Course calendar

WEEK 1 - MARCH 7-11, 2022

Lesson 1 (8/3, 15.00-17.00 - Room 706)

• • Introduction to the topics of the course, discussion on logistic aspects

  • Basics of learning theory

  • Inductive bias and the problem of approximation

Lesson 2 (10/3, 15.00-17.00 - Room 704)

• • Basics of neural networks

  • Expressivity of neural networks

  • Width vs. depth and the curse of dimensionality

WEEK 2 - MARCH 14-18, 2022

Lesson 3 (15/3, 15.00-17.00 - Room 706)

• Convolutional neural networks - why effective? why unstable?

• Rethinking priors: geometric regularity

Lesson 4 (17/3, 15.00-17.00 - Room 704)

• Rethinking priors: symmetries, local vs global invariance, exact invariance vs stability

• A general model for exploiting geometric priors

WEEK 3 - MARCH 21-25, 2022

Lesson 5 (22/3, 15.00-17.00 - Room 706)

• Scale separation, the failure of Fourier modulus and autocorrelation

• Stabilizing high frequency information without deterioration

• Basics of wavelets and the principles of multiscale analysis

Lesson A (24/3, ***16.00-18.00 - Room 508***)

• 1D Wavelets, motivating example: feature extraction in audio signals

• Why wavelets: from Fourier transform to the continuous wavelet transform

• Discrete wavelet transform: frames

WEEK 4 - MARCH 28 - APRIL 1, 2022

Lesson B (29/3, ***16.00-18.00 - Room 508***)

• 1D Wavelets: orthonormal bases

• 1D Wavelets: multiresolution analysis

• Application: denoising audio signals

Lesson 6 (31/3, 15.00-17.00 - Room 704)

• The need of nonlinearities and recovery of lost information with wavelets

• Cascading and the definition of the scattering transform

• The scattering network architecture

WEEK 5 - APRIL 4-8, 2022

Lesson C (5/4, 15.00-17.00 - Room 706)

• 2D Wavelets 2D, motivating example: feature extraction in images

• Orthogonal wavelet basis in 2D

• Directional wavelet frames

• Curvelets and shearlets

Lesson 7 (7/4, 15.00-17.00 - Room 704)

• Contractivity of the scattering transform

• Energy propagation and norm preservation

WEEK 6 - APRIL 11-15, 2022

Lesson 8 (12/4, 15.00-17.00 - Room 706)

• Asymptotic translation invariance

• Stability to small deformations

Lesson D (13/4, 15.00-17.00 - Room 706)

• Scattering transform

• Scattering networks

• Example: digit classification

EASTER BREAK

(APRIL 18-30)

SECOND PART (MAY 2022)

Lesson 9 (5/5, 16.00-18.00 - Room 508)

• Overview of recent advances in the theory of scattering networks

Lesson 10 (11/5, 15.00-17.00 - Room 706)

• Generalized scattering networks

Lesson E (12/5, 15.00-17.00 - Room 704)

• Scattering networks in the landscape of machine learning