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
🏋🏼 Heavy tails I: extremes events and randomness (November 2023) - A presentation of heavy tails, how they behave, and a short list of where they come from.
🏋🏼 Heavy-tails II: is it really heavy? (December 2023) - A presentation of Hill's estimator for the heavy-tail index.
🏋🏼 Heavy tails III: Kesten's theorem (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.
Quadratic exponentials of Gaussian random vectors (2024) - Computation of E[exp(q(X))] where q is quadratic and X is gaussian.
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.
Maths & ML Gems (2024) - My personal curated list of old and recent outstanding papers in applied mathematics.
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.