Resolution Horizon – Finding the mathematical limit where AI overfits to noise (github.com)

Resolution Horizon is an innovative research framework introduced to investigate the limits of discovering mathematical structures from finite and noisy observations of dynamical systems. It shifts the perspective on structural recovery from being solely about the system's intrinsic properties to a more holistic view that includes the dynamics, the observer's capabilities, and the available computational resources. The central concept is the "resolution horizon," a boundary where the ability to recover structure begins to diminish as observation noise and estimation uncertainty increase. This work combines principles from differential geometry, dynamical systems, statistical estimation, and information theory to create a new empirical approach for studying how observation processes can define these limits. It highlights the need for an optimal structural resolution, while identifying regimes of discovery, misresolution, and beyond. By treating scientific discovery as a quantifiable process influenced by data and environmental constraints, Resolution Horizon has significant implications for the AI/ML community by providing a framework for understanding the limits of learning from noisy data and guiding the design of more efficient algorithms that can better handle uncertainty and noise in real-world applications.