Abstract:Forecasting systems in science must be accurate, physically consistent, and certifiably reliable. Most existing models address prediction, constraint enforcement, and verification separately, limiting scalability and interpretability. We introduce GeoCert, a geometric AI framework that unifies forecasting, physical reasoning, and formal verification within a single differentiable computation. GeoCert formulates forecasting as evolution along a hyperbolic manifold, where negative curvature induces contraction dynamics, intrinsic robustness, and logarithmic-time certification. A hierarchical constraint architecture separates universal physical laws from domain-specific dynamics, enabling certified generalization across energy, climate, finance, and transportation systems. GeoCert achieves state-of-the-art accuracy while reducing computational cost by 97.5% and maintaining better certification rates. By embedding verification into the geometry of learning, GeoCert transforms forecasting from empirical approximation to formally verified inference, offering a scalable foundation for trustworthy, reproducible, and physically grounded scientific AI.
Abstract:Machine learning has achieved remarkable advancements but at the cost of significant computational resources. This has created an urgent need for a novel and energy-efficient computational fabric. CMOS Oscillator Networks (OscNet) is a brain inspired and specially designed hardware for low energy consumption. In this paper, we propose a Hopfield Network based machine learning algorithm that can be implemented on OscNet. The network is trained using forward propagation alone to learn sparsely connected weights, yet achieves an 8% improvement in accuracy compared to conventional deep learning models on MNIST dataset. OscNet v1.5 achieves competitive accuracy on MNIST and is well-suited for implementation using CMOS-compatible ring oscillator arrays with SHIL. In oscillator-based implementation, we utilize only 24% of the connections used in a fully connected Hopfield network, with merely a 0.1% drop in accuracy. OscNet v1.5 relies solely on forward propagation and employs sparse connections, making it an energy-efficient machine learning pipeline designed for CMOS oscillator computing. The repository for OscNet family is: https://github.com/RussRobin/OscNet.