Mad Max: Affine Spline Insights into Deep Learning
summary
Argues that modern nets are compositions of max-affine spline operators, so each layer induces a convex power‑diagram partition and the whole net is a hierarchical VQ machine; gives closed‑form A,B formulas for the affine map on each tile, links rows of A to match‑filter saliency maps (rows visibly resemble class prototypes on CIFAR), defines a Hessian complexity on data manifolds, and shows on CIFAR‑100 that standard data augmentation empirically reduces that complexity.
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chapters (17)
- 0:00Intro
- 1:22deep nets and splines
- 2:24spline approximation
- 3:10kinds of splines
- 4:02max-affine spline (MAS)
- 6:44max-affine spline operator (MASO)
- 7:48theorem
- 9:34MASO spline partition
- 13:19learning
- 14:46geometry of the MASO partition
- 17:29a conclusion
- 18:55local affine mapping - CNN
- 22:25deep nets are matched filterbanks
- 23:43data memorization
- 25:05deep net complexity
- 31:06understanding data augmentation
- 35:21beyond piecewise affine nets
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