arXiv subjects

Mohamed Tamaazousti

Publications and source records attributed to Mohamed Tamaazousti.

33 records · Page 2Linked to original sources

arXiv2022

HyperPCA: a Powerful Tool to Extract Elemental Maps from Noisy Data Obtained in LIBS Mapping of Materials

Laser-induced breakdown spectroscopy is a preferred technique for fast and direct multi-elemental mapping of samples under ambient pressure, without any limitation on the targeted element. However, LIBS mapping data have two peculiarities: an intrinsically low signal-to-noise ratio due to single-shot measurements, and a high dimensionality due to the high number of spectra acquired for imaging. This is all the truer as lateral resolution gets higher: in this case, the ablation spot diameter is reduced, as well as the ablated mass and the emission signal, while the number of spectra for a given surface increases. Therefore, efficient extraction of physico-chemical information from a noisy and large dataset is a major issue. Multivariate approaches were introduced by several authors as a means to cope with such data, particularly Principal Component Analysis. This technique is useful to analyse correlations between different elements, but it is limited to low signal-to-noise ratios. In this paper, we introduce HyperPCA, a new analysis tool for hyperspectral images based on a sparse representation of the data using Discrete Wavelet Transform and kernel-based sparse PCA to reduce the impact of noise on the data and to consistently extract the spectroscopic signal, with a particular emphasis on LIBS data. The method is first illustrated using simulated LIBS mapping datasets to emphasise its performances with an extremely low shot-to-shot signal-to-noise ratio, and with a variable degree of spectral interference. Comparisons to standard PCA and to traditional univariate data analyses are provided. Finally, it is used to process real data in two cases that clearly illustrate the potential of the proposed algorithm. We show that the method presents advantages both in quantity and quality of the information recovered, thus improving the physico-chemical characterization of analysed surfaces.

physics.app-ph↗

arXiv2022

Trustworthiness of Laser-Induced Breakdown Spectroscopy Predictions via Simulation-based Synthetic Data Augmentation and Multitask Learning

We consider quantitative analyses of spectral data using laser-induced breakdown spectroscopy. We address the small size of training data available, and the validation of the predictions during inference on unknown data. For the purpose, we build robust calibration models using deep convolutional multitask learning architectures to predict the concentration of the analyte, alongside additional spectral information as auxiliary outputs. These secondary predictions can be used to validate the trustworthiness of the model by taking advantage of the mutual dependencies of the parameters of the multitask neural networks. Due to the experimental lack of training samples, we introduce a simulation-based data augmentation process to synthesise an arbitrary number of spectra, statistically representative of the experimental data. Given the nature of the deep learning model, no dimensionality reduction or data selection processes are required. The procedure is an end-to-end pipeline including the process of synthetic data augmentation, the construction of a suitable robust, homoscedastic, deep learning model, and the validation of its predictions. In the article, we compare the performance of the multitask model with traditional univariate and multivariate analyses, to highlight the separate contributions of each element introduced in the process.

physics.app-ph↗

arXiv2022

The Tensor Track VII: From Quantum Gravity to Artificial Intelligence

Assuming some familiarity with quantum field theory and with the tensor track approach that one of us presented in the previous series Tensor Track I to VI, we provide, as usual, the developments in quantum gravity of the last two years. Next we present in some detail two algorithms inspired by Random Tensor Theory which has been developed in the quantum gravity context. One is devoted to the detection and recovery of a signal in a random tensor, that can be associated to the noise, with new theoretical guarantees for more general cases such as tensors with different dimensions. The other, SMPI, is more ambitious but maybe less rigorous. It is devoted to significantly and fundamentally improve the performance of algorithms for Tensor principal component analysis but without complete theoretical guarantees yet. Then we sketch all sorts of application relevant to information theory and artificial intelligence and provide their corresponding bibliography.

hep-th↗

arXiv2021

Selective Multiple Power Iteration: from Tensor PCA to gradient-based exploration of landscapes

We propose Selective Multiple Power Iterations (SMPI), a new algorithm to address the important Tensor PCA problem that consists in recovering a spike $\bf{v_0}^{\otimes k}$ corrupted by a Gaussian noise tensor $\bf{Z} \in (\mathbb{R}^n)^{\otimes k}$ such that $\bf{T}=\sqrt{n} β\bf{v_0}^{\otimes k} + \bf{Z}$ where $β$ is the signal-to-noise ratio (SNR). SMPI consists in generating a polynomial number of random initializations, performing a polynomial number of symmetrized tensor power iterations on each initialization, then selecting the one that maximizes $\langle \bf{T}, \bf{v}^{\otimes k} \rangle$. Various numerical simulations for $k=3$ in the conventionally considered range $n \leq 1000$ show that the experimental performances of SMPI improve drastically upon existent algorithms and becomes comparable to the theoretical optimal recovery. We show that these unexpected performances are due to a powerful mechanism in which the noise plays a key role for the signal recovery and that takes place at low $β$. Furthermore, this mechanism results from five essential features of SMPI that distinguish it from previous algorithms based on power iteration. These remarkable results may have strong impact on both practical and theoretical applications of Tensor PCA. (i) We provide a variant of this algorithm to tackle low-rank CP tensor decomposition. These proposed algorithms also outperforms existent methods even on real data which shows a huge potential impact for practical applications. (ii) We present new theoretical insights on the behavior of SMPI and gradient descent methods for the optimization in high-dimensional non-convex landscapes that are present in various machine learning problems. (iii) We expect that these results may help the discussion concerning the existence of the conjectured statistical-algorithmic gap.

cs.LG↗

arXiv2021

Quantum error mitigation for parametric circuits

Reducing errors is critical to the application of modern quantum computers. In the current Letter, we investigate the quantum error mitigation considering parametric circuits accessible by classical computations in some range of their parameters. We present a method of global randomized error cancellations (GREC) mitigating quantum errors by summing a linear combination of additionally randomized quantum circuits with weights determined by comparison with the referent classically computable data. We illustrate the performance of this method on the example of the $n = 4$ spins anti-ferromagnetic Ising model in the transverse field.

quant-ph↗

arXiv2021

Field theoretical approach for signal detection in nearly continuous positive spectra I: Matricial data

Renormalization group techniques are widely used in modern physics to describe the low energy relevant aspects of systems involving a large number of degrees of freedom. Those techniques are thus expected to be a powerful tool to address open issues in data analysis when data sets are very larges. Signal detection and recognition for covariance matrix having a nearly continuous spectra is currently one of these opened issues. First investigations in this direction has been proposed in [Journal of Statistical Physics, 167, Issue 3-4, pp 462-475, (2017)] and [arXiv:2002.10574], from an analogy between coarse-graining and principal component analysis (PCA), regarding separation of sampling noise modes as a UV cut-off for small eigenvalues of the covariance matrix. The field theoretical framework proposed in this paper is a synthesis of these complementary point of views, aiming to be a general and operational framework, both for theoretical investigations and for experimental detection. Our investigations focus on signal detection, and exhibit experimental evidences in favor of a connection between symmetry breaking and the existence of an intrinsic detection threshold.

hep-th↗

arXiv2021

Deep multi-task mining Calabi-Yau four-folds

We continue earlier efforts in computing the dimensions of tangent space cohomologies of Calabi-Yau manifolds using deep learning. In this paper, we consider the dataset of all Calabi-Yau four-folds constructed as complete intersections in products of projective spaces. Employing neural networks inspired by state-of-the-art computer vision architectures, we improve earlier benchmarks and demonstrate that all four non-trivial Hodge numbers can be learned at the same time using a multi-task architecture. With 30% (80%) training ratio, we reach an accuracy of 100% for $h^{(1,1)}$ and 97% for $h^{(2,1)}$ (100% for both), 81% (96%) for $h^{(3,1)}$, and 49% (83%) for $h^{(2,2)}$. Assuming that the Euler number is known, as it is easy to compute, and taking into account the linear constraint arising from index computations, we get 100% total accuracy.

hep-th↗

arXiv2021

Field theoretical approach for signal detection in nearly continuous positive spectra II: Tensorial data

The tensorial principal component analysis is a generalization of ordinary principal component analysis, focusing on data which are suitably described by tensors rather than matrices. This paper aims at giving the nonperturbative renormalization group formalism based on a slight generalization of the covariance matrix, to investigate signal detection for the difficult issue of nearly continuous spectra. Renormalization group allows constructing effective description keeping only relevant features in the low ``energy'' (i.e. large eigenvalues) limit and thus provides universal descriptions allowing to associate the presence of the signal with objectives and computable quantities. Among them, in this paper, we focus on the vacuum expectation value. We exhibit experimental evidence in favor of a connection between symmetry breaking and the existence of an intrinsic detection threshold, in agreement with our conclusions for matrices, providing a new step in the direction of a universal statement.

hep-th↗

arXiv2021

Signal detection in nearly continuous spectra and symmetry breaking

The large scale behavior of systems having a large number of interacting degrees of freedom is suitably described using renormalization group, from non-Gaussian distributions. Renormalization group techniques used in physics are then expected to be helpful for issues when standard methods in data analysis break down. Signal detection and recognition for covariance matrices having nearly continuous spectra is currently an open issue in data science and machine learning. Using the field theoretical embedding introduced in arXiv:2011.02376 to reproduces experimental correlations, we show in this paper that the presence of a signal may be characterized by a phase transition with $\mathbb{Z}_2$-symmetry breaking. For our investigations, we use the nonperturbative renormalization group formalism, using a local potential approximation to construct an approximate solution of the flow. Moreover, we focus on the nearly continuous signal build as a perturbation of the Marchenko-Pastur law with many discrete spikes.

hep-th↗

arXiv2021

Generalized scale behavior and renormalization group for data analysis

Some recent results showed that renormalization group can be considered as a promising framework to address open issues in data analysis. In this work, we focus on one of these aspects, closely related to principal component analysis for the case of large dimensional data sets with covariance having a nearly continuous spectrum. In this case, the distinction between "noise-like" and "non-noise" modes becomes arbitrary and an open challenge for standard methods. Observing that both renormalization group and principal component analysis search for simplification for systems involving many degrees of freedom, we aim to use the renormalization group argument to clarify the turning point between noise and information modes. The analogy between coarse-graining renormalization and principal component analysis has been investigated in [Journal of Statistical Physics,167, Issue 3-4, pp 462-475, (2017)], from a perturbative framework, and the implementation with real sets of data by the same authors showed that the procedure may reflect more than a simple formal analogy. In particular, the separation of sampling noise modes may be controlled by a non-Gaussian fixed point, reminiscent of the behaviour of critical systems. In our analysis, we go beyond the perturbative framework using nonperturbative techniques to investigate non-Gaussian fixed points and propose a deeper formalism allowing going beyond power-law assumptions for explicit computations.

hep-th↗

arXiv2021

Constructive expansion for quartic vector fields theories. I. Low dimensions

This paper is the first of a series aiming at proving rigorously the analyticity and the Borel summability of generic quartic bosonic and fermionic vector models (generalizing the O(N) vector model) in diverse dimensions. Both non-relativistic (Schrödinger) and relativistic (Klein-Gordon and Dirac) kinetic terms are considered. The 4-tensor defining the interactions is constant but otherwise arbitrary, up to the symmetries imposed by the statistics of the field. In this paper, we focus on models of low dimensions: bosons and fermions for d = 0, 1, and relativistic bosons for d = 2. Moreover, we investigate the large N and massless limits along with quenching for fermions in d = 1. These results are established using the loop vertex expansion (LVE) and have applications in different fields, including data sciences, condensed matter and string field theory. In particular, this establishes the Borel summability of the SYK model both at finite and large N.

hep-th↗

arXiv2020

Random Matrix Theory Proves that Deep Learning Representations of GAN-data Behave as Gaussian Mixtures

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 \textit{concentrated} random vectors. Further exploiting the fact that Gram matrices, of the type $G = X^T X$ with $X=[x_1,\ldots,x_n]\in \mathbb{R}^{p\times n}$ and $x_i$ independent concentrated random vectors from a mixture model, behave asymptotically (as $n,p\to \infty$) as if the $x_i$ were drawn from a Gaussian mixture, suggests that DL representations of GAN-data can be fully described by their first two statistical moments for a wide range of standard classifiers. Our theoretical findings are validated by generating images with the BigGAN model and across different popular deep representation networks.

cs.LG↗

arXiv2019

Deep Multi-class Adversarial Specularity Removal

We propose a novel learning approach, in the form of a fully-convolutional neural network (CNN), which automatically and consistently removes specular highlights from a single image by generating its diffuse component. To train the generative network, we define an adversarial loss on a discriminative network as in the GAN framework and combined it with a content loss. In contrast to existing GAN approaches, we implemented the discriminator to be a multi-class classifier instead of a binary one, to find more constraining features. This helps the network pinpoint the diffuse manifold by providing two more gradient terms. We also rendered a synthetic dataset designed to help the network generalize well. We show that our model performs well across various synthetic and real images and outperforms the state-of-the-art in consistency.

cs.CV↗

arXiv2019

Generative Collaborative Networks for Single Image Super-Resolution

A common issue of deep neural networks-based methods for the problem of Single Image Super-Resolution (SISR), is the recovery of finer texture details when super-resolving at large upscaling factors. This issue is particularly related to the choice of the objective loss function. In particular, recent works proposed the use of a VGG loss which consists in minimizing the error between the generated high resolution images and ground-truth in the feature space of a Convolutional Neural Network (VGG19), pre-trained on the very "large" ImageNet dataset. When considering the problem of super-resolving images with a distribution "far" from the ImageNet images distribution (\textit{e.g.,} satellite images), their proposed \textit{fixed} VGG loss is no longer relevant. In this paper, we present a general framework named \textit{Generative Collaborative Networks} (GCN), where the idea consists in optimizing the \textit{generator} (the mapping of interest) in the feature space of a \textit{features extractor} network. The two networks (generator and extractor) are \textit{collaborative} in the sense that the latter "helps" the former, by constructing discriminative and relevant features (not necessarily \textit{fixed} and possibly learned \textit{mutually} with the generator). We evaluate the GCN framework in the context of SISR, and we show that it results in a method that is adapted to super-resolution domains that are "far" from the ImageNet domain.

cs.CV↗

arXiv2018

Learning More Universal Representations for Transfer-Learning

A representation is supposed universal if it encodes any element of the visual world (e.g., objects, scenes) in any configuration (e.g., scale, context). While not expecting pure universal representations, the goal in the literature is to improve the universality level, starting from a representation with a certain level. To do so, the state-of-the-art consists in learning CNN-based representations on a diversified training problem (e.g., ImageNet modified by adding annotated data). While it effectively increases universality, such approach still requires a large amount of efforts to satisfy the needs in annotated data. In this work, we propose two methods to improve universality, but pay special attention to limit the need of annotated data. We also propose a unified framework of the methods based on the diversifying of the training problem. Finally, to better match Atkinson's cognitive study about universal human representations, we proposed to rely on the transfer-learning scheme as well as a new metric to evaluate universality. This latter, aims us to demonstrates the interest of our methods on 10 target-problems, relating to the classification task and a variety of visual domains.

cs.CV↗