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In-context learning is a remarkable capability of transformers, referring to their ability to adapt to specific tasks based on a short history or context. Previous research has found that task-specific information is locally encoded within models, though their emergence and functionality remain unclear due to opaque pre-training processes. In this work, we investigate the formation of task vectors in a controlled setting, using models trained from scratch on synthetic datasets. Our findings confirm that task vectors naturally emerge under certain conditions, but the tasks may be relatively weakly and/or non-locally encoded within the model. To promote strong task vectors encoded at a prescribed location within the model, we propose an auxiliary training mechanism based on a task vector prompting loss (TVP-loss). This method eliminates the need to search for task-correlated encodings within the trained model and demonstrably improves robustness and generalization.