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. *