Interpreting Arithmetic Reasoning in Large Language Models using Game-Theoretic Interactions

In recent years, large language models (LLMs) have made significant advancements in arithmetic reasoning. However, the internal mechanism of how LLMs solve arithmetic problems remains unclear. In this paper, we propose explaining arithmetic reasoning in LLMs using game-theoretic interactions. Specifically, we disentangle the output score of the LLM into numerous interactions between the input words. We quantify different types of interactions encoded by LLMs during forward propagation to explore the internal mechanism of LLMs for solving arithmetic problems. We find that (1) the internal mechanism of LLMs for solving simple one-operator arithmetic problems is their capability to encode operand-operator interactions and high-order interactions from input samples. Additionally, we find that LLMs with weak one-operator arithmetic capabilities focus more on background interactions.

(2) The internal mechanism of LLMs for solving relatively complex two-operator arithmetic problems is their capability to encode operator interactions and operand interactions from input samples. (3) We explain the task-specific nature of the LoRA method from the perspective of interactions. * Corresponding author. 2 Note that each interaction is equivalently encoded by the entire DNN, rather than by a specific neuron. 39th Conference on Neural Information Processing Systems (NeurIPS 2025).

operand 𝐼 plus =-1.29 𝜙 𝒙 = 𝑆⊆𝑁 𝐼 𝑆 + background interactions 𝐼 What,plus =1.09 𝐼 plus,is b =1.07 𝐼 2 =-2.08 𝐼 2,7 =2.27 𝐼 2,plus =1.77 𝐼 plus,7 =1.18 𝐼 What,is a =-0.72 𝐼 What,Answer,is b =-0.29 𝐼 2,7,is b =-0.50 𝐼 2,plus,7 =-0.70