Related papers: xPert: Computer algebra for metric perturbation th…
The implementation of reliable and efficient geometric algorithms is a challenging task. The reason is the following conflict: On the one hand, computing with rounded arithmetic may question the reliability of programs while, on the other…
We often use perturbations to regularize neural models. For neural encoder-decoders, previous studies applied the scheduled sampling (Bengio et al., 2015) and adversarial perturbations (Sato et al., 2019) as perturbations but these methods…
We discuss a general setup which allows the study of the perturbation theory of an arbitrary, locally harmonic 1D quantum mechanical potential as well as its multi-variable (many-body) generalization. The latter may form a prototype for…
Efficient probability density estimation is a core challenge in statistical machine learning. Tensor-based probabilistic graph methods address interpretability and stability concerns encountered in neural network approaches. However, a…
Recently, tensor algebra have witnessed significant applications across various domains. Each operator in tensor algebra features different computational workload and precision. However, current general accelerators, such as VPU, GPGPU, and…
The problem of tensor completion has applications in healthcare, computer vision, and other domains. However, past approaches to tensor completion have faced a tension in that they either have polynomial-time computation but require…
Perturbation theory is an important technique for reducing computational cost and providing physical insights in simulating quantum systems with classical computers. Here, we provide a quantum algorithm to obtain perturbative energies on…
We present an alternating least squares type numerical optimization scheme to estimate conditionally-independent mixture models in $\mathbb{R}^n$, without parameterizing the distributions. Following the method of moments, we tackle an…
We develop algebraic methods for computations with tensor data. We give 3 applications: extracting features that are invariant under the orthogonal symmetries in each of the modes, approximation of the tensor spectral norm, and…
This text is a support for different courses of the master of Mechanics of the University Paris-Saclay. The content of this text is an introduction, for graduate students, to tensor algebra and analysis. Far from being exhaustive, the text…
We develop the Fourier-Laplace Inversion of the Perturbation Theory (FLIPT), a novel numerically exact "black box" method to compute perturbative expansions of the density matrix with rigorous convergence conditions. Specifically, the FLIPT…
Tensor network methods strike a middle ground between fully-fledged quantum computing and classical computing, as they take inspiration from quantum systems to significantly speed up certain classical operations. Their strength lies in…
We use computational algorithms recently developed by us to study completely four index divergence free quadratic in Riemann tensor polynomials in GR. Some results are new and some other reproduce and/or correct known ones. The algorithms…
Models trained on data composed of different groups or domains can suffer from severe performance degradation under distribution shifts. While recent methods have largely focused on optimizing the worst-group objective, this often comes at…
Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine…
Perturbation theory (PT) might be one of the most powerful and fruitful tools for both physicists and chemists, which evoked an explosion of applications with the blooming of atomic and subatomic physics. Even though PT is well-used today,…
We describe how Computational Group Theory provides tools for manipulating tensors in explicit index notation. In special, we present an algorithm that puts tensors with free indices obeying permutation symmetries into the canonical form.…
Tucker decomposition has been widely used in a variety of applications to obtain latent factors of tensor data. In these applications, a common need is to compute Tucker decomposition for a given time range. Furthermore, real-world tensor…
A method of fast linear transform algorithm synthesis for an arbitrary tensor, matrix, or vector is proposed. The method is based on factorization of a tensor and using the factors for building computational structures performing fast…
Choosing a basis set is the first step of a quantum chemistry calculation and it sets its maximum accuracy. This choice of orbitals is limited by strong technical constraints as one must be able to compute a large number of six dimensional…