CSD seminar

Recordings of human brain suggest that concepts are represented through sparse sets of neurons that fire together when the concept is activated: we talk about neuronal assemblies. Neuroscientists have identified local learning rules to adjust synaptic weights, but to our knowledge there is no mathematical proof that such local rules enable to learn, nor that they create neuronal assemblies. In this purpose, we propose a spiking neural network named CHANI (Correlation-based Hawkes Aggregation of Neurons with bio-Inspiration), whose neurons activity is modeled by Hawkes processes. Synaptic weights are updated thanks […]

Disentanglement, or identifying salient statistically independent factors of the data, is of interest in many areas of machine learning and statistics, with relevance to synthetic data generation with controlled properties, robust classification of features, parsimonious encoding, and a greater understanding of the generative process underlying the data. Disentanglement arises in several generative paradigms, including Variational Autoencoders (VAEs), Generative Adversarial Networks and diffusion models. Particular progress has recently been made in understanding disentanglement in VAEs, where the choice of diagonal posterior covariance matrices is shown to promote mutual orthogonality between columns […]

Title: Plug-and-Play image restoration with Stochastic deNOising REgularization.   Abstract: Plug-and-Play (PnP) algorithms are a class of iterative algorithms that address image inverse problems by combining a physical model and a deep neural network for regularization. Even if they produce impressive image restoration results, these algorithms rely on a non-standard use of a denoiser on images that are less and less noisy along the iterations, which contrasts with recent algorithms based on Diffusion Models (DM), where the denoiser is applied only on re-noised images. In this presentation, we propose a new PnP […]

Title: Optimal denoising of geometrically regular images with scattering coefficients   Abstract: Optimal suppression of additive Gaussian white noise has many image processing applications and is a key step to generate images with score diffusion algorithms. For images with edges that are piecewise regular, nearly optimal denoisers can be computed by thresholding a sparse representation in a dictionary of curvelets or bandlets. It requires to adapt the support of selected dictionary vectors to geometric image properties. In contrast, convolutional deep neural networks can implement optimal denoising algorithms with a cascade […]

The geometry of dynamical systems estimated from trajectory data is a major challenge for machine learning applications. Koopman and transfer operators provide a linear representation of nonlinear dynamics through their spectral decomposition, offering a natural framework for comparison. We propose a novel approach representing each system as a distribution of its joint operator eigenvalues and spectral projectors and defining a metric between systems leveraging optimal transport. The proposed metric is invariant to the sampling frequency of trajectories. It is also computationally efficient, supported by finite-sample convergence guarantees, and enables the […]

La première partie de l’exposé présentera, à l’aide d’un exemple simple et didactique, les résultats mathématiques développés dans la seconde partie, de manière à en rendre l’intuition accessible au plus grand nombre.  Du fait d’une régularisation implicite qui favorise les « bons » réseaux, les réseaux de neurones avec un grand nombre de paramètres ne surapprennent généralement pas. Parmi les phénomènes connexes et encore mal compris figurent les propriétés des minima plats, les dynamiques de type saddle-to-saddle et l’alignement des neurones. Pour analyser ces phénomènes, nous étudions la géométrie locale […]

Machine learning models are often seen as black-box systems that output point predictions without indicating how confident they are in those predictions. Recently, Conformal Prediction (CP) has emerged as a powerful framework to address this issue by transforming point predictions into set-valued predictions with probabilistic guarantees. In this talk, I will introduce CP and briefly present some key challenges and recent advances in the area. I will first discuss how to perform CP in a Federated Learning setting, showing that a single round of communication is sufficient to match the […]

Conformal prediction (CP) constructs uncertainty sets for model outputs with finite-sample coverage guarantees. A candidate output is included in the prediction set if its non-conformity score is not considered extreme relative to the scores observed on a set of calibration examples. However, this procedure is only straightforward when scores are scalar-valued, which has limited CP to real-valued scores or ad-hoc reductions to one dimension. The problem of ordering vectors has been studied via optimal transport (OT), which provides a principled method for defining vector-ranks and multivariate quantile regions, though typically […]

Gauthier Thurin - "Convergence Rates for Distribution Matching with Sliced Optimal Transport"Valérie Castin - "Balanced Low-Rank Adaptation: Removing Parameter Invariance to Accelerate Convergence"