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Latent manifold

As explained in Deep Learning with R, Third Edition

A latent manifold is a low-dimensional, structured subspace in which encoded data points can be continuously interpolated.

A latent manifold is a low-dimensional, highly structured subspace within a high-dimensional data space. Natural data such as handwritten digits, faces, voices, and language may lie on such manifolds, allowing continuous paths between related examples. section 5.1.2

Interpolation on a latent manifold supports local generalization: unseen points can be understood by relating them to nearby observed points. This differs from averaging inputs directly, which can produce invalid data such as an unintelligible average of two digits. section 5.1.2

Morphing handwritten digits

A sequence of MNIST digits gradually morphs from one example into another, illustrating continuous movement through the manifold of valid handwritten digits.

How Deep Learning with R, Third Edition covers it

How deep it goes
Defines manifolds and contrasts latent interpolation with input averaging, while stopping short of formal derivation or construction.
Examples
Uses MNIST digits, morphing sequences, and comparisons between valid manifold paths and pixel averages.
What you can do after
Evaluate/understand why interpolation supports local generalization and why input-space averages can be invalid.
How it connects
Connects the manifold hypothesis with interpolation, local generalization, and deep learning.
Cover of Deep Learning with R, Third Edition
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This explainer was generated by Manning's knowledge graph from the text of Deep Learning with R, Third Edition. The section links point to the parts of the book it draws on.