Platonic Task Arithmetic

When distinct pre-trained models are specialized for the same task, they often converge to nearly equivalent functional behaviors, while the underlying parameter-space changes share no common coordinate system. Existing approaches that compose such changes arithmetically are therefore confined to a single model, leaving task knowledge stranded inside the network that acquired it. Drawing on Plato's allegory of the cave, we hypothesize that these model-specific updates are shadows cast by a shared, model-agnostic object that governs how task specialization reshapes a model's behavior, and we refer to this object as the platonic task vector. To make this view operational, we introduce Universal Task Descriptors, matrices whose shape is fixed independently of architecture or embedding dimension and that capture a task's functional effect in a model-transferable form. Universal Task Descriptors admit addition, negation, and analogy in closed form, and a lightweight realization step then transfers any composed descriptor into a chosen target model. Experiments across a range of models and tasks indicate that this pipeline transfers and composes task knowledge across heterogeneous models.