Structure over Pixels: Learning Variable-Length Visual Programs

Discrete visual tokenizers translate images into ordered sequences of codes, providing a natural representation for structural description of scenes. Yet existing adaptive tokenizers either require post-hoc search or select among a discrete set of pre-trained rates, rather than learning a continuous per-image sequence length coupled to the model and scene, and they typically train against pixel reconstruction, emphasizing texture rather than structure. We propose STROP, a discrete visual tokenizer architecture that forms structural scene representations and simultaneously learns how long an image's visual program should be. Using a four-phase curriculum supervised by local rate--distortion probes against frozen DINOv3 features, STROP optimizes a dedicated length head that estimates the active prefix length in a single forward pass. By bypassing pixel-level reconstruction gradients, the codebook is shaped entirely by the quality of higher-level latent representations. Program length grows with scene complexity, and signs of compositional structure emerge both in downstream dense-prediction transfer and in direct inspection of the learned code vocabulary.

Learning Semantics-aware Search Operators for Genetic Programming

Fitness landscapes in test-based program synthesis are known to be extremely rugged, with even minimal modifications of programs often leading to fundamental changes in their behavior and, consequently, fitness values. Relying on fitness as the only guidance in iterative search algorithms like genetic programming is thus unnecessarily limiting, especially when combined with purely syntactic search operators that are agnostic about their impact on program behavior. In this study, we propose a semantics-aware search operator that steers the search towards candidate programs that are valuable not only actually (high fitness) but also only potentially, i.e. are likely to be turned into high-quality solutions even if their current fitness is low. The key component of the method is a graph neural network that learns to model the interactions between program instructions and processed data, and produces a saliency map over graph nodes that represents possible search decisions. When applied to a suite of symbolic regression benchmarks, the proposed method outperforms conventional tree-based genetic programming and the ablated variant of the method.