Those are mostly blog posts, notes, talk slides, nice pictures and various things about mathematics, statistics, CS and machine learning.
Diffusion models (March 2023)
- A small mathematical summary.
The double descent phenomenon (November 2021)
- Why do overparametrized networks do well?
The dimension of invariant and equivariant linear layers (July 2021)
- We compute the dimension of equivariant linear layers in neural architectures.
The ConvMixer architecture: 🤷 (December 2021)
- I am training a deep network on a GPU using the Flux.jl library. There are two takeaway messages: 1) patches are all you need, 2) in Julia, the ConvMixer *largely* fits in one Tweet.
Gradient descent I: strongly convex functions (April 2022)
- For strongly convex functions, the speed of convergence is determined by the conditionning number of the Hessian.
Gradient descent II: stochastic gradient descent for convex functions (October 2023)
- Stochastic Gradient Descent over strongly convex functions nearly behaves like gradient descent.
Gradient descent III: SGD for Polyak-Łojasiewicz functions (October 2023)
- Convex functions are not my friends anymore. Now I am best friend with Polyak-Łojasiewicz functions.
Importance sampling ⚖️ (June 2023)
- On the sample size required to get a good approximation
Importance sampling ⚖️⚖️ : The Jarzynski connection (March 2022)
- Change-of-measure for out-of-equilibrium systems
🐘 The Elephant Random Walk (May 2023)
- Long-time memory results in non-diffusivity
Robbins' version of the Stirling approximation (November 2022)
- A handy, easy-to-remember estimate for the error in Stirling's approximation.
Super-Catalan (Janvier 2022)
- Une question non-résolue, vieille de 150 ans, et probablement très inutile.
Random analytic functions: Ryll-Nardzewski's theorem (April 2021)
- What happens at the boundary of the disk of convergence of random analytic series.
Théorème de Mercer et Kernel Trick (Octobre 2023)
- Le théorème de représentation des noyaux positifs
Kesten's theorem on affine recursions (November 2023)
- The solutions of the distributional equation X = AX+B can have heavy tails: a sketch of proof, plus a presentation of the Renewal theorem.
Gaussian conditioning (September 2023)
- The conditional distribution of some part of a gaussian vector given the other
The Kullback-Leibler divergence between Gaussians (June 2022)
- I'll know once and for all where to find this damn formula.
Mouvement brownien I 📈 : avec une base d'ondelettes (Septembre 2023)
- Une généralisation de la construction de Paul Lévy: on construit un mouvement brownien continu en s'aidant d'une base orthonormale.
Mouvement brownien II 📈📈: représentation de Karhunen-Loève (Octobre 2023)
- Cette fois on construit un mouvement brownien directement dans une base orthonormale et pas implicitement comme dans la construction de Paul Lévy.
An inverse visualization for the elliptic law (March 2021)
- A beautiful colorplot of the characteristic polynomial of random matrices.
Random line on the plane (August 2021)
- How can we draw random lines on the plane?
Waves on donuts (August 2021)
- A nice plot of random Laplace eigenfuctions on the torus, also called random arithmetic waves.
Tips and tricks in the Julia language (August 2022)
- A personnal collection of nice tricks in Julia.
The point of view of Professor Parapine (November 2022)
- An interesting vision of Science from one century ago.