发表机构
School of Information Science and Engineering, Lanzhou University; City University of Hong Kong; School of Science, Great Bay University（兰州大学信息科学与工程学院; 香港城市大学; 大湾区大学理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出基于动态系统（DS）的模型压缩框架，通过将高维参数编码为动态系统轨迹索引实现压缩，在ResNet-18及Qwen系列模型上验证其无需事后微调即可实现可控误差的高效压缩。
AI 中文摘要
预训练神经网络规模不断扩大，使得模型压缩成为在严格内存和计算约束下部署的必要前提。以无理缠绕为例，早期工作提出了动态系统（DS）范式，将压缩重新概念化为紧凑权重表示：高维参数由动态系统生成的轨迹索引编码，解压时可从中恢复向量，该机制与剪枝、量化、知识蒸馏及低秩分解根本不同。沿此方向，我们证明在丢番图条件下，无理缠绕中M=O(ε^-(d+ν))个状态的有限轨迹构成d维权重空间的ε-网，从而以可预测方式关联状态分辨率、解压误差与压缩率。此外，我们提出一种广义的基于DS的模型压缩框架，统一四类DS族：空间填充曲线（希尔伯特、皮亚诺、莫顿/Z序、蛇形）、混沌系统（洛伦兹）、同余与伪随机生成器（LCG、PCG）及低差异序列（哈尔顿）。我们还引入KD树和坐标模板加速以扩展至大模型，同时引入异常识别控制误差。在ResNet-18及Qwen2.5-1.5B/Qwen1.5-7B上的实验验证，基于DS的压缩无需事后微调即可实现有竞争力的压缩率，且解压误差可控、状态空间设计灵活，是一种有原则且实用的压缩方法。
英文摘要
The escalating size of pretrained neural networks has rendered model compression a prerequisite for deployment under stringent memory and compute constraints. With the irrational winding as an example, earlier work introduced a dynamic system (DS) paradigm that reconceptualizes compression as compact weight representation: high-dimensional parameters are encoded by the index of a trajectory produced by a dynamic system, from which the vector is recovered during decompression. This mechanism is fundamentally distinct from pruning, quantization, knowledge distillation, and low-rank decomposition. Along this direction, we prove that under a Diophantine condition, a finite trajectory of \(M = O(ε^{-(d+ν)})\) states in the irrational winding constitutes an \(ε\)-net over the \(d\)-dimensional weight space, thereby linking state resolution, decompression error, and compression ratio in a predictable manner. Furthermore, we propose a generalized DS-based model compression framework by unifying four DS families---space-filling curves (Hilbert, Peano, Morton/Z-order, Snake), chaotic systems (Lorenz), congruential and pseudo-random generators (LCG, PCG), and low-discrepancy sequences (Halton). Also, we introduce the KD-tree and coordinate-template acceleration to scale to large models as well as outlier identification to control the error. Experiments on ResNet-18 and Qwen2.5-1.5B/Qwen1.5-7B validate that DS-based compression achieves competitive compression ratios without post-hoc retraining, with controllable decompression error and flexible state-space design, establishing it as a principled and practical compression approach.
Comments17 pages including supplementary material
