Transporting Task Vectors across Different Architectures without Training

Adapting large pre-trained models to downstream tasks often produces task-specific parameter updates that are expensive to relearn for every model variant. While recent work has shown that such updates can be transferred between models with identical architectures, transferring them across models of different widths remains unexplored. In this work, we introduce Theseus, a training-free method for transporting task updates across heterogeneous-width models. Rather than matching parameters, we characterize a task update by the functional effect it induces on intermediate representations. We formalize task-vector transport as a functional matching problem on observed activations and show that, after aligning representation spaces via orthogonal Procrustes analysis, it admits a stable closed-form solution that preserves the geometry of the update. We evaluate Theseus on vision and language models across different widths, showing consistent improvements over baselines without additional training or backpropagation. Our results show that task updates can be meaningfully transferred across architectures when task identity is defined functionally rather than parametrically. Code is available at https://github.com/apanariello4/merge-and-rebase.

Large AI models are often adapted to new tasks by slightly changing their internal parameters. However, these task-specific updates usually need to be learned again for every version of a model, especially when models differ in size or architecture. This process can be expensive in terms of computation, energy, and time. In this work, we introduce Theseus, a method that allows task-specific updates learned by one AI model to be transferred directly to another model without any additional training. Instead of matching model parameters directly, our method focuses on preserving how the update changes the model’s internal representations. We align the internal structures of two different models and then transport the task update between them using a simple mathematical procedure. We test our approach on both vision and language models of different sizes and architectures. Across many experiments, Theseus consistently improves performance over existing baselines and remains competitive with approaches that require additional optimization. Our results suggest that task knowledge can be reused across different AI systems more efficiently than previously thought, opening new possibilities for modular, reusable, and more sustainable AI development.