The Universal Weight Subspace Hypothesis

TL;DR

Deep neural networks across various tasks converge to similar low-dimensional spectral subspaces, revealing universal structures that could improve model efficiency and reusability.

Contribution

This paper provides the first large-scale empirical evidence of shared spectral subspaces in neural networks, regardless of architecture, initialization, or task.

Findings

Neural networks converge to shared spectral subspaces across diverse tasks.

A few principal directions capture most variance in weight matrices.

Universal subspaces are consistently exploited across architectures and datasets.

Abstract

We show that deep neural networks trained across diverse tasks exhibit remarkably similar low-dimensional parametric subspaces. We provide the first large-scale empirical evidence that demonstrates that neural networks systematically converge to shared spectral subspaces regardless of initialization, task, or domain. Through mode-wise spectral analysis of over 1100 models - including 500 Mistral-7B LoRAs, 500 Vision Transformers, and 50 LLaMA-8B models - we identify universal subspaces capturing majority variance in just a few principal directions. By applying spectral decomposition techniques to the weight matrices of various architectures trained on a wide range of tasks and datasets, we identify sparse, joint subspaces that are consistently exploited, within shared architectures across diverse tasks and datasets. Our findings offer new insights into the intrinsic organization of information within deep networks and raise important questions about the possibility of discovering these universal subspaces without the need for extensive data and computational resources. Furthermore, this inherent structure has significant implications for model reusability, multi-task learning, model merging, and the development of training and inference-efficient algorithms, potentially reducing the carbon footprint of large-scale neural models.