The Fréchet Mean Prototype is the center point in a metric space that minimizes the sum of the squared distances to all data points. It extends the averaging operation from flat vector spaces to arbitrary curved spaces or complex objects.

The curse of dimensionality is not a specific geometric structure, but a collection of phenomena induced by the intrinsic properties of high-dimensional spaces.

The von Mises–Fisher distribution (vMF) distribution is often regarded as the hyperspherical analogue of the Normal distribution, as it models data concentrated around a mean direction on the unit hypersphere.

Linearity requires additivity and scaling, but neural networks need nonlinearity to break free from simple affine transformations. While affine layers only stretch and rotate data without changing its topology, activation functions enable complex reshaping—allowing networks to untangle data manifolds and learn intricate patterns effectively.

Stirling's formula finds a relationship of n!,nⁿ,eⁿ while n trends to infinity.