Superpose Singular Features for Model Merging

Model merging is a critical technique for combining the capabilities of multiple fine-tuned models without requiring additional training. While existing methods treat parameters as vectors, they overlook the intrinsic structure of linear transformation matrices - the core components that comprise the majority of model parameters. These matrices are fundamental to neural networks, mapping input representations to output features through linear combinations. Motivated by the linear representation hypothesis, we introduce task matrix and propose to Superpose Features from Task Matrix (SFTM), a novel approach that superposes features from individual task models into a merged model. SFTM employs singular value decomposition to identify feature bases of linear transformation matrices and solves a linear system to optimally combine them while preserving input-output mappings from individual task models. Extensive experiments on vision transformers and language models demonstrate that our method consistently outperforms existing methods, achieving superior performance and enhanced out-of-distribution generalization.