Geometric Morphology Learning integrates geometry into foundation models
Original title: Geometric Morphology Learning: Empowering Foundation Models from Structure to Spacetime Intelligence
New framework enables AI models to learn geometric and topological structures for reasoning and action.
Deep learning architectures are blind to geometry. Geometric Morphology Learning constructs a neural bundle with differentiable operators for connection and curvature. It supports representation learning, reasoning, planning, graph modeling, and physical simulation. This provides a pathway for systematic geometry in artificial intelligence.
- Neural bundle links local and global structures
- Uses Riemannian geometry concepts like holonomy and cohomology
- Applies to PDE systems and dynamics modeling
- Addresses incompatibility of Riemannian geometry with deep learning
From the original article
1 min read at arxiv.orgGeometry is the very form that connects space, time, and matter, serving as the fundamental fabric of the physical world, from continuous fields to discrete structures. Despite its importance, deep learning is inherently blind to geometry. Riemannian geometry stands as a well-established mathematical foundation for studying geometry, yet it remains largely incompatible with deep learning architectures.
By Li Sun · arxiv.org
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