Local convergence of alternating low‐rank optimization methods with overrelaxation

The local convergence of alternating optimization methods with overrelaxation for low-rank matrix and tensor problems is established. The analysis is based on the linearization of the method which takes the form of an SOR iteration for a positive semidefinite Hessian and can be studied in the corresponding quotient geometry of equivalent low-rank representations. In the matrix case, the optimal relaxation parameter for accelerating the local convergence can be determined from the convergence rate of the standard method. This result relies on a version of Young's SOR theorem for positive semidefinite 2x2 block systems

Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition

Hierarchical uncertainty quantification can reduce the computational cost of stochastic circuit simulation by employing spectral methods at different levels. This paper presents an efficient framework to simulate hierarchically some challenging stochastic circuits/systems that include high-dimensional subsystems. Due to the high parameter dimensionality, it is challenging to both extract surrogate models at the low level of the design hierarchy and to handle them in the high-level simulation. In this paper, we develop an efficient ANOVA-based stochastic circuit/MEMS simulator to extract efficiently the surrogate models at the low level. In order to avoid the curse of dimensionality, we employ tensor-train decomposition at the high level to construct the basis functions and Gauss quadrature points. As a demonstration, we verify our algorithm on a stochastic oscillator with four MEMS capacitors and 184 random parameters. This challenging example is simulated efficiently by our simulator at the cost of only 10 minutes in MATLAB on a regular personal computer.Comment: 14 pages (IEEE double column), 11 figure, accepted by IEEE Trans CAD of Integrated Circuits and System

Problems with Jumping Coefficients

We study separability properties of solutions of elliptic equations with piecewise constant coefficients in R d, d ≥ 2. Besides that, we develop efficient tensor-structured preconditioner for the diffusion equation with variable coefficients. It is based only on rank structured decomposition of the tensor of reciprocal coefficient and on the decomposition of the inverse of the Laplacian operator. It can be applied to full vector with linear-logarithmic complexity in the number of unknowns N. It also allows lowrank tensor representation, which has linear complexity in dimension d, hence, it gets rid of the “curse of dimensionality ” and can be used for large values of d. Extensive numerical tests are presented. AMS Subject Classification: 65F30, 65F50, 65N35, 65F10 Key words: structured matrices, elliptic operators, Poisson equation, matrix approximations

CISA: Context Substitution for Image Semantics Augmentation

Large datasets catalyze the rapid expansion of deep learning and computer vision. At the same time, in many domains, there is a lack of training data, which may become an obstacle for the practical application of deep computer vision models. To overcome this problem, it is popular to apply image augmentation. When a dataset contains instance segmentation masks, it is possible to apply instance-level augmentation. It operates by cutting an instance from the original image and pasting to new backgrounds. This article challenges a dataset with the same objects present in various domains. We introduce the Context Substitution for Image Semantics Augmentation framework (CISA), which is focused on choosing good background images. We compare several ways to find backgrounds that match the context of the test set, including Contrastive Language–Image Pre-Training (CLIP) image retrieval and diffusion image generation. We prove that our augmentation method is effective for classification, segmentation, and object detection with different dataset complexity and different model types. The average percentage increase in accuracy across all the tasks on a fruits and vegetables recognition dataset is 4.95%. Moreover, we show that the Fréchet Inception Distance (FID) metrics has a strong correlation with model accuracy, and it can help to choose better backgrounds without model training. The average negative correlation between model accuracy and the FID between the augmented and test datasets is 0.55 in our experiments