相关论文: Complex-to-Real Sketches for Tensor Products with …

This paper considers the problem of recovering an unknown sparse p\times p matrix X from an m\times m matrix Y=AXB^T, where A and B are known m \times p matrices with m << p. The main result shows that there exist constructions of the…

3D modeling of non-linear objects from stylized sketches is a challenge even for experts in Computer Graphics (CG). The extrapolation of objects parameters from a stylized sketch is a very complex and cumbersome task. In the present study,…

We address the problem of accelerating thin-shell deformable object simulations by dimension reduction. We present a new algorithm to embed a high-dimensional configuration space of deformable objects in a low-dimensional feature space,…

We present space-efficient linear sketches for estimating trimmed statistics of an $n$-dimensional frequency vector $x$, e.g., the sum of $p$-th powers of the largest $k$ frequencies (i.e., entries) in absolute value, or the $k$-trimmed…

We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…

Consider a projector matrix P, representing the first order reduced density matrix in a basis of orthonormal atom-centric basis functions. A mathematical question arises, and that is, how to break P into its natural component kernel…

We study how well one can recover sparse principal components of a data matrix using a sketch formed from a few of its elements. We show that for a wide class of optimization problems, if the sketch is close (in the spectral norm) to the…

Modern approaches to generative modeling of continuous data using tensor networks incorporate compression layers to capture the most meaningful features of high-dimensional inputs. These methods, however, rely on traditional Matrix Product…

Graph neural networks that model 3D data, such as point clouds or atoms, are typically desired to be $SO(3)$ equivariant, i.e., equivariant to 3D rotations. Unfortunately equivariant convolutions, which are a fundamental operation for…

Random data sketching (or projection) is now a classical technique enabling, for instance, approximate numerical linear algebra and machine learning algorithms with reduced computational complexity and memory. In this context, the…

The need to compactly and robustly represent item-attribute relations arises in many important tasks, such as faceted browsing and recommendation systems. A popular machine learning approach for this task denotes that an item has an…

Despite the significance of probabilistic time-series forecasting models, their evaluation metrics often involve intractable integrations. The most widely used metric, the continuous ranked probability score (CRPS), is a strictly proper…

Categorical attributes are those that can take a discrete set of values, e.g., colours. This work is about compressing vectors over categorical attributes to low-dimension discrete vectors. The current hash-based methods compressing vectors…

Random projections have proven extremely useful in many signal processing and machine learning applications. However, they often require either to store a very large random matrix, or to use a different, structured matrix to reduce the…

One of the key problems in tensor network based quantum circuit simulation is the construction of a contraction tree which minimizes the cost of the simulation, where the cost can be expressed in the number of operations as a proxy for the…

Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…

Very often, in the course of uncertainty quantification tasks or data analysis, one has to deal with high-dimensional random variables (RVs). A high-dimensional RV can be described by its probability density (pdf) and/or by the…

Traditional feature engineering approaches for molecular sequence classification suffer from sparsity issues and computational complexity, while deep learning models often underperform on tabular biological data. This paper introduces a…

We present efficient, sketching-based methods for the summation of tensors in Tucker format. Leveraging the algebraic structure of Khatri-Rao and Kronecker products, our approach enables compressed arithmetic on Tucker tensors while…

This work proposes a novel tensor train random projection (TTRP) method for dimension reduction, where pairwise distances can be approximately preserved. Our TTRP is systematically constructed through a tensor train (TT) representation with…