TT-net：条件生成对抗网络中受量子启发的张量网络去噪

中文摘要 AI 辅助

张量网络方法作为量子算法和量子多体系统经典模拟的核心工具，已成为量子物理学领域的主流科学方法。在各类张量网络中，张量列车（Tensor Trains，在量子计算领域通常称为矩阵乘积态）已应用于机器学习，这些方法常依赖奇异值分解（SVD）这一强大线性代数工具。多个用于图像去噪的条件生成对抗网络（conditional GAN）架构将SVD作为单切分解步骤应用于生成器特征图。本研究提出TT-Net，用双切张量列车分解取代逐通道SVD去噪块，该分解可直接获取跨通道信息，这是现有替代方法不具备的能力。在仅分解机制不同的受控对比实验中，TT-Net在所有三种测试噪声类型（高斯噪声、运动模糊噪声、椒盐噪声）下的峰值信噪比（PSNR）和结构相似性指数（SSIM）均优于SVD-Net，支持跨通道访问可提升去噪质量的假设。训练动态分析进一步显示，TT-Net的对抗损失项在所有三种噪声类型下均稳定进入停滞状态，且比SVD-Net更明显，而重构质量仍持续提升，这引发了本研究识别但未解决的关于对抗组件贡献的开放性问题。此外，对于高斯噪声，本方法优于EigenGAN和未采用任何线性代数分解、未保留线性代数信息的当前最优方法Pix2pix。本论文展示了受量子启发的工具如何用作深度学习应用的实用现实世界特征滤波器。

英文摘要

Developed as a workhorse for classical simulations of quantum algorithms and quantum many-body systems, Tensor Network methods have entered the scientific mainstream in quantum physics. Among various types of tensor networks, Tensor Trains (commonly know as Matrix Product States in the quantum computing community) have already found applications in machine learning. These methods often rely on a powerful linear algebra tool called the Singular Value Decomposition (SVD). Several conditional GAN architectures for image denoising incorporate SVD as a single-cut decomposition step applied to generator feature maps. In this work we introduce TT-Net, which replaces the per-channel SVD denoising block with a two-cut tensor-train decomposition capable of accessing cross-channel information directly, a capability absent from contemporary alternatives. In a controlled comparison differing only in this decomposition mechanism, TT-Net outperforms SVD-Net on PSNR and SSIM across all three noise types tested (Gaussian, motion blur, and salt-and-pepper), supporting the hypothesis that cross-channel access improves denoising quality. Training-dynamics analysis further shows that TT-Net's adversarial loss term consistently saturates to a stagnant state across all three noise types, more so than SVD-Net's, while reconstruction quality continues to improve regardless, raising an open question about the adversarial component's contribution that this work identifies but does not resolve. Furthermore, for Gaussian noise our method outperforms both the EigenGAN and the state of the art Pix2pix method which does not assume any linear algebra decompositions and does not retain any linear algebra information. Our manuscript shows how quantum inspired tools can be used as practical real world feature filters for deep learning applications.

发表机构

• University of Luxembourg（卢森堡大学）

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