Chandan Singh | scattering transform

scattering transform

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some papers involving the scattering transform and similar developments bringing structure to replace learned filters

  • some of the researchers involved
    • edouard oyallan, joan bruna, stephan mallat, Helmut Bölcskei, max welling

goals

  • benefits
    • all filters are defined
    • more interpretable
    • more biophysically plausible
  • scattering transform - computes a translation invariant repr. by cascading wavelet transforms and modulus pooling operators, which average the amplitude of iterated wavelet coefficients

review-type

initial papers

scat_conv

neuro style

  • https://arxiv.org/pdf/1809.10504.pdf

papers by other groups

wavelet style transfer

helmut lab papers

  • Deep Convolutional Neural Networks Based on Semi-Discrete Frames (wiatowski et al. 2015)
    • allowing for different and, most importantly, general semidiscrete frames (such as, e.g., Gabor frames, wavelets, curvelets, shearlets, ridgelets) in distinct network layers
    • translation-invariant, and we develop deformation stability results
  • wiatoski_18 “A mathematical theory of deep convolutional neural networks for feature extraction
    • encompasses general convolutional transforms - general semi-discrete frames (including Weyl-Heisenberg filters, curvelets, shearlets, ridgelets, wavelets, and learned filters), general Lipschitz-continuous non-linearities (e.g., rectified linear units, shifted logistic sigmoids, hyperbolic tangents, and modulus functions), and general Lipschitz-continuous pooling operators emulating, e.g., sub-sampling and averaging
      • all of these elements can be different in different network layers.
    • translation invariance result of vertical nature in the sense of the features becoming progressively more translation-invariant with increasing network depth
    • deformation sensitivity bounds that apply to signal classes such as, e.g., band-limited functions, cartoon functions, and Lipschitz functions.
  • wiatowski_18 “Energy Propagation in Deep Convolutional Neural Networks

nano papers

  • yu_06 “A Nanoengineering Approach to Regulate the Lateral Heterogeneity of Self-Assembled Monolayers”
    • regulate heterogeneity of self-assembled monlayers
      • used nanografting + self-assembly chemistry
  • bu_10 nanografting - makes more homogenous morphology
  • fleming_09 “dendrimers”
    • scanning tunneling microscopy - provides highest spatial res
    • combat this for insulators
  • lin_12_moire
    • prob moire effect with near-field scanning optical microscopy
  • chen_12_crystallization

l2 functions

  • $L^2$ function is a function $f: X \to \mathbb{R}$ that is square integrable: $ f ^2 = \int_X f ^2 d\mu$ with respect to the measure $\mu$
    • $ f $ is its $L^2$-norm
  • **measure ** = nonnegative real function from a delta-ring F such that $m(\empty) = 0$ and $m(A) = \sum_n m(A_n)$
  • Hilbert space H: a vectors space with an innor product $<f, g>$ such that the following norm turns H into a complete metric space: $ f = \sqrt{<f, f>}$
  • diffeomorphism is an isomorphism of smooth manifolds. It is an invertible function that maps one differentiable manifold to another such that both the function and its inverse are smooth.

reversible/invertible models

unsupervised learning