Algorithm Modelization: Transforming Optimization Algorithms into Evolvable Intelligence

Can algorithms be learned and evolved as models, rather than repeatedly redesigned as programs? We explore this question by introducing Algorithm Modelization, a new paradigm that turns iterative algorithms into trainable models. Its central idea is to regard algorithm execution trajectories as computational experience: by learning how algorithmic states evolve over iterations, a model can internalize the knowledge embodied in existing algorithms, reproduce their computational behaviors, and further evolve beyond them through training. As a first realization of this paradigm, we modelize iterative optimization as an autoregressive process, where preceding generations constitute the computational context for generating the next population. We develop a dimension-independent population-temporal architecture to capture both population interactions and iterative dynamics, together with an imitation-to-surpassing learning framework that first acquires algorithmic knowledge from heterogeneous teachers and then improves the resulting optimizer directly through optimization feedback. The modelized optimizer consequently goes beyond reproducing individual algorithms: it consolidates heterogeneous search knowledge into a single trainable model, achieves stronger optimization capability through subsequent improvement, and generalizes its acquired knowledge across problems and substantially larger unseen dimensions. More fundamentally, Algorithm Modelization makes algorithmic capability accumulable through learning, where new algorithms and problem-solving experience can become training resources for progressively improving the model. Our results establish a promising path from manually designed algorithms toward general algorithm models that learn, generalize, and evolve from computational experience.