# Dynamics as Code: On Model Compression via Dynamic System

arXiv: https://arxiv.org/abs/2610.11115 · HTML: https://mlsanity.com/paper/2610.11115/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 65 references that are in the map.
- First posted on arXiv 8 Oct 2026.

## Builds on (most cited first, 10 of 10)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [A Survey on Efficient Inference for Large Language Models](https://mlsanity.com/paper/2404.14294/) (2024)
- [Efficient Large Language Models: A Survey](https://mlsanity.com/paper/2312.03863/) (2023)
- [Reasoning Models Can be Accurately Pruned Via Chain-of-Thought Reconstruction](https://mlsanity.com/paper/2509.12464/) (2025)
- [Compress Any Segment Anything Model (SAM)](https://mlsanity.com/paper/2507.08765/) (2025)
- [COLI: A Hierarchical Efficient Compressor for Large Images](https://mlsanity.com/paper/2507.11443/) (2025)

## Abstract (arXiv)

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+nu))) 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.