Interpreting the Latent Structure of Operator Precedence in Language Models
This addresses the problem of understanding internal arithmetic structures in LLMs for researchers, but it is incremental as it builds on existing interpretability techniques.
The researchers investigated whether large language models encode operator precedence in their internal representations, using the LLaMA 3.2-3B model, and found that intermediate computations are present in the residual stream and that precedence is linearly encoded in operator embeddings.
Large Language Models (LLMs) have demonstrated impressive reasoning capabilities but continue to struggle with arithmetic tasks. Prior works largely focus on outputs or prompting strategies, leaving the open question of the internal structure through which models do arithmetic computation. In this work, we investigate whether LLMs encode operator precedence in their internal representations via the open-source instruction-tuned LLaMA 3.2-3B model. We constructed a dataset of arithmetic expressions with three operands and two operators, varying the order and placement of parentheses. Using this dataset, we trace whether intermediate results appear in the residual stream of the instruction-tuned LLaMA 3.2-3B model. We apply interpretability techniques such as logit lens, linear classification probes, and UMAP geometric visualization. Our results show that intermediate computations are present in the residual stream, particularly after MLP blocks. We also find that the model linearly encodes precedence in each operator's embeddings post attention layer. We introduce partial embedding swap, a technique that modifies operator precedence by exchanging high-impact embedding dimensions between operators.