arXiv subjects

Cyril Labbé

Publications and source records attributed to Cyril Labbé.

At least 37 records · Page 2Linked to original sources

arXiv2021

Tortured phrases: A dubious writing style emerging in science. Evidence of critical issues affecting established journals

Probabilistic text generators have been used to produce fake scientific papers for more than a decade. Such nonsensical papers are easily detected by both human and machine. Now more complex AI-powered generation techniques produce texts indistinguishable from that of humans and the generation of scientific texts from a few keywords has been documented. Our study introduces the concept of tortured phrases: unexpected weird phrases in lieu of established ones, such as 'counterfeit consciousness' instead of 'artificial intelligence.' We combed the literature for tortured phrases and study one reputable journal where these concentrated en masse. Hypothesising the use of advanced language models we ran a detector on the abstracts of recent articles of this journal and on several control sets. The pairwise comparisons reveal a concentration of abstracts flagged as 'synthetic' in the journal. We also highlight irregularities in its operation, such as abrupt changes in editorial timelines. We substantiate our call for investigation by analysing several individual dubious articles, stressing questionable features: tortured writing style, citation of non-existent literature, and unacknowledged image reuse. Surprisingly, some websites offer to rewrite texts for free, generating gobbledegook full of tortured phrases. We believe some authors used rewritten texts to pad their manuscripts. We wish to raise the awareness on publications containing such questionable AI-generated or rewritten texts that passed (poor) peer review. Deception with synthetic texts threatens the integrity of the scientific literature.

cs.DL↗

arXiv2021

The delocalized phase of the Anderson Hamiltonian in $1$-d

We introduce a random differential operator, that we call the $\mathtt{CS}_τ$ operator, whose spectrum is given by the $\mbox{Sch}_τ$ point process introduced by Kritchevski, Valkó and Virág (2012) and whose eigenvectors match with the description provided by Rifkind and Virág (2018). This operator acts on $\mathbf{R}^2$-valued functions from the interval $[0,1]$ and takes the form: $$ 2 \begin{pmatrix} 0 & -\partial_t \\ \partial_t & 0 \end{pmatrix} + \sqrtτ \begin{pmatrix} d\mathcal{B} + \frac1{\sqrt 2} d\mathcal{W}_1 & \frac1{\sqrt 2} d\mathcal{W}_2\\ \frac1{\sqrt 2} d\mathcal{W}_2 & d\mathcal{B} - \frac1{\sqrt 2} d\mathcal{W}_1\end{pmatrix}\,, $$ where $d\mathcal{B}$, $d\mathcal{W}_1$ and $d\mathcal{W}_2$ are independent white noises. Then, we investigate the high part of the spectrum of the Anderson Hamiltonian $\mathcal{H}_L := -\partial_t^2 + dB$ on the segment $[0,L]$ with white noise potential $dB$, when $L\to\infty$. We show that the operator $\mathcal{H}_L$, recentred around energy levels $E \sim L/τ$ and unitarily transformed, converges in law as $L\to\infty$ to $\mathtt{CS}_τ$ in an appropriate sense. This allows to answer a conjecture of Rifkind and Virág (2018) on the behavior of the eigenvectors of $\mathcal{H}_L$. Our approach also explains how such an operator arises in the limit of $\mathcal{H}_L$. Finally we show that at higher energy levels, the Anderson Hamiltonian matches (asymptotically in $L$) with the unperturbed Laplacian $-\partial_t^2$. In a companion paper, it is shown that at energy levels much smaller than $L$, the spectrum is localized with Poisson statistics: the present paper therefore identifies the delocalized phase of the Anderson Hamiltonian.

math.PR↗

arXiv2021

Localization crossover for the continuous Anderson Hamiltonian in $1$-d

We investigate the behavior of the spectrum of the continuous Anderson Hamiltonian $\mathcal{H}_L$, with white noise potential, on a segment whose size $L$ is sent to infinity. We zoom around energy levels $E$ either of order $1$ (Bulk regime) or of order $1\ll E \ll L$ (Crossover regime). We show that the point process of (appropriately rescaled) eigenvalues and centers of mass converge to a Poisson point process. We also prove exponential localization of the eigenfunctions at an explicit rate. In addition, we show that the eigenfunctions converge to well-identified limits: in the Crossover regime, these limits are universal. Combined with the results of our companion paper arXiv:2102.05393, this identifies completely the transition between the localized and delocalized phases of the spectrum of $\mathcal{H}_L$. The two main technical challenges are the proof of a two-points or Minami estimate, as well as an estimate on the convergence to equilibrium of a hypoelliptic diffusion, the proof of which relies on Malliavin calculus and the theory of hypocoercivity.

math.PR↗

arXiv2020

The stochastic Airy operator at large temperature

It was shown in [J. A. Ramírez, B. Rider and B. Virág. J. Amer. Math. Soc. 24, 919-944 (2011)] that the edge of the spectrum of $β$ ensembles converges in the large $N$ limit to the bottom of the spectrum of the stochastic Airy operator. In the present paper, we obtain a complete description of the bottom of this spectrum when the temperature $1/β$ goes to $\infty$: we show that the point process of appropriately rescaled eigenvalues converges to a Poisson point process on $\mathbb{R}$ of intensity $e^x dx$ and that the eigenfunctions converge to Dirac masses centered at IID points with exponential laws. Furthermore, we obtain a precise description of the microscopic behavior of the eigenfunctions near their localization centers.

math.PR↗

arXiv2020

Mixing time of the adjacent walk on the simplex

By viewing the $N$-simplex as the set of positions of $N-1$ ordered particles on the unit interval, the adjacent walk is the continuous time Markov chain obtained by updating independently at rate 1 the position of each particle with a sample from the uniform distribution over the interval given by the two particles adjacent to it. We determine its spectral gap and prove that both the total variation distance and the separation distance to the uniform distribution exhibit a cutoff phenomenon, with mixing times that differ by a factor $2$. The results are extended to the family of log-concave distributions obtained by replacing the uniform sampling by a symmetric log-concave Beta distribution.

math.PR↗

arXiv2020

Spectral gap and cutoff phenomenon for the Gibbs sampler of $\nablaφ$ interfaces with convex potential

We consider the Gibbs sampler, or heat bath dynamics associated to log-concave measures on $\mathbb{R}^N$ describing $\nablaφ$ interfaces with convex potentials. Under minimal assumptions on the potential, we find that the spectral gap of the process is always given by $\mathrm{gap}_N=1-\cos(π/N)$, and that for all $ε\in(0,1)$, its $ε$-mixing time satisfies $T_N(ε)\sim \frac{\log N}{2\mathrm{gap}_N}$ as $N\to\infty$, thus establishing the cutoff phenomenon. The results reveal a universal behavior in that they do not depend on the choice of the potential.

math.PR↗

arXiv2019

Semi-Supervised Neural Text Generation by Joint Learning of Natural Language Generation and Natural Language Understanding Models

In Natural Language Generation (NLG), End-to-End (E2E) systems trained through deep learning have recently gained a strong interest. Such deep models need a large amount of carefully annotated data to reach satisfactory performance. However, acquiring such datasets for every new NLG application is a tedious and time-consuming task. In this paper, we propose a semi-supervised deep learning scheme that can learn from non-annotated data and annotated data when available. It uses an NLG and a Natural Language Understanding (NLU) sequence-to-sequence models which are learned jointly to compensate for the lack of annotation. Experiments on two benchmark datasets show that, with limited amount of annotated data, the method can achieve very competitive results while not using any pre-processing or re-scoring tricks. These findings open the way to the exploitation of non-annotated datasets which is the current bottleneck for the E2E NLG system development to new applications.

cs.CL↗

arXiv2019

The continuous Anderson hamiltonian in $d\le 3$

We construct the continuous Anderson hamiltonian on $(-L,L)^d$ driven by a white noise and endowed with either Dirichlet or periodic boundary conditions. Our construction holds in any dimension $d\le 3$ and relies on the theory of regularity structures: it yields a self-adjoint operator in $L^2\big((-L,L)^d\big)$ with pure point spectrum. In $d\ge 2$, a renormalisation of the operator by means of infinite constants is required to compensate for ill-defined products involving functionals of the white noise. We also obtain left tail estimates on the distributions of the eigenvalues: in particular, for $d=3$ these estimates show that the eigenvalues do not have exponential moments.

math.PR↗

arXiv2019

Localization of the continuous Anderson Hamiltonian in $1$-d

We study the bottom of the spectrum of the Anderson Hamiltonian $\mathcal{H}_L := -\partial_x^2 + ξ$ on $[0,L]$ driven by a white noise $ξ$ and endowed with either Dirichlet or Neumann boundary conditions. We show that, as $L\rightarrow\infty$, the point process of the (appropriately shifted and rescaled) eigenvalues converges to a Poisson point process on $\mathbb{R}$ with intensity $e^x dx$, and that the (appropriately rescaled) eigenfunctions converge to Dirac masses located at independent and uniformly distributed points. Furthermore, we show that the shape of each eigenfunction, recentered around its maximum and properly rescaled, is given by the inverse of a hyperbolic cosine. We also show that the eigenfunctions decay exponentially from their localization centers at an explicit rate, and we obtain very precise information on the zeros and local maxima of these eigenfunctions. Finally, we show that the eigenvalues/eigenfunctions in the Dirichlet and Neumann cases are very close to each other and converge to the same limits.

math.PR↗

arXiv2019

Cutoff phenomenon for the asymmetric simple exclusion process and the biased card shuffling

We consider the biased card shuffling and the Asymmetric Simple Exclusion Process (ASEP) on the segment. We obtain the asymptotic of their mixing times: our result show that these two continuous-time Markov chains display cutoff. Our analysis combines several ingredients including: a study of the hydrodynamic profile for ASEP, the use of monotonic eigenfunctions, stochastic comparisons and concentration inequalities.

math.PR↗

arXiv2019

Existence of densities for the dynamic $Φ^4_3$ model

We apply Malliavin calculus to the $Φ^4_3$ equation on the torus and prove existence of densities for the solution of the equation evaluated at regular enough test functions. We work in the framework of regularity structures and rely on Besov-type spaces of modelled distributions in order to prove Malliavin differentiability of the solution. Our result applies to a large family of Gaussian space-time noises including white noise, in particular the noise may be degenerate as long as it is sufficiently rough on small scales.

math.PR↗

arXiv2018

On the scaling limits of weakly asymmetric bridges

We consider a discrete bridge from $(0,0)$ to $(2N,0)$ evolving according to the corner growth dynamics, where the jump rates are subject to an upward asymmetry of order $N^{-α}$ with $α\in (0,\infty)$. We provide a classification of the asymptotic behaviours - invariant measure, hydrodynamic limit and fluctuations - of this model according to the value of the parameter $α$.

math.PR↗

arXiv2018

Multiplicative stochastic heat equations on the whole space

We carry out the construction of some ill-posed multiplicative stochastic heat equations on unbounded domains. The two main equations our result covers are, on the one hand the parabolic Anderson model on $\mathbf{R}^3$, and on the other hand the KPZ equation on $\mathbf{R}$ via the Cole-Hopf transform. To perform these constructions, we adapt the theory of regularity structures to the setting of weighted Besov spaces. One particular feature of our construction is that it allows one to start both equations from a Dirac mass at the initial time.

math.AP↗

arXiv2017

The reconstruction theorem in Besov spaces

The theory of regularity structures sets up an abstract framework of modelled distributions generalising the usual Hölder functions and allowing one to give a meaning to several ill-posed stochastic PDEs. A key result in that theory is the so-called reconstruction theorem: it defines a continuous linear operator that maps spaces of "modelled distributions" into the usual space of distributions. In the present paper, we extend the scope of this theorem to analogues to the whole class of Besov spaces $\mathcal{B}^γ_{p,q}$ with non-integer regularity indices. We then show that these spaces behave very much like their classical counterparts by obtaining the corresponding embedding theorems and Schauder-type estimates.

math.FA↗

arXiv2017

Weakly asymmetric bridges and the KPZ equation

We consider the corner growth dynamics on discrete bridges from $(0,0)$ to $(2N,0)$, or equivalently, the weakly asymmetric simple exclusion process with $N$ particles on $2N$ sites. We take an asymmetry of order $N^{-α}$ with $α\in (0,1)$ and provide a complete description of the asymptotic behaviour of this model. In particular, we show that the hydrodynamic limit of the density of particles is given by the inviscid Burgers equation with zero-flux boundary condition. When the interface starts from the flat initial profile, we show that KPZ fluctuations occur whenever $α\in (0,1/3]$. In the particular regime $α=1/3$, these KPZ fluctuations suddenly vanish at a deterministic time.

math.PR↗

arXiv2017

A simple construction of the continuum parabolic Anderson model on $\mathbf{R}^2$

We propose a simple construction of the solution to the continuum parabolic Anderson model on $\mathbf{R}^2$ which does not rely on any elaborate arguments and makes extensive use of the linearity of the equation. A logarithmic renormalisation is required to counterbalance the divergent product appearing in the equation. Furthermore, we use time-dependent weights in our spaces of distributions in order to construct the solution on the unbounded space $\mathbf{R}^2$.

math.PR↗

arXiv2014

Scaling limits of weakly asymmetric interfaces

We consider three models of evolving interfaces intimately related to the weakly asymmetric simple exclusion process with $N$ particles on a finite lattice of $2N$ sites. Our Model 1 defines an evolving bridge on $[0,1]$, our Model 1-w an evolving excursion on $[0,1]$ while our Model 2 consists of an evolving pair of non-crossing bridges on $[0,1]$. Based on the observation that the invariant measures of the dynamics depend on the area under (or between) the interface(s), we characterise the scaling limits of the invariant measures when the asymmetry of the exclusion process scales like $N^{-\frac{3}{2}}$. Then, we show that the scaling limits of the dynamics themselves are expressed in terms of variants of the stochastic heat equation. In particular, in Model 1-w we obtain the well-studied reflected stochastic heat equation introduced by Nualart and Pardoux.

math.PR↗

arXiv2014

Genealogy of flows of continuous-state branching processes via flows of partitions and the Eve property

We encode the genealogy of a continuous-state branching process associated with a branching mechanism $Ψ$ - or $Ψ$-CSBP in short - using a stochastic flow of partitions. This encoding holds for all branching mechanisms and appears as a very tractable object to deal with asymptotic behaviours and convergences. In particular we study the so-called Eve property - the existence of an ancestor from which the entire population descends asymptotically - and give a necessary and sufficient condition on the $Ψ$-CSBP for this property to hold. Finally, we show that the flow of partitions unifies the lookdown representation and the flow of subordinators when the Eve property holds.

math.PR↗