Natural task vectors emerge weakly in deep models; a TVP loss forces a layer to carry the task
measured in 1 paperYang et al. train small GPT-2-style transformers from scratch on synthetic ICL tasks and define a task vector behaviorally by whether its injection recovers ICL performance [yang-etal-2025-task-vectors-emergence-formation-benefit] On a shallow 3-layer model the natural task vector is causally effective (linear-regression MSE ~0.25 vs ~1.2 random) with layer-swap specificity [yang-etal-2025-task-vectors-emergence-formation-benefit] In deeper 8-layer models task information becomes distributed across layers and task-vector prompting performance is nearly random [yang-etal-2025-task-vectors-emergence-formation-benefit] An auxiliary task-vector-prompting loss trains a prescribed layer to serve as an injectable task vector, matching full ICL performance and improving out-of-distribution robustness [yang-etal-2025-task-vectors-emergence-formation-benefit]