Leveraging Parameter Space Symmetries for Reasoning Skill Transfer in LLMs

TL;DR

This paper introduces a method to improve skill transfer in large language models by aligning their parameter spaces, addressing negative interference, and enabling better transfer of reasoning abilities across different models.

Contribution

The authors propose a novel parameter space alignment technique for Transformer-based LLMs, enhancing skill transfer and reducing negative interference during model merging.

Findings

Outperforms standard task arithmetic on reasoning benchmarks

Effectively transfers reasoning skills to non-reasoning models

Reduces redundant fine-tuning in LLM development

Abstract

Task arithmetic is a powerful technique for transferring skills between Large Language Models (LLMs), but it often suffers from negative interference when models have diverged during training. We address this limitation by first aligning the models' parameter spaces, leveraging the inherent permutation, rotation, and scaling symmetries of Transformer architectures. We adapt parameter space alignment for modern Grouped-Query Attention (GQA) and SwiGLU layers, exploring both weight-based and activation-based approaches. Using this alignment-first strategy, we successfully transfer advanced reasoning skills to a non-reasoning model. Experiments on challenging reasoning benchmarks show that our method consistently outperforms standard task arithmetic. This work provides an effective approach for merging and transferring specialized skills across evolving LLM families, reducing redundant fine-tuning and enhancing model adaptability.