Essential Subspace Merging for Multi-Task Learning

2026-06-17

AI Summary

This work addresses interference in model merging for multi-task learning, which often arises from conflicting parameter updates across tasks. The authors observe that output shifts induced by task-specific updates concentrate their energy within a low-dimensional “essential subspace” spanned by a few dominant directions. Building on this insight, they propose two training-free merging strategies: a static Essential Subspace Merging (ESM) method that mitigates interference through orthogonal fusion, and a dynamic variant (ESM++) that combines low-rank expert decomposition with prototype-based routing to enable task-adaptive integration. Experiments demonstrate that both approaches substantially alleviate inter-task interference across diverse task sets and model scales while effectively preserving individual task performance.

Abstract

Model merging aims to enable multi-task learning by integrating the capabilities of multiple models fine-tuned from the same pre-trained checkpoint into a single model. Its core challenge is inter-task interference among task-specific parameter updates. In this paper, we analyze the output shifts induced by task updates and observe that their energy is concentrated in a small number of principal directions. We call the subspace spanned by these directions the essential subspace. In contrast, most remaining directions carry little task-relevant energy, but their accumulation across multiple task updates can cause severe interference during merging. Motivated by this observation, we propose Essential Subspace Decomposition (ESD), which decomposes each task update according to the principal components of its activation shift. Based on ESD, we introduce Essential Subspace Merging (ESM), a training-free static merging method that orthogonalizes and fuses essential components into one compact multi-task model. We further extend ESM to ESM++, a training-free dynamic merging method that decomposes task-specific residuals into low-rank experts and selects the most relevant expert through prototype-based routing during forward inference. Extensive experiments across multiple task sets and model scales demonstrate that ESM and ESM++ effectively preserves task knowledge while reducing inter-task interference.

Problem

• model merging
• multi-task learning
• inter-task interference
• essential subspace
• parameter updates

Innovation

• Essential Subspace
• Model Merging
• Multi-Task Learning
• Training-Free Fusion
• Low-Rank Experts