Hyper-Compression: Model Compression via Hyperfunction

TL;DR

Hyper-Compression reframes model size reduction as a parameter-encoding problem via hyperfunctions driven by ergodic dynamics with irrational winding, offering a theoretical error bound and a pragmatic pipeline that avoids retraining. The authors show favorable compression ratios (e.g., about $2.6\\times$ on LLaMA2-7B) with minimal task-driven degradation and near-$int4$ quality, and demonstrate compatibility with pruning variants across diverse architectures including UNet and MobileNetV3. Key contributions include a four-part compression algorithm, acceleration techniques (KD-trees and matrix ops), and an open-source implementation, enabling fast compression (often under an hour for large LMs) with no post-hoc retraining. The work promises to alleviate the memory bottleneck in serving large models and complements existing pruning/quantization methods, potentially transforming deployment of massive models.

Abstract

The rapid growth of large models' size has far outpaced that of computing resources. To bridge this gap, encouraged by the parsimonious relationship between genotype and phenotype in the brain's growth and development, we propose the so-called hyper-compression that turns the model compression into the issue of parameter representation via a hyperfunction. Specifically, it is known that the trajectory of some low-dimensional dynamic systems can fill the high-dimensional space eventually. Thus, hyper-compression, using these dynamic systems as the hyperfunctions, represents the parameters of the target network by their corresponding composition number or trajectory length. This suggests a novel mechanism for model compression, substantially different from the existing pruning, quantization, distillation, and decomposition. Along this direction, we methodologically identify a suitable dynamic system with the irrational winding as the hyperfunction and theoretically derive its associated error bound. Next, guided by our theoretical insights, we propose several engineering twists to make the hyper-compression pragmatic and effective. Lastly, systematic and comprehensive experiments confirm that hyper-compression enjoys the following \textbf{PNAS} merits: 1) \textbf{P}referable compression ratio; 2) \textbf{N}o post-hoc retraining; 3) \textbf{A}ffordable inference time; and 4) \textbf{S}hort compression time. It compresses LLaMA2-7B in an hour and achieves close-to-int4-quantization performance, without retraining and with a performance drop of less than 1\%. We have open-sourced our code in https://github.com/Juntongkuki/Hyper-Compression.git for free download and evaluation.

Figures (9)

• Figure S1: The rapid growth of large models' sizes has outpaced the growth of GPU memory, creating huge challenges in serving large models.
• Figure S2: $G_2$
• Figure S6: An illustrative scheme for using ergodic theory to learn a low-dimensional representation of high-dimensional points.
• Figure S8: Different $\mathbf{a}$ will result in different distribution of points. Upper three subfigures use Eq. (\ref{['vector_m1']}), while lower three figures utilize Eq. (\ref{['vector_m2']}).
• Figure S9: The rapid growth of LLM's size has outpaced the growth of GPU memory, creating challenges in serving these increasingly massive models.

Theorems & Definitions (8)

• Definition 1: Graph, Vertex, Edge
• Definition 2: Open and Closed
• Definition 3: Open Cluster
• Definition 4: Percolation probability and critical probability
• Proposition 1: Critical Probability of $G_2$
• proof : Proof of Proposition \ref{['prop:p_c,2']}
• Proposition 2: Critical Probability of $G_r, r\geq 3$
• proof : Proof of Proposition \ref{['prop:p_c,r']}