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Defined using differential forms on a smooth manifold, providing a link between topology and calculus. This is mainly a “cry” for help with my project. Project Substrate (Please don’t hesitate to reach out
) From GNNs to Sheaves: The Geometry of Reasoning We’ve hit the limit of brute-force scaling. If you’ve been tracking the trajectory from GNNs to modern reasoning models, you’ve felt it: the " Expressivity Wall ." The industry is quietly pivoting from Graph Neural Networks to Sheaf Theory . This is the inflection point. The Problem Current AI treats data like flat graphs. It averages neighbors (message passing), which leads to over smoothing and total failure on heterophilic data (where connected nodes aren’t similar). It’s like trying to understand 3D physics through a 2D projection. The Solution Sheaf Neural Networks (SNNs) . Instead of simple links, we use possets (partially ordered sets) and restriction maps . We aren’t just connecting A to B; we’re defining the mathematical rule for how information transforms as it moves . Why This Matters Now Recent signals from Nvidia and others point to a fundamental shift: from probabilistic weights to topological consistency . Using tools like cohomology , we can now rigorously detect “logical holes” or hallucinations in a model’s latent space before it outputs text . This isn’t just theory—it’s becoming implementable. What This Means Simple graphs are a dying investment. Sheaves allow AI to handle: Joint causation natively Nested hierarchies without flattening Consistency guarantees at the architectural level We’re not just building bigger brains. We’re finally building better geometry . I believe the hard part has been solved—we just didn’t know it yet! A Call to Collaborate If you’re working on: Sheaf neural networks or topological deep learning Formal verification for reasoning architectures The alignment implications of geometric AI Please reach out. The goal is to keep what comes next open source and, more importantly, aligned . TL;DR: Simple graphs are a dying investment. Sheaves allow AI to handle joint causation and nested hierarchies natively. We’re not just building bigger brains; we’re finally building better geometry. I’m extra excited to see the replies and hopefully find like-minded people to keep the future of Super Intelligence open source and ALIGNED. submitted by /u/lil-Zavy

Originally posted by u/lil-Zavy on r/ArtificialInteligence