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 over convex landscapes (April 2022)
- A note on the most elementary result of convex optimization: the speed of convergence is determined by the conditionning number of the Hessian.
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.
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 dans les ondelettes (Septembre 2023)
- Une généralisation de 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.