Spatially-Aware Self-Organizing Graph Autoencoders via Localized Hebbian Learning

Traditional autoencoders rely on static network architectures to learn latent representations. Recently we suggested a dynamic architecture inspired by Hebbian plasticity, enabling topological self-organization among convolutional feature maps (R. Koç et al., Proceedings of the SIU, 2026). Early implementations of this paradigm infer relationships among feature maps using global average pooling and model their interactions through scalar-valued connections. This approach falls short to fully exploit the underlying spatial information, embedded in input images. Furthermore, abrupt transitions between different loss functions and training dynamics can introduce representation shocks, leading to unstable feature learning. In this paper, we introduce a Spatially-Aware Self-Organizing Graph Autoencoder (S-LooM) to address these structural bottlenecks. By using spatial cross-correlation, and spatial kernels, S-LooM establishes dynamic connections among feature maps. We replace static scalar message passing of autoencoders with learnable spatial kernels and eliminate high-frequency deconvolutional artifacts observed in decoders using nearest-neighbor upsampling. Via a soft-blending training curriculum, the latent topology aligns smoothly during training. Our experiments show that S-LooM yields a more stable topology, compared to the state of the art dynamic architectures. Meaning, the graph structure that emerge has more resistance to feature entanglement and noise. It forms functional communities responsible for visual attributes, such as illumination, shape and texture even under high connection densities.