7 accepted papers
The recently discovered Neural collapse (NC) phenomenon states that the last-layer weights of Deep Neural Networks (DNN), converge to the so-called Equiangular Tight Frame (ETF) simplex, at the terminal phase of their training. This ETF geometry is equivalent to vanishing within-class variability of…
In this article, we investigate the spectral behavior of random features kernel matrices of the type ${\bf K} = \mathbb{E}_{{\bf w}} \left[\sigma\left({\bf w}^{\sf T}{\bf x}_i\right)\sigma\left({\bf w}^{\sf T}{\bf x}_j\right)\right]_{i,j=1}^n$, with nonlinear function $\sigma(\cdot)$, data ${\bf x}_…
This article provides theoretical insights into the inner workings of multi-task and transfer learning methods, by studying the tractable least-square support vector machine multi-task learning (LS-SVM MTL) method, in the limit of large ($p$) and numerous ($n$) data. By a random matrix analysis appl…
We propose a method for simultaneously detecting shared and unshared communities in heterogeneous multilayer weighted and undirected networks. The multilayer network is assumed to follow a generative probabilistic model that takes into account the similarities and dissimilarities between the communi…
We study in this article the asymptotic performance of spectral clustering with inner product kernel for Gaussian mixture models of high dimension with numerous samples. As is now classical in large dimensional spectral analysis, we establish a phase transition phenomenon by which a minimum distance…
Recurrent neural networks, especially in their linear version, have provided many qualitative insights on their performance under different configurations. This article provides, through a novel random matrix framework, the quantitative counterpart of these performance results, specifically in the c…
This article proposes a spectral analysis of dense random graphs generated by (a modified version of) the degree-corrected stochastic block model, for a setting where the inter block probabilities differ by O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/x…