 
        
            The Manifold Hypothesis: How Data Resides on Low-Dimensional Structures.
Imagine a tangled ball of string. At first glance, it looks messy, complex, and impossible to unravel. But when carefully pulled apart, you realise that all the chaos is still just one long thread, coiled into an intricate shape. Data in high-dimensional space often behaves the same way—it may appear overwhelming, but it lies on…

