In the context of kernel machines, polynomial and Fourier features are
commonly used to provide a nonlinear extension to linear models by mapping the
data to a higher-dimensional space. Unless one considers the dual formulation
of the learning problem, which renders exact large-scale learning unfeasible,
the exponential increase of model parameters in the dimensionality of the data
caused by their tensor-product structure prohibits to tackle high-dimensional
problems. One of the possible approaches to circumvent this exponential scaling
is to exploit the tensor structure present in the features by constraining the
model weights to be an underparametrized tensor network. In this paper we
quantize, i.e. further tensorize, polynomial and Fourier features. Based on
this feature quantization we propose to quantize the associated model weights,
yielding quantized models. We show that, for the same number of model
parameters, the resulting quantized models have a higher bound on the
VC-dimension as opposed to their non-quantized counterparts, at no additional
computational cost while learning from identical features. We verify
experimentally how this additional tensorization regularizes the learning
problem by prioritizing the most salient features in the data and how it
provides models with increased generalization capabilities. We finally
benchmark our approach on large regression task, achieving state-of-the-art
results on a laptop computer.

在核机器的背景下，通过将数据映射到高维空间，多项式特征和傅里叶特征常用于为线性模型提供非线性扩展。本文提出一种基于特征量化的方法，可以对相关模型的权重进行量化，生成量化模型。通过这种额外张量化策略，增加模型的广义能力和正则化效果，同时在相同数量的模型参数条件下无需额外计算代价。

更具表现力的张量网络模型的量化傅里叶和多项式特征

Quantized Fourier and Polynomial Features for more Expressive Tensor  Network Models

In recent years, Video Object Segmentation (VOS) has emerged as a
complementary method to Video Object Tracking (VOT). VOS focuses on classifying
all the pixels around the target, allowing for precise shape labeling, while
VOT primarily focuses on the approximate region where the target might be.
However, traditional segmentation modules usually classify pixels frame by
frame, disregarding information between adjacent frames.
In this paper, we propose a new algorithm that addresses this limitation by
analyzing the motion pattern using the inherent tensor structure. The tensor
structure, obtained through Tucker2 tensor decomposition, proves to be
effective in describing the target's motion. By incorporating this information,
we achieved competitive results on Four benchmarks LaSOT\cite{fan2019lasot},
AVisT\cite{noman2022avist}, OTB100\cite{7001050}, and
GOT-10k\cite{huang2019got} LaSOT\cite{fan2019lasot} with SOTA. Furthermore, the
proposed tracker is capable of real-time operation, adding value to its
practical application.

通过分析运动模式使用固有的张量结构进行片段分割和目标追踪，该算法在 LaSOT、AVisT、OTB100 和 GOT-10k 等基准测试中取得了有竞争力的结果，并能够实现实时操作。

运动分析的鲁棒视觉跟踪

Robust Visual Tracking by Motion Analyzing

Convolutional neural networks and their ilk have been very successful for
many learning tasks involving images. These methods assume that the input is a
scalar image representing the intensity in each pixel, possibly in multiple
channels for color images. In natural-science domains however, image-like data
sets might have vectors (velocity, say), tensors (polarization, say),
pseudovectors (magnetic field, say), or other geometric objects in each pixel.
Treating the components of these objects as independent channels in a CNN
neglects their structure entirely. Our formulation -- the GeometricImageNet --
combines a geometric generalization of convolution with outer products, tensor
index contractions, and tensor index permutations to construct geometric-image
functions of geometric images that use and benefit from the tensor structure.
The framework permits, with a very simple adjustment, restriction to function
spaces that are exactly equivariant to translations, discrete rotations, and
reflections. We use representation theory to quantify the dimension of the
space of equivariant polynomial functions on 2-dimensional vector images. We
give partial results on the expressivity of GeometricImageNet on small images.
In numerical experiments, we find that GeometricImageNet has good
generalization for a small simulated physics system, even when trained with a
small training set. We expect this tool will be valuable for scientific and
engineering machine learning, for example in cosmology or ocean dynamics.

通过对几何卷积、外积、张量索引收缩和张量索引排列的结合，我们提出了几何图像网络，可以更好地处理科学领域中粒子、向量和张量层面的图像信息。在小规模数值实验中，我们发现该网络具有很好的泛化性能，可以应用于宇宙学或海洋动力学等科学机器学习问题。