manifold-interpolation-underlies-dl-generalization
IN premise — summaries/2026/08/24/wiki-Manifold_hypothesis.md
Created 2026-08-24T17:11:18+00:00
The manifold hypothesis posits that any two data points can be connected by a continuous path remaining on the data manifold, and this interpolation capability is identified as the key theoretical mechanism underlying generalization in deep learning (Chollet, 2021)
Summary
This idea says the data a network learns from lives on a smooth, continuous surface, and the network's real skill is learning to fill in the gaps along that surface rather than just memorizing individual points. That framing matters because it gives the system a concrete theoretical reason for why deep learning works on examples it has never seen: it is interpolating along the underlying structure of the data, not simply pattern-matching on the training set.