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Luca Zhou, Daniele Solombrino, Donato Crisostomi, Maria Sofia Bucarelli, Giuseppe Alessio D'Inverno, Fabrizio Silvestri, Emanuele Rodol a
Theoretical Foundations of Task Arithmetic
Outline
Task arithmetic has emerged as a simple yet powerful model merging technique that combines multiple fine-tuned models into one. This paper establishes the connection between the task vector and the gradient of the task loss to provide a theoretical foundation for task arithmetic. Under standard gradient descent, the task vector generated by one-epoch fine-tuning is shown to be exactly equivalent to the negative gradient of the loss scaled by the learning rate. For multi-epoch settings, we prove that this equivalence approximately holds, using an explicitly bounded quadratic error term for feedforward networks.
Takeaways, Limitations
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Takeaways:
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Provides clear evidence for why task arithmetic is effective.
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Emphasizes the importance of early learning dynamics in model merging.
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This suggests that merging models fine-tuned for only one epoch can achieve similar performance as merging fully converged models.
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Reframe task arithmetic as a form of approximate multi-task learning.
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Limitations:
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Limited to the analysis of second-order error terms for feedforward networks (not mentioned in the paper).
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Experiments were limited to visual benchmarks (not mentioned in the paper).
