Friday, June 12, 2026

Crumpled Manifolds


"The whole process of applying this complex geometric transformation to the input data can be visualized in 3D by imagining a person trying to uncrumple a paper ball: the crumpled paper ball is the manifold of the input data that the model starts with. Each movement operated by the person on the paper ball is similar to a simple geometric transformation operated by one layer. The full uncrumpling gesture sequence is the complex transformation of the entire model. Deep learning models are mathematical machines for uncrumpling complicated manifolds of high-dimensional data. [...] Our own understanding of images, sounds, and language, is grounded in our sensorimotor experience as humans -as embodied earthly creatures. Machine learning models have no access to such experiences and thus cannot 'understand' their inputs in any human-relatable way [...] this mapping is just a simplistic sketch of the original model in our minds, the one developed from our experience as embodied agents—it is like a dim image in a mirror."

- François Chollet (1989 - )

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