The lack of an efficient preamble detection algorithm remains a challenge for
solving preamble collision problems in intelligent massive random access (RA)
in practical communication scenarios. To solve this problem, we present a novel
early preamble detection scheme based on a maximum likelihood estimation (MLE)
model at the first step of the grant-based RA procedure. A novel blind
normalized Stein variational gradient descent (SVGD)-based detector is proposed
to obtain an approximate solution to the MLE model. First, by exploring the
relationship between the Hadamard transform and wavelet transform, a new
modified Hadamard transform (MHT) is developed to separate high-frequencies
from important components using the second-order derivative filter. Next, to
eliminate noise and mitigate the vanishing gradients problem in the SVGD-based
detectors, the block MHT layer is designed based on the MHT, scaling layer,
soft-thresholding layer, inverse MHT and sparsity penalty. Then, the blind
normalized SVGD algorithm is derived to perform preamble detection without
prior knowledge of noise power and the number of active devices. The
experimental results show the proposed block MHT layer outperforms other
transform-based methods in terms of computation costs and denoising
performance. Furthermore, with the assistance of the block MHT layer, the
proposed blind normalized SVGD algorithm achieves a higher preamble detection
accuracy and throughput than other state-of-the-art detection methods.

提出了一种基于极大似然估计模型的新型早期前导检测方案，通过探索 Hadamard 变换和小波变换之间的关系，发展出了改进的 Hadamard 变换（MHT），并通过引入块 MHT 层、缩放层、软阈值层、逆 Hadamard 变换和稀疏惩罚来建模和解决了噪声和渐消梯度问题，通过引入盲化归一化 Stein 变分梯度下降算法，实现了无先验噪声功率和活动设备数量的前导检测，实验结果表明，所提出的方法在计算成本和去噪性能方面胜过其他基于变换的方法，并且在辅助下的盲化归一化 Stein 变分梯度下降算法实现了比其他最先进的检测方法更高的前导检测准确度和吞吐量。

智能大规模随机接入的盲标准化 Stein 变分梯度下降检测

The Blind Normalized Stein Variational Gradient Descent-Based Detection  for Intelligent Massive Random Access

In this paper, we propose a novel Hadamard Transform (HT)-based neural
network layer for hybrid quantum-classical computing. It implements the regular
convolutional layers in the Hadamard transform domain. The idea is based on the
HT convolution theorem which states that the dyadic convolution between two
vectors is equivalent to the element-wise multiplication of their HT
representation. Computing the HT is simply the application of a Hadamard gate
to each qubit individually, so the HT computations of our proposed layer can be
implemented on a quantum computer. Compared to the regular Conv2D layer, the
proposed HT-perceptron layer is computationally more efficient. Compared to a
CNN with the same number of trainable parameters and 99.26\% test accuracy, our
HT network reaches 99.31\% test accuracy with 57.1\% MACs reduced in the MNIST
dataset; and in our ImageNet-1K experiments, our HT-based ResNet-50 exceeds the
accuracy of the baseline ResNet-50 by 0.59\% center-crop top-1 accuracy using
11.5\% fewer parameters with 12.6\% fewer MACs.

本文提出了一种基于 Hadamard 变换的 HT-perceptron 层，用于混合量子经典计算，相较于常规的 Conv2D 层，在 MNIST 和 ImageNet-1K 数据集上分别减少了 57.1% 和 12.6% 的 MACs 且精度有所提升。

基于 Hadamard 变换的混合量子经典方法用于卷积层

A Hybrid Quantum-Classical Approach based on the Hadamard Transform for  the Convolutional Layer

Constrained least-squares regression problems, such as the Nonnegative Least
Squares (NNLS) problem, where the variables are restricted to take only
nonnegative values, often arise in applications. Motivated by the recent
development of the fast Johnson-Lindestrauss transform, we present a fast
random projection type approximation algorithm for the NNLS problem. Our
algorithm employs a randomized Hadamard transform to construct a much smaller
NNLS problem and solves this smaller problem using a standard NNLS solver. We
prove that our approach finds a nonnegative solution vector that, with high
probability, is close to the optimum nonnegative solution in a relative error
approximation sense. We experimentally evaluate our approach on a large
collection of term-document data and verify that it does offer considerable
speedups without a significant loss in accuracy. Our analysis is based on a
novel random projection type result that might be of independent interest. In
particular, given a tall and thin matrix $\Phi \in \mathbb{R}^{n \times d}$ ($n
\gg d$) and a vector $y \in \mathbb{R}^d$, we prove that the Euclidean length
of $\Phi y$ can be estimated very accurately by the Euclidean length of
$\tilde{\Phi}y$, where $\tilde{\Phi}$ consists of a small subset of
(appropriately rescaled) rows of $\Phi$.

本篇研究文章使用快速 Johnson-Lindestrauss 变换以及基于随机 Hadamard 变换的方法，构造了一个较小的 Nonnegative Least Squares 问题，并在相对误差逼近意义下找到一个非负解，实验结果表明其在速度上有显著提升且不会丢失太多精度。