Procedural Content Metageneration via Program Search and Continual Abstraction Discovery

Large language models can generate executable programs, which makes it possible to search directly over procedural content generators rather than individual levels. We study this approach in Sokoban, Zelda, Dangerous Dave, and Lode Runner. Each run evolves complete Python generators through language-model mutation and crossover. We introduce Continual Abstraction Discovery, or CAD, which extracts reusable primitives from high-fitness programs into a run-specific helper module. A 2x2 experiment crosses CAD with access to a fixed hand-written domain API. The completed data set contains 160 complete runs, with at least ten 50-generation runs in every cell. CAD raises mean final best fitness in all eight domain and API comparisons. Across all CAD runs, learned libraries are adopted by most later programs and repeatedly rediscover validation, reachability, and structural utilities. These results support that discovering reusable primitives improves evolutionary program search for content generators.

Emergent Models: Intelligence from Tiny Substrates

Emergent Models (EMs) are a machine learning paradigm based on simple yet open-ended substrates, such as cellular automata, in which modeling is treated not as the learning of a closed-form input-output map but as the emergence, within simple dynamical systems, of computational behaviors that solve external tasks. Such substrates typically iterate a fixed local rule over a latent space for an adaptive number of steps, with an interface linking the latent state to external input/output signals. Training proceeds by evolutionary search. We hypothesize that some instances of this framework are biased toward global generalization: capturing the rule generating the data over its full domain, and therefore extrapolating beyond the training range. Theoretically, we prove that some EMs are latent-universal: with the update rule and interface held fixed, they can realize any partial computable function by varying only the initial condition of the latent state. Empirically, we study a zoo of minimal EM instantiations across discrete and continuous substrates, showing that local-recursive computation at a tiny scale (tens to hundreds of parameters) can extrapolate exactly on simple arithmetic functions, can support control behaviour and online adaptation, while still exposing several limitations. This work is foundational: it does not propose a competitive architecture, but a framework meant to widen the design space of machine learning beyond differentiable feed-forward maps.

Evolutionary Wave Function Collapse

Wave Function Collapse (WFC) is a widely used procedural content generation method that learns local adjacency constraints from example inputs to generate larger outputs. In this paper, we explore combining WFC with evolutionary search by evolving the small input examples used by WFC rather than directly evolving complete levels. In this approach, WFC acts as a genotype-to-phenotype mapping. The generated levels are then evaluated through domain-specific fitness functions. We evaluate the method in two domains with different relationships between local and global structure: Maze connectivity maps and Zelda-style dungeon layouts. Our results show that evolutionary optimization over WFC inputs improves generation quality in domains where properties emerge from local relationships, while domains requiring global constraints remain challenging. These findings suggest that evolutionary search can effectively guide WFC generation when target objectives align with local structure.