Related papers: Residual Tensor Train: A Quantum-inspired Approach…
Reduced Rank Regression (RRR) is a widely used method for multi-response regression. However, RRR assumes a linear relationship between features and responses. While linear models are useful and often provide a good approximation, many…
We consider an approximate computation of several minimal eigenpairs of large Hermitian matrices which come from high--dimensional problems. We use the tensor train format (TT) for vectors and matrices to overcome the curse of…
Spatial entanglement of quantum states has become a central paradigm of many-body physics. Here, we unearth a fundamentally different form of entanglement, the entanglement between imaginary time scales. This time-scale entanglement is…
Deep learning algorithms face great challenges with long-tailed data distribution which, however, is quite a common case in real-world scenarios. Previous methods tackle the problem from either the aspect of input space (re-sampling classes…
Tensor networks have in recent years emerged as the powerful tools for solving the large-scale optimization problems. One of the most popular tensor network is tensor train (TT) decomposition that acts as the building blocks for the…
Deep neural networks demonstrate to have a high performance on image classification tasks while being more difficult to train. Due to the complexity and vanishing gradient problem, it normally takes a lot of time and more computational…
Benefiting from its ability to efficiently learn how an object is changing, correlation filters have recently demonstrated excellent performance for rapidly tracking objects. Designing effective features and handling model drifts are two…
We present a novel high frequency residual learning framework, which leads to a highly efficient multi-scale network (MSNet) architecture for mobile and embedded vision problems. The architecture utilizes two networks: a low resolution…
Estimation of probability density function from samples is one of the central problems in statistics and machine learning. Modern neural network-based models can learn high dimensional distributions but have problems with hyperparameter…
Modeling interactions between features improves the performance of machine learning solutions in many domains (e.g. recommender systems or sentiment analysis). In this paper, we introduce Exponential Machines (ExM), a predictor that models…
We propose a modular framework for multi-relational learning via tensor decomposition. In our learning setting, the training data contains multiple types of relationships among a set of objects, which we represent by a sparse three-mode…
Deep networks trained on large-scale data can learn transferable features to promote learning multiple tasks. Since deep features eventually transition from general to specific along deep networks, a fundamental problem of multi-task…
Image recognition is one of the primary applications of machine learning algorithms. Nevertheless, machine learning models used in modern image recognition systems consist of millions of parameters that usually require significant…
Vision Transformer (ViT) self-attention mechanism is characterized by feature collapse in deeper layers, resulting in the vanishing of low-level visual features. However, such features can be helpful to accurately represent and identify…
Quantum theory provides non-classical principles, such as superposition and entanglement, that inspires promising paradigms in machine learning. However, most existing quantum-inspired fusion models rely solely on unitary or unitary-like…
We propose a multilevel tensor-train (TT) framework for solving nonlinear partial differential equations (PDEs) in a global space-time formulation. While space-time TT solvers have demonstrated significant potential for compressed…
Research in machine learning has polarized into two general approaches for regression tasks: Transductive methods construct estimates directly from available data but are usually problem unspecific. Inductive methods can be much more…
Open many-body quantum systems play an important role in quantum optics and condensed-matter physics, and capture phenomena like transport, interplay between Hamiltonian and incoherent dynamics, and topological order generated by…
Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…
In this article, we design an original solver based on Quantized Tensor Trains (QTT) for linear elliptic equations with heterogeneous coefficient field, that allows for extremely fine meshes. It can achieve full-field simulations in…