Topological Persistence Homology for Latent-Space Navigation in Generative Adversarial Game-Asset Synthesis

Abstract

Generative adversarial networks (GANs) have demonstrated remarkable capacity for the de novo synthesis of high-fidelity game assets, yet the latent spaces of such models remain poorly understood from a geometric-topological standpoint, frustrating efforts at systematic, semantically meaningful traversal. We introduce a computational pipeline grounded in persistent homology — the principal invariant of topological data analysis — that extracts multi-scale Betti-number signatures from point-cloud samples of GAN latent manifolds, thereby furnishing a rigorous characterization of the homological structure governing asset-feature entanglement. By constructing Vietoris–Rips filtrations over latent encodings of 80,000 procedurally generated sprite assets and computing persistence diagrams via the standard algorithm with clearing optimization, we identify stable topological features (H₀ connected components, H₁ loops, H₂ voids) whose birth–death coordinates correspond to interpretable semantic axes such as silhouette complexity, chromatic saturation, and articulation pose. A persistence-guided interpolation scheme that routes latent trajectories through low-persistence (topologically simple) regions achieves a 41% reduction in Fréchet Inception Distance relative to linear interpolation and a 27% improvement in human-rated semantic coherence (N = 85, p < .001). These results establish persistent homology as a principled instrument for navigating and controlling generative latent spaces in game-asset production pipelines.

Keywords: persistent homology, topological data analysis, GAN, latent space, game assets, Betti numbers, Vietoris-Rips complex