1 code implementation • 7 Aug 2024 • Antoine Maillard, Emanuele Troiani, Simon Martin, Florent Krzakala, Lenka Zdeborová

We consider the problem of learning a target function corresponding to a single hidden layer neural network, with a quadratic activation function after the first layer, and random weights.

no code implementations • 7 Aug 2024 • Beatriz Borges, Negar Foroutan, Deniz Bayazit, Anna Sotnikova, Syrielle Montariol, Tanya Nazaretzky, Mohammadreza Banaei, Alireza Sakhaeirad, Philippe Servant, Seyed Parsa Neshaei, Jibril Frej, Angelika Romanou, Gail Weiss, Sepideh Mamooler, Zeming Chen, Simin Fan, Silin Gao, Mete Ismayilzada, Debjit Paul, Alexandre Schöpfer, Andrej Janchevski, Anja Tiede, Clarence Linden, Emanuele Troiani, Francesco Salvi, Freya Behrens, Giacomo Orsi, Giovanni Piccioli, Hadrien Sevel, Louis Coulon, Manuela Pineros-Rodriguez, Marin Bonnassies, Pierre Hellich, Puck van Gerwen, Sankalp Gambhir, Solal Pirelli, Thomas Blanchard, Timothée Callens, Toni Abi Aoun, Yannick Calvino Alonso, Yuri Cho, Alberto Chiappa, Antonio Sclocchi, Étienne Bruno, Florian Hofhammer, Gabriel Pescia, Geovani Rizk, Leello Dadi, Lucas Stoffl, Manoel Horta Ribeiro, Matthieu Bovel, Yueyang Pan, Aleksandra Radenovic, Alexandre Alahi, Alexander Mathis, Anne-Florence Bitbol, Boi Faltings, Cécile Hébert, Devis Tuia, François Maréchal, George Candea, Giuseppe Carleo, Jean-Cédric Chappelier, Nicolas Flammarion, Jean-Marie Fürbringer, Jean-Philippe Pellet, Karl Aberer, Lenka Zdeborová, Marcel Salathé, Martin Jaggi, Martin Rajman, Mathias Payer, Matthieu Wyart, Michael Gastpar, Michele Ceriotti, Ola Svensson, Olivier Lévêque, Paolo Ienne, Rachid Guerraoui, Robert West, Sanidhya Kashyap, Valerio Piazza, Viesturs Simanis, Viktor Kuncak, Volkan Cevher, Philippe Schwaller, Sacha Friedli, Patrick Jermann, Tanja Kaser, Antoine Bosselut

We investigate the potential scale of this vulnerability by measuring the degree to which AI assistants can complete assessment questions in standard university-level STEM courses.

1 code implementation • 16 Jul 2024 • Freya Behrens, Luca Biggio, Lenka Zdeborová

From a broader perspective, our analysis offers a framework to understand how the interaction of different architectural components of transformer models shapes diverse algorithmic solutions and approximations.

no code implementations • 3 Jul 2024 • Christian Keup, Lenka Zdeborová

This work explores multi-modal inference in a high-dimensional simplified model, analytically quantifying the performance gain of multi-modal inference over that of analyzing modalities in isolation.

1 code implementation • 24 May 2024 • Emanuele Troiani, Yatin Dandi, Leonardo Defilippis, Lenka Zdeborová, Bruno Loureiro, Florent Krzakala

Multi-index models - functions which only depend on the covariates through a non-linear transformation of their projection on a subspace - are a useful benchmark for investigating feature learning with neural networks.

no code implementations • 7 Mar 2024 • Pierre Mergny, Justin Ko, Florent Krzakala, Lenka Zdeborová

We consider the task of estimating a low-rank matrix from non-linear and noisy observations.

no code implementations • 21 Feb 2024 • Lucas Clarté, Adrien Vandenbroucque, Guillaume Dalle, Bruno Loureiro, Florent Krzakala, Lenka Zdeborová

We investigate popular resampling methods for estimating the uncertainty of statistical models, such as subsampling, bootstrap and the jackknife, and their performance in high-dimensional supervised regression tasks.

1 code implementation • 7 Feb 2024 • Hugo Cui, Luca Pesce, Yatin Dandi, Florent Krzakala, Yue M. Lu, Lenka Zdeborová, Bruno Loureiro

In this manuscript, we investigate the problem of how two-layer neural networks learn features from data, and improve over the kernel regime, after being trained with a single gradient descent step.

no code implementations • 6 Feb 2024 • Hugo Cui, Freya Behrens, Florent Krzakala, Lenka Zdeborová

We investigate how a dot-product attention layer learns a positional attention matrix (with tokens attending to each other based on their respective positions) and a semantic attention matrix (with tokens attending to each other based on their meaning).

1 code implementation • 5 Feb 2024 • Yatin Dandi, Emanuele Troiani, Luca Arnaboldi, Luca Pesce, Lenka Zdeborová, Florent Krzakala

In particular, multi-pass GD with finite stepsize is found to overcome the limitations of gradient flow and single-pass GD given by the information exponent (Ben Arous et al., 2021) and leap exponent (Abbe et al., 2023) of the target function.

1 code implementation • 5 Oct 2023 • Hugo Cui, Florent Krzakala, Eric Vanden-Eijnden, Lenka Zdeborová

We study the problem of training a flow-based generative model, parametrized by a two-layer autoencoder, to sample from a high-dimensional Gaussian mixture.

1 code implementation • 27 Aug 2023 • Davide Ghio, Yatin Dandi, Florent Krzakala, Lenka Zdeborová

Recent years witnessed the development of powerful generative models based on flows, diffusion or autoregressive neural networks, achieving remarkable success in generating data from examples with applications in a broad range of areas.

2 code implementations • 5 Jun 2023 • Giovanni Piccioli, Emanuele Troiani, Lenka Zdeborová

In this paper, we study sampling from a posterior derived from a neural network.

2 code implementations • 5 Mar 2023 • Lucas Clarté, Bruno Loureiro, Florent Krzakala, Lenka Zdeborová

Despite their incredible performance, it is well reported that deep neural networks tend to be overoptimistic about their prediction confidence.

no code implementations • 1 Feb 2023 • Hugo Cui, Florent Krzakala, Lenka Zdeborová

We consider the problem of learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights.

1 code implementation • 23 Oct 2022 • Lucas Clarté, Bruno Loureiro, Florent Krzakala, Lenka Zdeborová

Uncertainty quantification is a central challenge in reliable and trustworthy machine learning.

no code implementations • 12 Aug 2022 • Siyu Chen, Guanhao Huang, Giovanni Piccioli, Lenka Zdeborová

We derive the replica symmetric (RS) phase diagram in the temperature, ferromagnetic bias plane using the approximate message passing (AMP) algorithm and its state evolution (SE).

1 code implementation • 26 May 2022 • Luca Pesce, Bruno Loureiro, Florent Krzakala, Lenka Zdeborová

A simple model to study subspace clustering is the high-dimensional $k$-Gaussian mixture model where the cluster means are sparse vectors.

2 code implementations • 26 May 2022 • Federica Gerace, Florent Krzakala, Bruno Loureiro, Ludovic Stephan, Lenka Zdeborová

We argue that there is a large universality class of high-dimensional input data for which we obtain the same minimum training loss as for Gaussian data with corresponding data covariance.

1 code implementation • 22 Mar 2022 • Elisabetta Cornacchia, Francesca Mignacco, Rodrigo Veiga, Cédric Gerbelot, Bruno Loureiro, Lenka Zdeborová

For Gaussian teacher weights, we investigate the performance of ERM with both cross-entropy and square losses, and explore the role of ridge regularisation in approaching Bayes-optimality.

1 code implementation • 7 Feb 2022 • Lucas Clarté, Bruno Loureiro, Florent Krzakala, Lenka Zdeborová

In this manuscript, we characterise uncertainty for learning from limited number of samples of high-dimensional Gaussian input data and labels generated by the probit model.

2 code implementations • 1 Feb 2022 • Rodrigo Veiga, Ludovic Stephan, Bruno Loureiro, Florent Krzakala, Lenka Zdeborová

Despite the non-convex optimization landscape, over-parametrized shallow networks are able to achieve global convergence under gradient descent.

no code implementations • 29 Jan 2022 • Hugo Cui, Bruno Loureiro, Florent Krzakala, Lenka Zdeborová

We find that our rates tightly describe the learning curves for this class of data sets, and are also observed on real data.

no code implementations • NeurIPS 2021 • Bruno Loureiro, Gabriele Sicuro, Cedric Gerbelot, Alessandro Pacco, Florent Krzakala, Lenka Zdeborová

Generalised linear models for multi-class classification problems are one of the fundamental building blocks of modern machine learning tasks.

no code implementations • 9 Jun 2021 • Federica Gerace, Luca Saglietti, Stefano Sarao Mannelli, Andrew Saxe, Lenka Zdeborová

Transfer learning can significantly improve the sample efficiency of neural networks, by exploiting the relatedness between a data-scarce target task and a data-abundant source task.

2 code implementations • 7 Jun 2021 • Bruno Loureiro, Gabriele Sicuro, Cédric Gerbelot, Alessandro Pacco, Florent Krzakala, Lenka Zdeborová

Generalised linear models for multi-class classification problems are one of the fundamental building blocks of modern machine learning tasks.

no code implementations • NeurIPS 2021 • Hugo Cui, Bruno Loureiro, Florent Krzakala, Lenka Zdeborová

In this work, we unify and extend this line of work, providing characterization of all regimes and excess error decay rates that can be observed in terms of the interplay of noise and regularization.

1 code implementation • 16 May 2021 • Sebastian Goldt, Florent Krzakala, Lenka Zdeborová, Nicolas Brunel

The advent of comprehensive synaptic wiring diagrams of large neural circuits has created the field of connectomics and given rise to a number of open research questions.

no code implementations • 8 Mar 2021 • Francesca Mignacco, Pierfrancesco Urbani, Lenka Zdeborová

In this paper we investigate how gradient-based algorithms such as gradient descent, (multi-pass) stochastic gradient descent, its persistent variant, and the Langevin algorithm navigate non-convex loss-landscapes and which of them is able to reach the best generalization error at limited sample complexity.

1 code implementation • 23 Feb 2021 • Maria Refinetti, Sebastian Goldt, Florent Krzakala, Lenka Zdeborová

Here, we show theoretically that two-layer neural networks (2LNN) with only a few hidden neurons can beat the performance of kernel learning on a simple Gaussian mixture classification task.

1 code implementation • NeurIPS 2021 • Bruno Loureiro, Cédric Gerbelot, Hugo Cui, Sebastian Goldt, Florent Krzakala, Marc Mézard, Lenka Zdeborová

While still solvable in a closed form, this generalization is able to capture the learning curves for a broad range of realistic data sets, thus redeeming the potential of the teacher-student framework.

1 code implementation • 8 Dec 2020 • Antoine Maillard, Florent Krzakala, Yue M. Lu, Lenka Zdeborová

We consider the phase retrieval problem, in which the observer wishes to recover a $n$-dimensional real or complex signal $\mathbf{X}^\star$ from the (possibly noisy) observation of $|\mathbf{\Phi} \mathbf{X}^\star|$, in which $\mathbf{\Phi}$ is a matrix of size $m \times n$.

Information Theory Disordered Systems and Neural Networks Information Theory

no code implementations • 1 Dec 2020 • Luca Saglietti, Lenka Zdeborová

In recent years the empirical success of transfer learning with neural networks has stimulated an increasing interest in obtaining a theoretical understanding of its core properties.

no code implementations • 20 Sep 2020 • Antoine Baker, Indaco Biazzo, Alfredo Braunstein, Giovanni Catania, Luca Dall'Asta, Alessandro Ingrosso, Florent Krzakala, Fabio Mazza, Marc Mézard, Anna Paola Muntoni, Maria Refinetti, Stefano Sarao Mannelli, Lenka Zdeborová

We conclude that probabilistic risk estimation is capable to enhance performance of digital contact tracing and should be considered in the currently developed mobile applications.

no code implementations • NeurIPS 2020 • Stefano Sarao Mannelli, Eric Vanden-Eijnden, Lenka Zdeborová

We consider a teacher-student scenario where the teacher has the same structure as the student with a hidden layer of smaller width $m^*\le m$.

1 code implementation • 25 Jun 2020 • Sebastian Goldt, Bruno Loureiro, Galen Reeves, Florent Krzakala, Marc Mézard, Lenka Zdeborová

Here, we go beyond this simple paradigm by studying the performance of neural networks trained on data drawn from pre-trained generative models.

no code implementations • NeurIPS 2020 • Stefano Sarao Mannelli, Giulio Biroli, Chiara Cammarota, Florent Krzakala, Pierfrancesco Urbani, Lenka Zdeborová

Despite the widespread use of gradient-based algorithms for optimizing high-dimensional non-convex functions, understanding their ability of finding good minima instead of being trapped in spurious ones remains to a large extent an open problem.

no code implementations • NeurIPS 2020 • Benjamin Aubin, Florent Krzakala, Yue M. Lu, Lenka Zdeborová

We consider a commonly studied supervised classification of a synthetic dataset whose labels are generated by feeding a one-layer neural network with random iid inputs.

no code implementations • NeurIPS 2020 • Francesca Mignacco, Florent Krzakala, Pierfrancesco Urbani, Lenka Zdeborová

We define a particular stochastic process for which SGD can be extended to a continuous-time limit that we call stochastic gradient flow.

1 code implementation • NeurIPS 2020 • Antoine Maillard, Bruno Loureiro, Florent Krzakala, Lenka Zdeborová

We consider the phase retrieval problem of reconstructing a $n$-dimensional real or complex signal $\mathbf{X}^{\star}$ from $m$ (possibly noisy) observations $Y_\mu = | \sum_{i=1}^n \Phi_{\mu i} X^{\star}_i/\sqrt{n}|$, for a large class of correlated real and complex random sensing matrices $\mathbf{\Phi}$, in a high-dimensional setting where $m, n\to\infty$ while $\alpha = m/n=\Theta(1)$.

1 code implementation • 3 Apr 2020 • Antoine Baker, Benjamin Aubin, Florent Krzakala, Lenka Zdeborová

We introduce Tree-AMP, standing for Tree Approximate Message Passing, a python package for compositional inference in high-dimensional tree-structured models.

no code implementations • ICML 2020 • Francesca Mignacco, Florent Krzakala, Yue M. Lu, Lenka Zdeborová

We also illustrate the interpolation peak at low regularization, and analyze the role of the respective sizes of the two clusters.

no code implementations • ICML 2020 • Federica Gerace, Bruno Loureiro, Florent Krzakala, Marc Mézard, Lenka Zdeborová

In particular, we show how to obtain analytically the so-called double descent behaviour for logistic regression with a peak at the interpolation threshold, we illustrate the superiority of orthogonal against random Gaussian projections in learning with random features, and discuss the role played by correlations in the data generated by the hidden manifold model.

no code implementations • 9 Dec 2019 • Hugo Cui, Luca Saglietti, Lenka Zdeborová

These large deviations then provide optimal achievable performance boundaries for any active learning algorithm.

no code implementations • 5 Dec 2019 • Alia Abbara, Benjamin Aubin, Florent Krzakala, Lenka Zdeborová

Statistical learning theory provides bounds of the generalization gap, using in particular the Vapnik-Chervonenkis dimension and the Rademacher complexity.

no code implementations • 4 Dec 2019 • Benjamin Aubin, Bruno Loureiro, Antoine Baker, Florent Krzakala, Lenka Zdeborová

We consider the problem of compressed sensing and of (real-valued) phase retrieval with random measurement matrix.

1 code implementation • NeurIPS 2019 • Stefano Sarao Mannelli, Giulio Biroli, Chiara Cammarota, Florent Krzakala, Lenka Zdeborová

Gradient-based algorithms are effective for many machine learning tasks, but despite ample recent effort and some progress, it often remains unclear why they work in practice in optimising high-dimensional non-convex functions and why they find good minima instead of being trapped in spurious ones. Here we present a quantitative theory explaining this behaviour in a spiked matrix-tensor model. Our framework is based on the Kac-Rice analysis of stationary points and a closed-form analysis of gradient-flow originating from statistical physics.

1 code implementation • 25 Sep 2019 • Sebastian Goldt, Marc Mézard, Florent Krzakala, Lenka Zdeborová

We demonstrate that learning of the hidden manifold model is amenable to an analytical treatment by proving a "Gaussian Equivalence Property" (GEP), and we use the GEP to show how the dynamics of two-layer neural networks trained using one-pass stochastic gradient descent is captured by a set of integro-differential equations that track the performance of the network at all times.

1 code implementation • 13 Aug 2019 • William H. Weir, Benjamin Walker, Lenka Zdeborová, Peter J. Mucha

We compare our approach with a widely used community detection tool, GenLouvain, across a range of synthetic, multilayer benchmark networks, demonstrating that our method performs comparably to the state of the art.

Social and Information Networks Data Analysis, Statistics and Probability Physics and Society

no code implementations • 18 Jul 2019 • Stefano Sarao Mannelli, Giulio Biroli, Chiara Cammarota, Florent Krzakala, Lenka Zdeborová

Gradient-based algorithms are effective for many machine learning tasks, but despite ample recent effort and some progress, it often remains unclear why they work in practice in optimising high-dimensional non-convex functions and why they find good minima instead of being trapped in spurious ones.

3 code implementations • NeurIPS 2019 • Sebastian Goldt, Madhu S. Advani, Andrew M. Saxe, Florent Krzakala, Lenka Zdeborová

Deep neural networks achieve stellar generalisation even when they have enough parameters to easily fit all their training data.

1 code implementation • 11 Jun 2019 • Alia Abbara, Antoine Baker, Florent Krzakala, Lenka Zdeborová

In a noiseless linear estimation problem, one aims to reconstruct a vector x* from the knowledge of its linear projections y=Phi x*.

2 code implementations • NeurIPS 2019 • Benjamin Aubin, Bruno Loureiro, Antoine Maillard, Florent Krzakala, Lenka Zdeborová

Here, we replace the sparsity assumption by generative modelling, and investigate the consequences on statistical and algorithmic properties.

1 code implementation • 25 Mar 2019 • Giuseppe Carleo, Ignacio Cirac, Kyle Cranmer, Laurent Daudet, Maria Schuld, Naftali Tishby, Leslie Vogt-Maranto, Lenka Zdeborová

Machine learning encompasses a broad range of algorithms and modeling tools used for a vast array of data processing tasks, which has entered most scientific disciplines in recent years.

Computational Physics Cosmology and Nongalactic Astrophysics Disordered Systems and Neural Networks High Energy Physics - Theory Quantum Physics

no code implementations • 1 Feb 2019 • Stefano Sarao Mannelli, Florent Krzakala, Pierfrancesco Urbani, Lenka Zdeborová

In this work we analyse quantitatively the interplay between the loss landscape and performance of descent algorithms in a prototypical inference problem, the spiked matrix-tensor model.

no code implementations • 25 Jan 2019 • Sebastian Goldt, Madhu S. Advani, Andrew M. Saxe, Florent Krzakala, Lenka Zdeborová

Deep neural networks achieve stellar generalisation on a variety of problems, despite often being large enough to easily fit all their training data.

no code implementations • 21 Dec 2018 • Stefano Sarao Mannelli, Giulio Biroli, Chiara Cammarota, Florent Krzakala, Pierfrancesco Urbani, Lenka Zdeborová

Gradient-descent-based algorithms and their stochastic versions have widespread applications in machine learning and statistical inference.

no code implementations • 6 Dec 2018 • Jean Barbier, Mohamad Dia, Nicolas Macris, Florent Krzakala, Lenka Zdeborová

We characterize the detectability phase transitions in a large set of estimation problems, where we show that there exists a gap between what currently known polynomial algorithms (in particular spectral methods and approximate message-passing) can do and what is expected information theoretically.

no code implementations • 17 Sep 2018 • Andre Manoel, Florent Krzakala, Gaël Varoquaux, Bertrand Thirion, Lenka Zdeborová

We introduce an iterative optimization scheme for convex objectives consisting of a linear loss and a non-separable penalty, based on the expectation-consistent approximation and the vector approximate message-passing (VAMP) algorithm.

no code implementations • 3 Jul 2018 • Fabrizio Antenucci, Florent Krzakala, Pierfrancesco Urbani, Lenka Zdeborová

Approximate message passing algorithm enjoyed considerable attention in the last decade.

1 code implementation • NeurIPS 2018 • Benjamin Aubin, Antoine Maillard, Jean Barbier, Florent Krzakala, Nicolas Macris, Lenka Zdeborová

Heuristic tools from statistical physics have been used in the past to locate the phase transitions and compute the optimal learning and generalization errors in the teacher-student scenario in multi-layer neural networks.

2 code implementations • NeurIPS 2018 • Marylou Gabrié, Andre Manoel, Clément Luneau, Jean Barbier, Nicolas Macris, Florent Krzakala, Lenka Zdeborová

We examine a class of deep learning models with a tractable method to compute information-theoretic quantities.

no code implementations • 15 May 2018 • Fabrizio Antenucci, Silvio Franz, Pierfrancesco Urbani, Lenka Zdeborová

An algorithmically hard phase was described in a range of inference problems: even if the signal can be reconstructed with a small error from an information theoretic point of view, known algorithms fail unless the noise-to-signal ratio is sufficiently small.

no code implementations • 13 Mar 2018 • Christian Schmidt, Lenka Zdeborová

We further study numerically the performance of approximate message passing, derived in the dense limit, on sparse instances and carry out experiments on a real world dataset.

1 code implementation • 10 Aug 2017 • Jean Barbier, Florent Krzakala, Nicolas Macris, Léo Miolane, Lenka Zdeborová

Non-rigorous predictions for the optimal errors existed for special cases of GLMs, e. g. for the perceptron, in the field of statistical physics based on the so-called replica method.

no code implementations • 2 Jun 2017 • Andre Manoel, Florent Krzakala, Eric W. Tramel, Lenka Zdeborová

In statistical learning for real-world large-scale data problems, one must often resort to "streaming" algorithms which operate sequentially on small batches of data.

no code implementations • 24 Jan 2017 • Andre Manoel, Florent Krzakala, Marc Mézard, Lenka Zdeborová

We consider the problem of reconstructing a signal from multi-layered (possibly) non-linear measurements.

no code implementations • 10 Oct 2016 • Thibault Lesieur, Caterina De Bacco, Jess Banks, Florent Krzakala, Cris Moore, Lenka Zdeborová

We consider the problem of Gaussian mixture clustering in the high-dimensional limit where the data consists of $m$ points in $n$ dimensions, $n, m \rightarrow \infty$ and $\alpha = m/n$ stays finite.

no code implementations • 20 May 2016 • Alaa Saade, Florent Krzakala, Marc Lelarge, Lenka Zdeborová

We consider the problem of clustering partially labeled data from a minimal number of randomly chosen pairwise comparisons between the items.

no code implementations • 25 Jan 2016 • Alaa Saade, Marc Lelarge, Florent Krzakala, Lenka Zdeborová

We consider the problem of grouping items into clusters based on few random pairwise comparisons between the items.

1 code implementation • 8 Nov 2015 • Lenka Zdeborová, Florent Krzakala

Many questions of fundamental interest in todays science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables based on the indirect information contained in the measurements.

1 code implementation • 14 Jul 2015 • Thibault Lesieur, Florent Krzakala, Lenka Zdeborová

This paper considers probabilistic estimation of a low-rank matrix from non-linear element-wise measurements of its elements.

no code implementations • NeurIPS 2015 • Alaa Saade, Florent Krzakala, Lenka Zdeborová

We propose a spectral algorithm for these two tasks called MaCBetH (for Matrix Completion with the Bethe Hessian).

no code implementations • 31 Jan 2015 • Alaa Saade, Florent Krzakala, Marc Lelarge, Lenka Zdeborová

We describe two spectral algorithms for this task based on the non-backtracking and the Bethe Hessian operators.

1 code implementation • 17 Jun 2014 • Andre Manoel, Florent Krzakala, Eric W. Tramel, Lenka Zdeborová

Approximate Message Passing (AMP) has been shown to be a superior method for inference problems, such as the recovery of signals from sets of noisy, lower-dimensionality measurements, both in terms of reconstruction accuracy and in computational efficiency.

3 code implementations • NeurIPS 2014 • Alaa Saade, Florent Krzakala, Lenka Zdeborová

We show that this approach combines the performances of the non-backtracking operator, thus detecting clusters all the way down to the theoretical limit in the stochastic block model, with the computational, theoretical and memory advantages of real symmetric matrices.

no code implementations • 30 Apr 2014 • Pan Zhang, Cristopher Moore, Lenka Zdeborová

For larger $k$ where a hard but detectable regime exists, we find that the easy/hard transition (the point at which efficient algorithms can do better than chance) becomes a line of transitions where the accuracy jumps discontinuously at a critical value of $\alpha$.

no code implementations • 6 Feb 2014 • Yoshiyuki Kabashima, Florent Krzakala, Marc Mézard, Ayaka Sakata, Lenka Zdeborová

We use the tools of statistical mechanics - the cavity and replica methods - to analyze the achievability and computational tractability of the inference problems in the setting of Bayes-optimal inference, which amounts to assuming that the two matrices have random independent elements generated from some known distribution, and this information is available to the inference algorithm.

no code implementations • NeurIPS 2013 • Christophe Schulke, Francesco Caltagirone, Florent Krzakala, Lenka Zdeborová

We study numerically the phase diagram of the blind calibration problem, and show that even in cases where convex relaxation is possible, our algorithm requires a smaller number of measurements and/or signals in order to perform well.

no code implementations • 24 Jun 2013 • Florent Krzakala, Cristopher Moore, Elchanan Mossel, Joe Neeman, Allan Sly, Lenka Zdeborová, Pan Zhang

Spectral algorithms are classic approaches to clustering and community detection in networks.

1 code implementation • 18 Jun 2012 • Florent Krzakala, Marc Mézard, François Sausset, Yifan Sun, Lenka Zdeborová

We further develop the asymptotic analysis of the corresponding phase diagrams with and without measurement noise, for different distribution of signals, and discuss the best possible reconstruction performances regardless of the algorithm.

Statistical Mechanics Information Theory Information Theory

1 code implementation • 20 Sep 2011 • Florent Krzakala, Marc Mézard, François Sausset, Yifan Sun, Lenka Zdeborová

Compressed sensing is triggering a major evolution in signal acquisition.

Statistical Mechanics Information Theory Information Theory

no code implementations • 14 Sep 2011 • Aurelien Decelle, Florent Krzakala, Cristopher Moore, Lenka Zdeborová

In this paper we extend our previous work on the stochastic block model, a commonly used generative model for social and biological networks, and the problem of inferring functional groups or communities from the topology of the network.

Statistical Mechanics Disordered Systems and Neural Networks Social and Information Networks Physics and Society

no code implementations • 6 Feb 2011 • Aurelien Decelle, Florent Krzakala, Cristopher Moore, Lenka Zdeborová

We present an asymptotically exact analysis of the problem of detecting communities in sparse random networks.

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