In this paper, we introduce the Convolutional Kolmogorov-Arnold Networks
(Convolutional KANs), an innovative alternative to the standard Convolutional
Neural Networks (CNNs) that have revolutionized the field of computer vision.
We integrate the non-linear activation functions presented in Kolmogorov-Arnold
Networks (KANs) into convolutions to build a new layer. Throughout the paper,
we empirically validate the performance of Convolutional KANs against
traditional architectures across MNIST and Fashion-MNIST benchmarks,
illustrating that this new approach maintains a similar level of accuracy while
using half the amount of parameters. This significant reduction of parameters
opens up a new approach to advance the optimization of neural network
architectures.

这篇论文提出了卷积科尔莫戈洛夫 - 阿诺德网络（Convolutional KANs），这是标准卷积神经网络（CNN）的一种创新替代方法，我们将科尔莫戈洛夫 - 阿诺德网络（KANs）中的非线性激活函数集成到卷积中，构建出一个新的层。我们在 MNIST 和 Fashion-MNIST 基准测试中对 Convolutional KANs 的性能进行了实证验证，表明这种新方法在准确性方面保持了类似水平，同时只使用了一半的参数。这种参数量的显著减少打开了推进神经网络架构优化的新途径。

卷积科尔莫哥洛夫 - 阿诺德网络

Convolutional Kolmogorov-Arnold Networks

Tensor networks approximate order-$N$ tensors with a reduced number of
degrees of freedom that is only polynomial in $N$ and arranged as a network of
partially contracted smaller tensors. As suggested in [arXiv:2205.15296] in the
context of quantum many-body physics, computation costs can be further
substantially reduced by imposing constraints on the canonical polyadic (CP)
rank of the tensors in such networks. Here we demonstrate how tree tensor
networks (TTN) with CP rank constraints and tensor dropout can be used in
machine learning. The approach is found to outperform other tensor-network
based methods in Fashion-MNIST image classification. A low-rank TTN classifier
with branching ratio $b=4$ reaches test set accuracy 90.3\% with low
computation costs. Consisting of mostly linear elements, tensor network
classifiers avoid the vanishing gradient problem of deep neural networks. The
CP rank constraints have additional advantages: The number of parameters can be
decreased and tuned more freely to control overfitting, improve generalization
properties, and reduce computation costs. They allow us to employ trees with
large branching ratios which substantially improves the representation power.

本文介绍如何将带有 CP 秩约束和张量丢弃功能的树张量网络应用于机器学习中，该方法在 Fashion-MNIST 图像分类中优于其他基于张量网络的方法，且分类器的参数数量可以减少并更灵活地进行控制。

利用树形张量网络、CP 秩约束和张量 Dropout 进行机器学习

Machine learning with tree tensor networks, CP rank constraints, and  tensor dropout

We present Fashion-MNIST, a new dataset comprising of 28x28 grayscale images
of 70,000 fashion products from 10 categories, with 7,000 images per category.
The training set has 60,000 images and the test set has 10,000 images.
Fashion-MNIST is intended to serve as a direct drop-in replacement for the
original MNIST dataset for benchmarking machine learning algorithms, as it
shares the same image size, data format and the structure of training and
testing splits. The dataset is freely available at
this https URL

介绍 Fashion-MNIST 数据集，该数据集由十个类别的七万张灰度图像组成，旨在作为 MNIST 数据集的替代品，用于机器学习算法的基准测试。