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Addition in Four Movements: Mapping Layer-wise Information Trajectories in LLMs

Created by
  • Haebom

Author

Yao Yan

Outline

This paper analyzes the multi-digit addition process in the LLaMA-3-8B-Instruct model using a combination of linear probing and logit-lens testing. Similar to human addition, it presents a hierarchical process consisting of four stages: linear decoding of the mathematical structure representation, emergence of core computational features, numeric abstraction of the result, and final solution generation. This suggests that the model relies on internal computation rather than memorization to perform multi-digit addition. The code and data are made publicly available, enhancing reproducibility.

Takeaways, Limitations

Takeaways:
The multi-digit addition process of the LLaMA-3-8B-Instruct model is explained as a four-step hierarchical process to reveal the internal working principles of the model.
Show that the model solves problems through internal computation rather than memorization.
Ensuring reproducibility of research through open code and data.
Limitations:
The analysis was limited to a specific model (LLaMA-3-8B-Instruct). Further research is needed to determine generalizability to other models.
It is necessary to verify whether the proposed four-step hierarchical process is applicable to all multi-digit addition problems.
Due to limitations in the analytical methods, a complete understanding of the model's internal workings is difficult.
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