Generative Neural Net for Spatial Concept-to-Image

Numerous artificial intelligence (AI) approaches, such as generative AI (GAI), large language models (LLM) and text-to-image networks, necessitate spatial intelligence for effective operation. Yet, a prevailing ideology embedded in contemporary solutions is their inclination to strictly adhere to a data-driven approach when addressing spatial learning. This viewpoint leads to opaque solutions, aka "black boxes", and it presupposes that the intricacies of spatial reasoning will effortlessly surface as an inherent byproduct of extensive data exposure. This simplistic reliance on data overlooks the wealth of established psychology and mathematics governing spatial relations and their inherent uncertainties. In this article, we delve into neural networks and learning strategies for incorporating well-established spatial relations mathematics into an effective and explainable GAI. Specifically, we showcase how to translate abstract concepts, expressed as sets of spatial relations, into visual imagery. This resulting imagery can be immediately used or passed on as a spatial prior to a larger and more sophisticated GAI. We present two synthetic use cases wherein spatial concepts materialize as intricate arrangements of multi-part colored geometric primitives, undergoing a spectrum of diverse planar affine transformations. Our exploration is categorized into two dimensions: discerning spatial placements (aka the "where") and shape depiction (aka the "what"). Overall, we’ve noted a strength in our proposed neural networks in discerning spatial placements. However, while our nets also exhibit a competence in determining "what" to depict, we recognize the necessity for additional fine-tuning to achieving visual imagery consistent with state-of-the-art works like DALL-E and stable diffusion.