styles; the framework is instantiated with Qwen3-8B as the default execution model, and the transfer experiment swaps in Gemma-4-E4B-it. The authors explicitly exclude zero-shot generalization to arbitrary unseen domains from the main claim and name broader cross-domain training and refinement of the GuideLM experts as directions for improvement.

The authors note that the framework depends on execution-derived feedback to build guidance data and train the steering model, a process that can be computationally expensive and may limit scaling to very large datasets or newly added paradigms; the steering and guidance modules are trained from the behavior of a particular execution model, so transfer to other execution models, while positive, may be imperfect. On unseen domains, only 22.4% of failed instances are routed to a paradigm different from the source category, and the remaining errors come more often from downstream formulation or execution, with GuideLM formulation transfer seen as the main bottleneck.