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Aurélien Decelle

Aurélien Decelle appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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cond-mat.dis-nncond-mat.stat-mechastro-ph.COComputational ComplexityMachine Learningphysics.soc-ph

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Published work

10 published item(s)

preprint2026arXiv

Distributional simplicity bias and effective convexity in Energy Based Models

Energy-based learning is a powerful framework for generative modelling, but its training is inherently non-convex, leading potentially to sensitivity to initialisation, poor local optima, and unstable gradient dynamics. We present a dynamical analysis of energy-based learning through the lens of the effective model, which can be interpreted as either a generalised Ising model with higher-order interactions or the Fourier expansion of the energy. Under sufficient expressivity, we show that the gradient flow induced by learning strictly positive distributions over binary variables admits two types of fixed points: data-consistent points, which exactly reproduce the target distribution, and spurious points, which satisfy stationarity without matching the target distribution. Around data-consistent points, we show that perturbations are either stable or neutral, with neutral directions leaving the effective model invariant. Finally, we show that gradient dynamics induce a hierarchy in which lower-order interactions are learned before higher-order ones. This provides a mechanistic explanation for the distributional simplicity bias and clarifies why fixed points that are not data-consistent at low orders are not observed in practice.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Cosmology with cosmic web environments I. Real-space power spectra

We undertake the first comprehensive and quantitative real-space analysis of the cosmological information content in the environments of the cosmic web (voids, filaments, walls, and nodes) up to non-linear scales, $k = 0.5$ $h$/Mpc. Relying on the large set of $N$-body simulations from the Quijote suite, the environments are defined through the eigenvalues of the tidal tensor and the Fisher formalism is used to assess the constraining power of the power spectra derived in each of the four environments and their combination. Our results show that there is more information available in the environment-dependent power spectra, both individually and when combined all together, than in the matter power spectrum. By breaking some key degeneracies between parameters of the cosmological model such as $M_ν$--$σ_\mathrm{8}$ or $Ω_\mathrm{m}$--$σ_8$, the power spectra computed in identified environments improve the constraints on cosmological parameters by factors $\sim 15$ for the summed neutrino mass $M_ν$ and $\sim 8$ for the matter density $Ω_\mathrm{m}$ over those derived from the matter power spectrum. We show that these tighter constraints are obtained for a wide range of the maximum scale, from $k_\mathrm{max} = 0.1$ $h$/Mpc to highly non-linear regimes with $k_\mathrm{max} = 0.5$ $h$/Mpc. We also report an eight times higher value of the signal-to-noise ratio for the combination of spectra compared to the matter one. Importantly, we show that all the presented results are robust to variations of the parameters defining the environments hence suggesting a robustness to the definition we chose to define them.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Cycle-based Cluster Variational Method for Direct and Inverse Inference

We elaborate on the idea that loop corrections to belief propagation could be dealt with in a systematic way on pairwise Markov random fields, by using the elements of a cycle basis to define region in a generalized belief propagation setting. The region graph is specified in such a way as to avoid dual loops as much as possible, by discarding redundant Lagrange multipliers, in order to facilitate the convergence, while avoiding instabilities associated to minimal factor graph construction. We end up with a two-level algorithm, where a belief propagation algorithm is run alternatively at the level of each cycle and at the inter-region level. The inverse problem of finding the couplings of a Markov random field from empirical covariances can be addressed region wise. It turns out that this can be done efficiently in particular in the Ising context, where fixed point equations can be derived along with a one-parameter log likelihood function to minimize. Numerical experiments confirm the effectiveness of these considerations both for the direct and inverse MRF inference.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Data quality for the inverse Ising problem

There are many methods proposed for inferring parameters of the Ising model from given data, that is a set of configurations generated according to the model itself. However little attention has been paid until now to the data, e.g. how the data is generated, whether the inference error using one set of data could be smaller than using another set of data, etc. In this paper we address the data quality problem in the kinetic inverse Ising problem. We quantify the quality of data using effective rank of the correlation matrix, and show that data gathered in a out of-equilibrium regime has a better quality than data gathered in equilibrium for coupling reconstruction. We also propose a matrix-perturbation based method for tuning the quality of given data and for removing bad-quality (i.e. redundant) configurations from data.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Inference of the sparse kinetic Ising model using the decimation method

In this paper we study the inference of the kinetic Ising model on sparse graphs by the decimation method. The decimation method, which was first proposed in [Phys. Rev. Lett. 112, 070603] for the static inverse Ising problem, tries to recover the topology of the inferred system by setting the weakest couplings to zero iteratively. During the decimation process the likelihood function is maximized over the remaining couplings. Unlike the $\ell_1$-optimization based methods, the decimation method does not use the Laplace distribution as a heuristic choice of prior to select a sparse solution. In our case, the whole process can be done automatically without fixing any parameters by hand. We show that in the dynamical inference problem, where the task is to reconstruct the couplings of an Ising model given the data, the decimation process can be applied naturally into a maximum-likelihood optimization algorithm, as opposed to the static case where pseudo-likelihood method needs to be adopted. We also use extensive numerical studies to validate the accuracy of our methods in dynamical inference problems. Our results illustrate that on various topologies and with different distribution of couplings, the decimation method outperforms the widely-used $\ell _1$-optimization based methods.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Solving the inverse Ising problem by mean-field methods in a clustered phase space with many states

In this work we explain how to properly use mean-field methods to solve the inverse Ising problem when the phase space is clustered, that is many states are present. The clustering of the phase space can occur for many reasons, e.g. when a system undergoes a phase transition. Mean-field methods for the inverse Ising problem are typically used without taking into account the eventual clustered structure of the input configurations and may led to very bad inference (for instance in the low temperature phase of the Curie-Weiss model). In the present work we explain how to modify mean-field approaches when the phase space is clustered and we illustrate the effectiveness of the new method on different clustered structures (low temperature phases of Curie-Weiss and Hopfield models).

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Belief-Propagation Guided Monte-Carlo Sampling

A Monte-Carlo algorithm for discrete statistical models that combines the full power of the Belief Propagation algorithm with the advantages of a detailed-balanced heat bath approach is presented. A sub-tree inside the factor graph is first extracted randomly; Belief Propagation is then used as a perfect sampler to generate a configuration on the tree given the boundary conditions and the procedure is iterated. This appoach is best adapted for locally tree like graphs, it is therefore tested on the hard cases of spin-glass models for random graphs demonstrating its state-of-the art status in those cases.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Computational Complexity, Phase Transitions, and Message-Passing for Community Detection

We take a whirlwind tour of problems and techniques at the boundary of computer science and statistical physics. We start with a brief description of P, NP, and NP-completeness. We then discuss random graphs, including the emergence of the giant component and the k-core, using techniques from branching processes and differential equations. Using these tools as well as the second moment method, we give upper and lower bounds on the critical clause density for random k-SAT. We end with community detection in networks, variational methods, the Bethe free energy, belief propagation, the detectability transition, and the non-backtracking matrix.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Ensemble renormalization group for the random field hierarchical model

The Renormalization Group (RG) methods are still far from being completely understood in quenched disordered systems. In order to gain insight into the nature of the phase transition of these systems, it is common to investigate simple models. In this work we study a real-space RG transformation on the Dyson hierarchical lattice with a random field, which led to a reconstruction of the RG flow and to an evaluation of the critical exponents of the model at T = 0. We show that this method gives very accurate estimations of the critical exponents, by comparing our results with the ones obtained by some of us using an independent method.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Pseudolikelihood Decimation Algorithm Improving the Inference of the Interaction Network in a General Class of Ising Models

In this Letter we propose a new method to infer the topology of the interaction network in pairwise models with Ising variables. By using the pseudolikelihood method (PLM) at high temperature, it is generally possible to distinguish between zero and nonzero couplings because a clear gap separate the two groups. However at lower temperatures the PLM is much less effective and the result depends on subjective choices, such as the value of the $\ell_1$ regularizer and that of the threshold to separate nonzero couplings from null ones. We introduce a decimation procedure based on the PLM that recursively sets to zero the less significant couplings, until the variation of the pseudolikelihood signals that relevant couplings are being removed. The new method is fully automated and does not require any subjective choice by the user. Numerical tests have been performed on a wide class of Ising models, having different topologies (from random graphs to finite dimensional lattices) and different couplings (both diluted ferromagnets in a field and spin glasses). These numerical results show that the new algorithm performs better than standard PLM

0 citations0 reviewsNo code linkedOpen access