no code implementations • 27 Aug 2024 • Jerome Garnier-Brun, Marc Mézard, Emanuele Moscato, Luca Saglietti

We introduce a hierarchical filtering procedure for generative models of sequences on trees, enabling control over the range of positional correlations in the data.

no code implementations • 11 Aug 2024 • Giulio Biroli, Marc Mézard

Our study reveals three distinct statistical regimes for the kernel-based estimate of the density $\hat \rho_h^{\mathcal {D}}(x)=\frac{1}{n h^d}\sum_{i=1}^n K\left(\frac{x-y_i}{h}\right)$, depending on the bandwidth $h$: a classical regime for large bandwidth where the Central Limit Theorem (CLT) holds, which is akin to the one found in traditional approaches.

no code implementations • 28 Feb 2024 • Giulio Biroli, Tony Bonnaire, Valentin De Bortoli, Marc Mézard

Using statistical physics methods, we study generative diffusion models in the regime where the dimension of space and the number of data are large, and the score function has been trained optimally.

no code implementations • 31 Jul 2023 • Francesco Camilli, Marc Mézard

Matrix factorization is an inference problem that has acquired importance due to its vast range of applications that go from dictionary learning to recommendation systems and machine learning with deep networks.

no code implementations • 28 Jun 2023 • Clarissa Lauditi, Emanuele Troiani, Marc Mézard

In recent years statistical physics has proven to be a valuable tool to probe into large dimensional inference problems such as the ones occurring in machine learning.

no code implementations • 5 Dec 2022 • Francesco Camilli, Marc Mézard

Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning.

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.

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.

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 • 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.

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.

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 • 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.

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

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