Bridging Topological Dynamics and Industrial Scalability: The Synergy of PLDS, Dynamic F-LoRA, and Non-Linear Latent Control

Large Language Models (LLMs) deployed in resource-constrained edge environmentsand multi-tenant cloud datacenters face a dual bottleneck: excessive memory bandwidthconsumption from spatial-domain parameter adapters and unconstrained entropydrift during multi-step Chain-of-Thought (CoT) reasoning. To resolve thesechallenges, we introduce a novel non-linear topological framework uniting DynamicF-LoRA (Frequency-Domain Low-Rank Adaptation) and Phase-Locked DynamicSampling (PLDS). Dynamic F-LoRA leverages two-dimensional Discrete CosineTransform (2D-DCT) spectral low-pass filtering to prune 80% of high-frequency syntacticnoise at the parameter level while preserving core semantic update manifolds.Simultaneously, PLDS employs continuous-time Rössler and Lorenz dynamic attractorsto govern latent trajectory dynamics and modulate sampling temperature in realtime. We provide a rigorous Lyapunov stability proof, guaranteeing global asymptoticconvergence and hallucination suppression. Empirical evaluations demonstratethat our unified framework achieves a 75.0% reduction in peak VRAM allocation, a1.59× inference speedup, a 5× increase in multi-tenant adapter serving density, andan improved Pass@1 reasoning accuracy of 79.1% on GSM8K.