# Platonic Task Arithmetic

arXiv: https://arxiv.org/abs/2610.00929 · HTML: https://mlsanity.com/paper/2610.00929/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 52 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 18 of 18)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [SigLIP 2: Multilingual Vision-Language Encoders with Improved Semantic Understanding, Localization, and Dense Features](https://mlsanity.com/paper/2502.14786/) (2025)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [EVA-CLIP: Improved Training Techniques for CLIP at Scale](https://mlsanity.com/paper/2303.15389/) (2023)
- [Contrastive Representation Distillation](https://mlsanity.com/paper/1910.10699/) (2019)
- [The Platonic Representation Hypothesis](https://mlsanity.com/paper/2405.07987/) (2024)
- [LoraHub: Efficient Cross-Task Generalization via Dynamic LoRA Composition](https://mlsanity.com/paper/2307.13269/) (2023)
- [Demystifying CLIP Data](https://mlsanity.com/paper/2309.16671/) (2023)
- [AdaMerging: Adaptive Model Merging for Multi-Task Learning](https://mlsanity.com/paper/2310.02575/) (2023)
- [Relative representations enable zero-shot latent space communication](https://mlsanity.com/paper/2209.15430/) (2022)
- [Task Arithmetic with LoRA for Continual Learning](https://mlsanity.com/paper/2311.02428/) (2023)
- [Understanding the Emergence of Multimodal Representation Alignment](https://mlsanity.com/paper/2502.16282/) (2025)
- [On the Emergence of Cross-Task Linearity in the Pretraining-Finetuning Paradigm](https://mlsanity.com/paper/2402.03660/) (2024)
- [LoRA-X: Bridging Foundation Models with Training-Free Cross-Model Adaptation](https://mlsanity.com/paper/2501.16559/) (2025)
- [Cross-LoRA: A Data-Free LoRA Transfer Framework across Heterogeneous LLMs](https://mlsanity.com/paper/2508.05232/) (2025)
- [Proof of a perfect platonic representation hypothesis](https://mlsanity.com/paper/2507.01098/) (2025)
- [Transport and Merge: Cross-Architecture Merging for Large Language Models](https://mlsanity.com/paper/2602.05495/) (2026)
- [Transporting Task Vectors across Different Architectures without Training](https://mlsanity.com/paper/2602.12952/) (2026)

## Abstract (arXiv)

Distinct pre-trained models specialized for the same task converge to closely similar behavior, yet the parameter updates that produce it share no common coordinate system. Weight-space task arithmetic is therefore confined to a single model, and transporting an update between models requires a structural correspondence. Drawing on Plato's allegory of the cave, we hypothesize that these model-specific updates are shadows cast by one shared, model-agnostic object, the platonic task vector. To make it operational across models of different architectures, we introduce Universal Task Descriptors, matrices whose shape is independent of architecture and embedding dimension, which record a task's functional effect and admit addition and negation as ordinary matrix operations, and we transfer a descriptor into a target in two ways. A single least-squares solve returns a linear operator folded into the target's last layer, and a bank of such operators, one per source and task, realizes any composition as a signed sum of its entries. Alternatively, a low-rank adapter of the target's encoder is trained on the same objective at the price of one optimization per edit. Despite a model-specific residual comparable in norm to the shared component, transfer from another model retains 74 to 80 percent of the gain the target's own descriptors attain. Experiments across six model families, eight tasks and audio-text models confirm both realizations.