Platonic Task Arithmetic

Abstract:Models specialized for the same task converge to similar behavior, yet the parameter updates that produce it share no common coordinate system, so weight-space task arithmetic stays confined to a single model and cannot cross architectures without a structural correspondence. Drawing on Plato's allegory of the cave, we hypothesize that these model-specific updates are shadows of one shared, model-agnostic object, which we call the platonic task vector. To make it operational for models that pair an image or audio encoder with a text encoder, we introduce Universal Task Descriptors: matrices whose shape is independent of architecture and embedding dimension, which record a task's functional effect and support addition and negation as matrix operations. Transferring a descriptor into a target means editing the target until it reproduces the descriptor on the task's unlabeled probe images and class-name prompts, requiring no per-image labels. We realize this edit in two ways. First, the descriptor factorizes into a shift field on image embeddings, so a single least-squares solve yields a linear operator that folds into the target's last layer as a weight edit; by linearity, a bank of such operators admits any composition at any strength as a signed sum. Second, a low-rank adapter trained on the same objective reaches every layer and fits compositions jointly, at the cost of one optimization per edit. Heterogeneous models share this object only partially, with a model-specific residual comparable in norm to the shared component, yet cross-model transfer still retains 74-80 percent of the gain of the target's own descriptors. Experiments across six model families, eight classification tasks, and an audio-text setting show that task knowledge transfers and composes across heterogeneous models under both realizations.

Machine Learning (cs.LG); Computer Vision and Pattern Recognition (cs.CV); Machine Learning (stat.ML)

arXiv:2610.00929 [cs.LG]

(or arXiv:2610.00929v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.00929 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.