Task Arithmetic is a model editing technique that represents task-specific knowledge as "task vectors" (the difference between fine-tuned and pre-trained weights) — these vectors can be added, negated, or combined to create models with new task capabilities.

How Does Task Arithmetic Work?

• Task Vector: $ au_A = heta_A - heta_0$ (difference between fine-tuned $ heta_A$ and pre-trained $ heta_0$).
• Addition: $ heta_{A+B} = heta_0 + au_A + au_B$ (combine capabilities of tasks A and B).
• Negation: $ heta_{-A} = heta_0 - au_A$ (remove task A capabilities, e.g., forget toxic behavior).
• Scaling: $ heta_0 + lambda au_A$ (control the strength of task A).
• Paper: Ilharco et al. (2023).

Why It Matters

• Model Editing: Add, remove, or modify model capabilities without retraining.
• Multi-Task: Combine task-specific fine-tunes into a single multi-task model.
• Safety: Negate toxic task vectors to reduce harmful model behaviors.

Task Arithmetic is algebra for neural network capabilities — adding and subtracting task knowledge using simple vector operations in weight space.