Addition in Four Movements: Mapping Layer-wise Information Trajectories in LLMs
This work provides insights into the internal computational processes of LLMs for arithmetic tasks, which is incremental but useful for understanding model behavior in specific domains.
The researchers investigated how LLaMA-3-8B-Instruct performs multi-digit addition by analyzing a four-stage trajectory in its forward pass, revealing that the model hierarchically processes formula structures, computational features, numerical abstractions, and final output generation to achieve near-perfect digit decoding.
Multi-digit addition is a clear probe of the computational power of large language models. To dissect the internal arithmetic processes in LLaMA-3-8B-Instruct, we combine linear probing with logit-lens inspection. Inspired by the step-by-step manner in which humans perform addition, we propose and analyze a coherent four-stage trajectory in the forward pass:Formula-structure representations become linearly decodable first, while the answer token is still far down the candidate list.Core computational features then emerge prominently.At deeper activation layers, numerical abstractions of the result become clearer, enabling near-perfect detection and decoding of the individual digits in the sum.Near the output, the model organizes and generates the final content, with the correct token reliably occupying the top rank.This trajectory suggests a hierarchical process that favors internal computation over rote memorization. We release our code and data to facilitate reproducibility.