Algorithm modelization is a new paradigm that treats iterative algorithms as trainable models. The key idea is to regard algorithm execution trajectories as computational experience; by learning how states evolve across iterations, a model can internalize the knowledge of existing algorithms, reproduce their behavior, and further surpass them after training.
We first model iterative optimization as an autoregressive process, where previous generations form the computational context for generating the next population. To capture both population interactions and iterative dynamics, we design a dimension‑independent population‑temporal architecture and propose an imitation‑to‑surpassing learning framework: first acquire search knowledge by imitating heterogeneous teacher algorithms, then improve the optimizer directly through optimization feedback.
The modelized optimizer not only reproduces individual algorithms but also consolidates heterogeneous search knowledge into a single trainable model. After subsequent improvement it achieves stronger performance and generalizes to unseen problems and substantially higher dimensions. More fundamentally, algorithm modelization makes algorithmic capability accumulable via learning; new algorithms and problem‑solving experiences become training resources for progressively enhancing the model.
Our results demonstrate a promising path from manually designed algorithms toward general algorithm models that learn, generalize, and evolve.
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