25 citations · 47 across the 19 of their papers we have counts for
24 papers
Minimal time for heat observability on almost-Riemannian surfaces
Vincent Boulard, Amaury Hayat, Emmanuel Trélat
We determine the minimal observation time for the heat equation on a closed almost-Riemannian surface, for a class of observation sets leaving sufficiently thin collars around simp…
Learning to Discover Interesting Mathematics
Niket Patel, Ahmad Rammal, Amaury Hayat +2
Recently, Large Language Models (LLMs) have been increasingly able to solve advanced mathematical problems, including many that have been open for decades. This opens the door to e…
Optimal geometric barriers for weighted observability of heat semigroups on metric measure spaces
Vincent Boulard, Amaury Hayat, Emmanuel Trélat
Weighted integrated observability inequalities for heat equations usually involve a small-time factor of the form . We prove that this scale is not an artefact of Carlema…
Formalizing Mathematics at Scale
Ahmad Rammal, Niket Patel, Fabian Gloeckle +5
We present AutoformBot, a multi-agent system for building an Autoformalized Textbook Library At Scale (Atlas) in Lean 4. AutoformBot orchestrates thousands of LLM agents, equipped…
Quantitative Fredholm backstepping and rapid stabilization
Ludovick Gagnon, Amaury Hayat, Swann Marx +2
In this paper, we address the existence of Fredholm backstepping transformations for self-adjoint and skew-adjoint operators . Under suitable assumptions on the operator and…
WybeCoder: Verified Imperative Code Generation
Fabian Gloeckle, Mantas Baksys, Darius Feher +5
Recent progress in large language models (LLMs) has substantially advanced automatic code generation and formal theorem proving, yet software verification has not seen comparable g…
Global boundary stabilization of 1d systems of scalar conservation laws
Georges Bastin, Jean-Michel Coron, Amaury Hayat
We study a system of several one-dimensional scalar conservation laws coupled through boundary feedback conditions that combine physical boundary constraints with static feedback c…
Automatic Textbook Formalization
Fabian Gloeckle, Ahmad Rammal, Charles Arnal +4
We present a case study where an automatic AI system formalizes a textbook with more than 500 pages of graduate-level algebraic combinatorics to Lean. The resulting formalization r…
Exponential stability of the linearized viscous Saint-Venant equations using a quadratic Lyapunov function
Amaury Hayat, Nathan Lichtlé
In this work, we investigate the exponential stability of the viscous Saint-Venant equations by adding to the standard hyperbolic Saint-Venant equations a viscosity term coming fro…
Boundary stabilization of flows in networks of open channels modeled by Saint-Venant equations
Amaury Hayat, Yating Hu, Peipei Shang
This work investigates the boundary stabilization of flows in star-shaped and tree-shaped networks of open channels governed by the Saint-Venant equations with a friction term. Due…
Rapid stabilization of general linear systems with F-equivalence
Amaury Hayat, Epiphane Loko
We study the rapid stabilization of general linear systems, when the differential operator has a Riesz basis of eigenvectors. We find simple sufficient conditions for…
Traffic Flow Reconstruction from Limited Collected Data
Nail Baloul, Amaury Hayat, Thibault Liard +1
We propose an efficient method for reconstructing traffic density with low penetration rate of probe vehicles. Specifically, we rely on measuring only the initial and final positio…
LemmaBench: A Live, Research-Level Benchmark to Evaluate LLM Capabilities in Mathematics
Antoine Peyronnet, Fabian Gloeckle, Amaury Hayat
We present a new approach for benchmarking Large Language Model (LLM) capabilities on research-level mathematics. Existing benchmarks largely rely on static, hand-curated sets of c…
F-equivalence for parabolic systems and applications to the stabilization of nonlinear PDE
Vincent Boulard, Amaury Hayat
We consider the -equivalence problem for parabolic systems: under which conditions a control system, governed by a parabolic operator and a control operator , can be made…
Global Lyapunov functions: a long-standing open problem in mathematics, with symbolic transformers
Alberto Alfarano, François Charton, Amaury Hayat
Despite their spectacular progress, language models still struggle on complex reasoning tasks, such as advanced mathematics. We consider a long-standing open problem in mathematics…
Traffic Control via Connected and Automated Vehicles: An Open-Road Field Experiment with 100 CAVs
Jonathan W. Lee, Han Wang, Kathy Jang +61
The CIRCLES project aims to reduce instabilities in traffic flow, which are naturally occurring phenomena due to human driving behavior. These "phantom jams" or "stop-and-go waves,…
Traffic smoothing using explicit local controllers
Amaury Hayat, Arwa Alanqary, Rahul Bhadani +16
The dissipation of stop-and-go waves attracted recent attention as a traffic management problem, which can be efficiently addressed by automated driving. As part of the 100 automat…
Reinforcement Learning in Control Theory: A New Approach to Mathematical Problem Solving
Kala Agbo Bidi, Jean-Michel Coron, Amaury Hayat +1
One of the central questions in control theory is achieving stability through feedback control. This paper introduces a novel approach that combines Reinforcement Learning (RL) wit…
HyperTree Proof Search for Neural Theorem Proving
Guillaume Lample, Marie-Anne Lachaux, Thibaut Lavril +5
We propose an online training procedure for a transformer-based automated theorem prover. Our approach leverages a new search algorithm, HyperTree Proof Search (HTPS), inspired by…
A rigorous multi-population multi-lane hybrid traffic model and its mean-field limit for dissipation of waves via autonomous vehicles
Nicolas Kardous, Amaury Hayat, Sean T. McQuade +7
In this paper, a multi-lane multi-population microscopic model, which presents stop and go waves, is proposed to simulate traffic on a ring-road. Vehicles are divided between human…
Stability of multi-population traffic flows
Amaury Hayat, Benedetto Piccoli, Shengquan Xiang
Traffic waves, known also as stop-and-go waves or phantom hams, appear naturally as traffic instabilities, also in confined environments as a ring-road. A multi-population traffic…
A deep language model to predict metabolic network equilibria
François Charton, Amaury Hayat, Sean T. McQuade +2
We show that deep learning models, and especially architectures like the Transformer, originally intended for natural language, can be trained on randomly generated datasets to pre…
Integrated Framework of Vehicle Dynamics, Instabilities, Energy Models, and Sparse Flow Smoothing Controllers
Jonathan W. Lee, George Gunter, Rabie Ramadan +25
This work presents an integrated framework of: vehicle dynamics models, with a particular attention to instabilities and traffic waves; vehicle energy models, with particular atten…
Limitations and Improvements of the Intelligent Driver Model (IDM)
Saleh Albeaik, Alexandre Bayen, Maria Teresa Chiri +7
This contribution analyzes the widely used and well-known "intelligent driver model (briefly IDM), which is a second order car-following model governed by a system of ordinary diff…