Samuel Vaiter @samuelvaiter.com · 20/06/2026Bienvenue à Nice, ville avec une des plus basses températures de France ! (ps: je recrute potentiellement un.e postdoc sur 24 mois d'ici fin 2026 sur des questions, plutôt théoriques, liées aux LLMs en post-training / alignment, je dis ça, je dis rien) 0135
Samuel Vaiter @samuelvaiter.com · 20/03/2026Our last plenary speaker was Stephane Gaubert on tropical geometry applied to optimization. 000
Samuel Vaiter @samuelvaiter.com · 20/03/2026For the last day, Julie Delon gives an introduction to Flow Matching with the PoV of an applied mathematician. 130
Samuel Vaiter @samuelvaiter.com · 19/03/2026And before our conference dinner, we had the pleasure to hear Yann Brenier with an outreach talk on the role of optimal transport in applied mathematics. 140
Samuel Vaiter @samuelvaiter.com · 19/03/2026The second day started with a brillant plenary talk of @pierreablin.bsky.social on LLM pretraining and some explanations of scaling laws. 120
Samuel Vaiter @samuelvaiter.com · 18/03/2026This afternoon, we start with Irène Waldspurger on semidefinite optimization 140
Samuel Vaiter @samuelvaiter.com · 18/03/2026We listened this morning to the talk of Francisco Silva Álvarez on mean field games in a packed room! 130
Samuel Vaiter @samuelvaiter.com · 17/03/2026We hosted in Nice @aymericdieuleveut.bsky.social & A. Taylor for the SMAI-MODE 2026 mini-course on Performance Estimation Problems with 9 hours of lectures + practicals in two days All material freely available 👇 performanceestimation.github.io/Tutorial-SMA... Thanks to both of them! 1113
Samuel Vaiter @samuelvaiter.com · 09/03/2026We validate everything empirically on 11 models (GPT-2, Gemma 3, Qwen 3, Llama 2, Mistral 7B) across 8 safety-related concepts. All our theorems are confirmed experimentally. 6/7 100
Samuel Vaiter @samuelvaiter.com · 09/03/2026Result 3: Steering always hurts global performance. Cross-entropy increases quadratically around α = 0, i.e., there's no free lunch. For large α, performance plateaus because the output becomes input-independent. 5/7 110
Samuel Vaiter @samuelvaiter.com · 09/03/2026Result 2: Concept probability follows a sigmoidal curve. The probability that the target concept appears in the output increases smoothly with α, following a tanh shape. Off-target concepts decrease or vanish. 4/7 100
Samuel Vaiter @samuelvaiter.com · 09/03/2026Result 1: Next-token probabilities have a bump shape. As α increases, most token probabilities rise, peak for α>0, then fall. In particular, off-target tokens peak _before_ target tokens. 3/7 100
Samuel Vaiter @samuelvaiter.com · 09/03/2026Take contrastive prompts (for ex, safe vs malicious), evaluate them through the model, compute the mean difference of representations at layer ℓ. That's your steering vector v. Then shift activations by αv at layer ℓ. Question: what does α actually do? 2/7 100
Samuel Vaiter @samuelvaiter.com · 09/03/2026🧵 New preprint! Towards Understanding Steering Strength w/ M. Taimeskhanov and D. Garreau Activation steering is a popular way to control LLM behavior at inference. But how much should you steer? We provide the first theoretical analysis of the steering strength α. 📄 arxiv.org/abs/2602.02712 1/7 1103
Samuel Vaiter @samuelvaiter.com · 22/01/2026Vu que le chauffage est visiblement un détail, on trouve des alternatives. Startup-nation 🤘 050
Samuel Vaiter @samuelvaiter.com · 15/12/2025Les inscriptions aux journées MODE 2026 à Nice sont désormais ouvertes. Elles se dérouleront du 18 au 20 mars à l'Hôtel Saint-Paul. Les inscriptions sont ouvertes jusqu'au 1 mars (majoration > 9/02). La deadline pour soumettre une communication est le **15 janvier**. 157
Samuel Vaiter @samuelvaiter.com · 09/07/2025Congratulations to Dr. Sophie Jaffard @sophiejaffard.bsky.social for a brillant PhD defense! We were very lucky with Patricia to have you as a PhD student, and I am sure that you will have a brillant career ahead. 1141
Samuel Vaiter @samuelvaiter.com · 17/06/2025I am sure that the number of faculty follows the same curve /s 020
Samuel Vaiter @samuelvaiter.com · 11/06/2025Do you know the power of CHANI? arxiv.org/abs/2405.18828 010
Samuel Vaiter @samuelvaiter.com · 02/06/2025Even more striking, DGSWP leads to a sliced-OT based Conditional Flow Matching method with state-of-the-art results. On CIFAR-10, we show practical improvements in terms of FID wrt to I-CFM, OT-CFM and we show the practical effect of the increased expressivity of the NN-based DGSWP. 5/5 150
Samuel Vaiter @samuelvaiter.com · 02/06/2025The method is competitive on gradient flow tasks using either linear projection as in minSWGG, but also neural networks. We can use DGSWP either on Euclidean spaces or hyperbolic ones. 4/5 130
Samuel Vaiter @samuelvaiter.com · 02/06/2025We show that thanks to Stein's lemma, it admits a nice differentiable approximation DGSWP, our estimator of interest. In particular, it is consistent with the original estimator, and and it yields a distance on the space of measures. 3/5 120
Samuel Vaiter @samuelvaiter.com · 02/06/2025A slicing scheme (min-SWGG) lifts a single 1D plan back to the original multidimensional space, selecting the slice that yields the lowest Wasserstein distance as an approximation of the full OT plan. Here, we reformulate min-SWGG as a bilevel optimization 2/5 110
Samuel Vaiter @samuelvaiter.com · 02/06/2025📣 New preprint 📣 **Differentiable Generalized Sliced Wasserstein Plans** w/ L. Chapel @rtavenar.bsky.social We propose a Generalized Sliced Wasserstein method that provides an approximated transport plan and which admits a differentiable approximation. arxiv.org/abs/2505.22049 1/5 1236
Samuel Vaiter @samuelvaiter.com · 07/05/2025Convolution theorem: Fourier transform of the convolution of two functions (under suitable assumptions) is the product of the Fourier transforms of these two functions. buff.ly/aOamDMF 1142
Samuel Vaiter @samuelvaiter.com · 06/05/2025Dual numbers correspond to the completion of the real line with an nilpotent element ε different from 0. It can be thought as a universal linearization of functions, or as the forward-mode of automatic differentiation. buff.ly/vahZ0Fk 0151
Samuel Vaiter @samuelvaiter.com · 05/05/2025Convergence of iterates does not imply convergence of the derivatives. Nevertheless, Gilbert (1994) proposed an interversion limit-derivative theorem under strong assumption on the spectrum of the derivatives. buff.ly/MhK7qiI 071
Samuel Vaiter @samuelvaiter.com · 02/05/2025Leader-follower games, also known as Stackelberg games, are models in game theory where one player (the leader) makes a decision first, and the other player (the follower) responds, considering the leader’s action. This is one the first instance of bilevel optimization. 060
Samuel Vaiter @samuelvaiter.com · 01/05/2025The Matrix Mortality Problem asks if a given set of square matrices can multiply to the zero matrix after a finite sequence of multiplications of elements. It is is undecidable for matrices of size 3x3 or larger. buff.ly/lLmvvlo 163
Samuel Vaiter @samuelvaiter.com · 30/04/2025The SAT problem asks whether a logical formula, composed of variables and (AND, OR, NOT), can be satisfied by assigning True to the variables. SAT is NP-complete along with 3-SAT, with clauses of three literals, while 2-SAT, is in P! buff.ly/mMLGbw4 080
Samuel Vaiter @samuelvaiter.com · 29/04/2025The Krein-Milman theorem states that any compact convex subset of a locally convex topological vector space is the closed convex hull of its extreme points. In particular, the set of extreme points of a nonempty compact convex set is nonempty. buff.ly/6aYS8ox 040
Samuel Vaiter @samuelvaiter.com · 28/04/2025The Stone-Weierstrass theorem states that any continuous function on a compact Hausdorff space can be uniformly approximated by elements of a subalgebra, provided the subalgebra separates points and contains constants. buff.ly/MbZOAG0 072
Samuel Vaiter @samuelvaiter.com · 25/04/2025The Nesterov Accelerated Gradient (NAG) algorithm refines gradient descent by using an extrapolation step before computing the gradient. It leads to faster convergence for smooth convex functions, achieving the optimal rate of O(1/k^2). www.mathnet.ru/links/ceedfb... 0163
Samuel Vaiter @samuelvaiter.com · 24/04/2025The pinhole camera model illustrates the concept of projective projection. Light rays from a 3D scene pass through an (infinitely) small aperture — the pinhole — and project onto a 2D surface, creating an inverted image on the focal plan. monoskop.org/images/f/ff/... 092
Samuel Vaiter @samuelvaiter.com · 23/04/2025Łojasiewicz inequality provides a way to control how close points are to the zeros of a real analytic function based on the value of the function itself. Extension of this result to semialgebraic or o-minimal functions exist. matwbn.icm.edu.pl/ksiazki/sm/s... 082
Samuel Vaiter @samuelvaiter.com · 22/04/2025The fast inverse square root trick from Quake III is an algorithm to quickly approximate 1/√x, crucial for 3D graphics (normalisation). It uses bit-level manipulation and Newton's method for refinement. web.archive.org/web/20170729... 1282
Samuel Vaiter @samuelvaiter.com · 21/04/2025A Monge map, i.e., a solution to optimal transport Monge problems, may not always exist, be unique, or be symmetric with respect to the source and target distributions. It was one of the motivation to introduce Kantorovich relaxation. math.univ-lyon1.fr/~santambrogi... 1155
Samuel Vaiter @samuelvaiter.com · 18/04/2025Attouch’ theorem relates the (epi-) convergence of convex lsc functions to the convergence of their subdifferential seen as graph on the product between the space and its dual. gallica.bnf.fr/ark:/12148/b... 161
Samuel Vaiter @samuelvaiter.com · 17/04/2025Brenier's theorem states that the optimal transport map between two probability measures for quadratic cost is the gradient of a convex function. Moreover, it is uniquely defined up to a Lebesgue negligible set. www.ceremade.dauphine.fr/~carlier/Bre... 0101
Samuel Vaiter @samuelvaiter.com · 16/04/2025The Weierstrass function is a famous example of a continuous function that is nowhere differentiable. It defies intuition by being continuous everywhere but having no tangent at any point. Introduced by Karl Weierstrass in 1872. 2190
