Task Vector Bases: A Unified and Scalable Framework for Compressed Task Arithmetic

Fuente: arXiv
Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Zeng, Siqi, He, Yifei, Liu, Meitong, You, Weiqiu, Hao, Yifan, Tsai, Yao-Hung Hubert, Yamada, Makoto, Zhao, Han
Format: Preprint
Veröffentlicht: 2025
Schlagworte:
Online-Zugang:
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
_version_ 1866915540070563840
author Zeng, Siqi
He, Yifei
Liu, Meitong
You, Weiqiu
Hao, Yifan
Tsai, Yao-Hung Hubert
Yamada, Makoto
Zhao, Han
author_facet Zeng, Siqi
He, Yifei
Liu, Meitong
You, Weiqiu
Hao, Yifan
Tsai, Yao-Hung Hubert
Yamada, Makoto
Zhao, Han
contents Task arithmetic, representing downstream tasks through linear operations on task vectors, has emerged as a simple yet powerful paradigm for transferring knowledge across diverse settings. However, maintaining a large collection of task vectors introduces scalability challenges in both storage and computation. We propose Task Vector Bases, a framework compressing $T$ task vectors into $M < T$ basis vectors while preserving the functionality of task arithmetic. By representing each task vector as a structured linear combination of basis atoms, our approach supports standard operations such as addition, negation, as well as more advanced arithmetic ones. The framework is orthogonal to other efficiency-oriented improvements in task arithmetic and can be used in combination with them. We provide theoretical analysis showing that basis compression retains addition generalization guarantees and enables principled unlearning, with error bounds depending on reconstruction quality. Empirically, our proposed basis construction methods consistently outperform heuristic basis construction baselines and, in some cases, even surpass the performance of full task vector collections across diverse downstream applications while reducing storage and computational requirements. The code is available at https://github.com/uiuctml/TaskVectorBasis.
format Preprint
id arxiv_https___arxiv_org_abs_2502_01015
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Task Vector Bases: A Unified and Scalable Framework for Compressed Task Arithmetic
Zeng, Siqi
He, Yifei
Liu, Meitong
You, Weiqiu
Hao, Yifan
Tsai, Yao-Hung Hubert
Yamada, Makoto
Zhao, Han
Machine Learning
Task arithmetic, representing downstream tasks through linear operations on task vectors, has emerged as a simple yet powerful paradigm for transferring knowledge across diverse settings. However, maintaining a large collection of task vectors introduces scalability challenges in both storage and computation. We propose Task Vector Bases, a framework compressing $T$ task vectors into $M < T$ basis vectors while preserving the functionality of task arithmetic. By representing each task vector as a structured linear combination of basis atoms, our approach supports standard operations such as addition, negation, as well as more advanced arithmetic ones. The framework is orthogonal to other efficiency-oriented improvements in task arithmetic and can be used in combination with them. We provide theoretical analysis showing that basis compression retains addition generalization guarantees and enables principled unlearning, with error bounds depending on reconstruction quality. Empirically, our proposed basis construction methods consistently outperform heuristic basis construction baselines and, in some cases, even surpass the performance of full task vector collections across diverse downstream applications while reducing storage and computational requirements. The code is available at https://github.com/uiuctml/TaskVectorBasis.
title Task Vector Bases: A Unified and Scalable Framework for Compressed Task Arithmetic
topic Machine Learning
url https://arxiv.org/abs/2502.01015