Classical orthogonal wavelets guarantee perfect reconstruction but rely on fixed bases optimized for polynomial smoothness, achieving suboptimal compression on signals with fractal spectral signatures. Conversely, learned methods offer adaptivity but typically enforce orthogonality via soft penalties, sacrificing structural guarantees. This work establishes a rigorous equivalence between Multiscale Entanglement Renormalization Ansatz (MERA) tensor networks and paraunitary filter banks. The resulting framework learns adaptive wavelets while enforcing exact orthogonality through manifold-constrained optimization, guaranteeing perfect reconstruction and energy conservation throughout training. Validation on Long-Range Dependent (LRD) network traffic demonstrates that learned filters outperform classical wavelets by 0.5--3.8~dB PSNR on six MAWI backbone traces (2020--2025, 314~Mbps--1.75~Gbps) while preserving the Hurst exponent within estimation uncertainty ($|ΔH| \le 0.03$). These results establish MERA-inspired wavelets as a principled approach for telemetry compression in 6G digital twin synchronization.

翻译：经典正交小波虽能保证完美重构，但其依赖为多项式平滑性优化的固定基，对具有分形谱特征的信号压缩效果欠佳。相反，学习方法虽具备自适应性，但通常通过软惩罚强制正交性，牺牲了结构保证。本研究建立了多尺度纠缠重整化拟设（MERA）张量网络与仿酉滤波器组之间的严格等价关系。所得框架通过学习自适应小波，并通过流形约束优化强制精确正交性，从而在整个训练过程中保证完美重构与能量守恒。在长程依赖（LRD）网络流量上的验证表明，学习得到的滤波器在六条MAWI骨干链路（2020–2025年，314 Mbps–1.75 Gbps）上比经典小波提升0.5–3.8 dB PSNR，同时将赫斯特指数保持在估计不确定度范围内（$|ΔH| \le 0.03$）。这些结果确立了MERA启发性小波作为6G数字孪生同步中遥测压缩的原理性方法。