相关论文: Reparameterized Tensor Ring Functional Decompositi…

To efficiently express tensor data using the Tucker format, a critical task is to minimize the multilinear rank such that the model would not be over-flexible and lead to overfitting. Due to the lack of rank minimization tools in tensor,…

Tensors, which provide a powerful and flexible model for representing multi-attribute data and multi-way interactions, play an indispensable role in modern data science across various fields in science and engineering. A fundamental task is…

Tensor robust principal component analysis (TRPCA) is a classical way for low-rank tensor recovery, which minimizes the convex surrogate of tensor rank by shrinking each tensor singular value equally. However, for real-world visual data,…

Numerous total variation (TV) regularizers, engaged in image restoration problem, encode the gradients by means of simple $[-1,1]$ FIR filter. Despite its low computational processing, this filter severely deviates signal's high frequency…

Higher-order tensors can represent scores in a rating system, frames in a video, and images of the same subject. In practice, the measurements are often highly quantized due to the sampling strategies or the quality of devices. Existing…

An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square…

Coupled tensor approximation has recently emerged as a promising approach for the fusion of hyperspectral and multispectral images, reconciling state of the art performance with strong theoretical guarantees. However, tensor-based…

We propose a method to construct the initial tensor representation of partition functions and observables for the tensor renormalization group (TRG). The TRG is a numerical calculation technique that utilizes a tensor network…

The tensor train (TT) format enjoys appealing advantages in handling structural high-order tensors. The recent decade has witnessed the wide applications of TT-format tensors from diverse disciplines, among which tensor completion has drawn…

Tensor factorization is a powerful tool to analyse multi-way data. Compared with traditional multi-linear methods, nonlinear tensor factorization models are capable of capturing more complex relationships in the data. However, they are…

We present a novel nonnegative tensor decomposition method, called Legendre decomposition, which factorizes an input tensor into a multiplicative combination of parameters. Thanks to the well-developed theory of information geometry, the…

Given a time-evolving tensor with missing entries, how can we effectively factorize it for precisely predicting the missing entries? Tensor factorization has been extensively utilized for analyzing various multi-dimensional real-world data.…

While neural radiance fields (NeRF) have shown promise in novel view synthesis, their implicit representation limits explicit control over object manipulation. Existing research has proposed the integration of explicit geometric proxies to…

Tensor decomposition is a fundamental framework to analyze data that can be represented by multi-dimensional arrays. In practice, tensor data is often accompanied by temporal information, namely the time points when the entry values were…

Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear inverse function of the dynamical system can be approximated…

Tensor train (TT) representation has achieved tremendous success in visual data completion tasks, especially when it is combined with tensor folding. However, folding an image or video tensor breaks the original data structure, leading to…

Low rank tensor ring model is powerful for image completion which recovers missing entries in data acquisition and transformation. The recently proposed tensor ring (TR) based completion algorithms generally solve the low rank optimization…

Recurrent Neural Networks (RNNs) are powerful sequence modeling tools. However, when dealing with high dimensional inputs, the training of RNNs becomes computational expensive due to the large number of model parameters. This hinders RNNs…

Tensor decompositions have become a central tool in data science, with applications in areas such as data analysis, signal processing, and machine learning. A key property of many tensor decompositions, such as the canonical polyadic…

High-dimensional token embeddings underpin Large Language Models (LLMs), as they can capture subtle semantic information and significantly enhance the modelling of complex language patterns. However, this high dimensionality also introduces…