arXiv subjects

Yoann L. Launay

Publications and source records attributed to Yoann L. Launay.

5 recordsLinked to original sources

arXiv2026

DMAP: A Distribution Map for Text

Large Language Models (LLMs) are a powerful tool for statistical text analysis, with derived sequences of next-token probability distributions offering a wealth of information. Extracting this signal typically relies on metrics such as perplexity, which do not adequately account for context; how one should interpret a given next-token probability is dependent on the number of reasonable choices encoded by the shape of the conditional distribution. In this work, we present DMAP, a mathematically grounded method that maps a text, via a language model, to a set of samples in the unit interval that jointly encode rank and probability information. This representation enables efficient, model-agnostic analysis and supports a range of applications. We illustrate its utility through three case studies: (i) validation of generation parameters to ensure data integrity, (ii) examining the role of probability curvature in machine-generated text detection, and (iii) a forensic analysis revealing statistical fingerprints left in downstream models that have been subject to post-training on synthetic data. Our results demonstrate that DMAP offers a unified statistical view of text that is simple to compute on consumer hardware, widely applicable, and provides a foundation for further research into text analysis with LLMs.

cs.CL↗

arXiv2025

Stochastic Inflation in Numerical Relativity

A set of 3+1 equations for stochastic inflation incorporating all metric and scalar matter degrees of freedom, first presented in previous work, are re-derived in a gauge invariant manner. We then present numerical implementations of these stochastic equations, cast in the BSSN formulation of Numerical Relativity, demonstrating their efficacy in both a slow-roll and an ultra slow-roll scenario. We find the evolution is correctly reproduced for all the dynamical variables, and the energy and momentum constraints are well-satisfied. This demonstrates that the stochastic equations are theoretically and numerically robust and ready to be applied to a wider inflationary landscape. Our simulations result in real space realizations of the fully non-linear stochastic dynamics with \new{gradients and anisotropic expansion retained. This work generalizes standard stochastic inflation, inflationary numerical relativity and lattice cosmology, opening up the possibility for reliable predictions of non-perturbative phenomena and providing} precise initial conditions for subsequent cosmological eras.

gr-qc↗

arXiv2025

Bunch-Davies initial conditions and non-perturbative inflationary dynamics in Numerical Relativity

We show that it is possible to simulate realistic inhomogeneities during cosmological inflation with high precision using {Numerical Relativity}. Stochastic initial conditions are set in line with the Bunch-Davies {vacuum} and satisfy the Hamiltonian and Momentum constraints of General Relativity to leading order in perturbation theory. The subsequent fully non-linear dynamical evolution is formulated within a family of geodesic gauges but can in principle be adapted to any choice of coordinates. We present 3 examples of inflationary dynamics: a simple quadratic potential, a potential with an inflection point and a strong resonance model. When perturbations are small, we recover standard predictions of cosmological perturbation theory, and we quantify strongly non-linear inhomogeneities when non-perturbative configurations emerge, such as in the strong resonance model. Our results pave the way towards the first realistic non-perturbative, and fully non-linear Numerical Relativity simulations of the early inflationary universe.

gr-qc↗

arXiv2024

Quantitative classicality in cosmological interactions during inflation

We examine the classical and quantum evolution of inflationary cosmological perturbations from quantum initial conditions, using the on-shell and off-shell contributions to correlators to investigate the signatures of interactions. In particular, we calculate the Keldysh contributions to the leading order bispectrum from past infinity, showing that the squeezed limit is dominated by the on-shell evolution. By truncating the time integrals in the analytic expressions for contributions to the bispectrum, we define a `quantum interactivity' and quantitatively identify scales and times for which it is sufficient to only assume classical evolution, given a fixed precision. In contrast to typical perceptions inspired by free two-point functions, we show that common non-linear contributions to inflationary perturbations can be well-described by classical evolution even prior to horizon crossing. The insights gained here can pave the way for quantitative criteria for justifying the validity of numerically simulating the generation and evolution of quantum fluctuations in inflation. In particular, we comment on the validity of using stochastic inflation to reproduce known in-in perturbative results. An extensive appendix provides a review of the Keldysh formulation of the in-in formalism with the initial state set at a finite, as opposed to infinite past, emphasizing the importance of considering temporal boundary terms and the initial state for correctly obtaining the propagators. We also show how stochastic dynamics can emerge as a sufficiently accurate approximation to the full quantum evolution. This becomes particularly transparent in the Keldysh description.

gr-qc↗

arXiv2024

Stochastic Inflation in General Relativity

We provide a formulation of Stochastic Inflation in full general relativity that goes beyond the slow-roll and separate universe approximations. We show how gauge invariant Langevin source terms can be obtained for the complete set of Einstein equations in their ADM formulation by providing a recipe for coarse-graining the spacetime in any small gauge. These stochastic source terms are defined in terms of the only dynamical scalar degree of freedom in single-field inflation and all depend simply on the first two time derivatives of the coarse-graining window function, on the gauge-invariant mode functions that satisfy the Mukhanov-Sasaki evolution equation, and on the slow-roll parameters. It is shown that this reasoning can also be applied to include gravitons as stochastic sources, thus enabling the study of all relevant degrees of freedom of general relativity for inflation. We validate the efficacy of these Langevin dynamics directly using an example in uniform field gauge, obtaining the stochastic e-fold number in the long wavelength limit without the need for a first-passage-time analysis. As well as investigating the most commonly used gauges in cosmological perturbation theory, we also derive stochastic source terms for the coarse-grained BSSN formulation of Einstein's equations, which enables a well-posed implementation for 3+1 numerical relativity simulations.

gr-qc↗