From Topology to Geometry: A Neural Ricci Flow Framework for Predicting Flash Crashes and Contagion

Early warning of systemic financial instability is a crucial issue for regulators and asset managers, especially in detecting flash crashes and concealed contagion paths, which cannot be detected using conventional surveillance mechanisms. In this context, conventional surveillance mechanisms refer to linear correlation based monitoring, volatility threshold rules, and static network centrality measures that rely on fixed topological summaries. Traditional regulatory mechanisms are based on a set of static measures of topology, such as Degree Centrality, PageRank, and matrices of linear correlations that assess the size of assets in terms of positioning in a financial network, systematically ignoring small and highly leveraged institutions that are sometimes crucial bridges in financial networks.We propose a novel geometric deep learning architecture, the Neuro Ricci Flow, a geometric framework that combines Financial Returns and ESG Momentum into a single Riemannian manifold, which conceptualizes systemic risk as real world changes in market topology and not statistical volatility, as commonly interpreted. Financial returns and ESG momentum are selected as universally observable and high frequency market indicators that directly encode dynamic interactions and stress propagation in financial systems. The framework is designed to detect market level structural instability and contagion dynamics, rather than to directly infer macroeconomic phenomena such as currency debasement or monetary policy driven effects.We consider a Neural Ordinary Differential Equation to learn the underlying physics of Ricci Flow, with dynamical simulation of market manifold evolution to subsequently find hyperbolic singularities, in which an area of extreme negative curvature indicates structural rupture in the network. Empirical valuation shows better predictive power with 100 percent recall of the geometric risk indicator with five percent baseline risk. The deeper meaning further elaborates on the practical implications of this framework, which include accurate alarm mechanisms for central banks, assisted by Ricci Curvature Analysis and geometric techniques for immunizing the portfolios of asset managers in need of protection against contagion. We discover that geometric deep learning has provided a more sensitive paradigm of systemic risk models compared to traditional topological models.