8 accepted papers
Neural networks are widely used for image–related tasks but typically demand considerable computing power. Once a network has been trained, however, its memory‑ and compute‑footprint can be reduced by compression. In this work, we focus on compression through tensorization and low‑rank representatio…
Most of the recent literature on image Super-Resolution (SR) can be classified into two main approaches. The first one involves learning a corruption model tailored to a specific dataset aiming to mimic the noise and corruption in low-resolution images such as sensor noise. However this approach is…
In this paper, based on an asymptotic analysis of the Softmax layer, we show that when training neural networks for classification tasks, the weight vectors corre sponding to each class of the Softmax layer tend to converge to the class-wise means computed at the representation layer (for specific c…
We propose a new framework for tensor decomposition based on trace invariants, which are particular cases of tensor networks. In general, tensor networks are diagrams/graphs that specify a way to "multiply" a collection of tensors together to produce another tensor, matrix or scalar. The particulari…
This paper provides a large dimensional analysis of the Softmax classifier. We discover and prove that, when the classifier is trained on data satisfying loose statistical modeling assumptions, its weights become deterministic and solely depend on the data statistical means and covariances. As a str…
This paper shows that deep learning (DL) representations of data produced by generative adversarial nets (GANs) are random vectors which fall within the class of so-called \emph{concentrated} random vectors. Further exploiting the fact that Gram matrices, of the type $G = X^\intercal X$ with $X=[x_1…
In this paper, we present a random matrix approach to recover sparse principal components from n p-dimensional vectors. Specifically, considering the large dimensional setting where n, p → ∞ with p/n → c ∈ (0, ∞) and under Gaussian vector observations, we study kernel random matrices of the type f (…
Based on recent random matrix advances in the analysis of kernel methods for classification and clustering, this paper proposes the study of large kernel methods for a wide class of random inputs, i.e., concentrated data, which are more generic than Gaussian mixtures. The concentration assumption is…