Neural support vector machines (NSVMs) allow for the incorporation of domain
knowledge in the design of the model architecture. In this article we introduce
a set of training algorithms for NSVMs that leverage the Pegasos algorithm and
provide a proof of concept by solving a set of standard machine learning tasks.

通过引入域知识，使用 Pegasos 算法为 NSVMs 提供一组训练算法，并通过解决一组标准机器学习任务展示其概念验证。

用于神经支持向量机训练的算法

Algorithms for the Training of Neural Support Vector Machines

Quantum support vector machines have the potential to achieve a quantum
speedup for solving certain machine learning problems. The key challenge for
doing so is finding good quantum kernels for a given data set -- a task called
kernel alignment. In this paper we study this problem using the Pegasos
algorithm, which is an algorithm that uses stochastic gradient descent to solve
the support vector machine optimization problem. We extend Pegasos to the
quantum case and and demonstrate its effectiveness for kernel alignment. Unlike
previous work which performs kernel alignment by training a QSVM within an
outer optimization loop, we show that using Pegasos it is possible to
simultaneously train the support vector machine and align the kernel. Our
experiments show that this approach is capable of aligning quantum feature maps
with high accuracy, and outperforms existing quantum kernel alignment
techniques. Specifically, we demonstrate that Pegasos is particularly effective
for non-stationary data, which is an important challenge in real-world
applications.

本文使用随机梯度下降算法 Pegasos 扩展至量子情形，以此解决量子支持向量机的核对齐问题。实验结果表明此算法可对非平稳数据实现高精度对准，优于现存的量子核对齐技术。