This paper notices that while symbolic instruction and neural parameters play different roles on steering LLMs’ behavior, both instructions and parameters are the compression of task data, they are supposed be strongly correlated and can be learned to predict one from the other. Therefore, This paper proposes a novel neural network framework, SHIP (Shuttle between the Instructions and the Parameters), to model and learn the bi-directional mappings between the instructions and the parameters of LLMs. We verify that SHIP can effectively map one of the instructions/parameters to the other by evaluating it on the tasks of instruction deduction and induction. The results show that SHIP performs better than existing baseline methods in terms of deductive capabilities while significantly surpassing them in inductive capabilities. Moreover, SHIP can effectively combine the two mapping processes to perform excellent inductive reasoning. We further discuss how the latent fusing methods and latent dimensions affect SHIP’s performance, and show SHIP can effectively generalize with pre-training. The code and data for this paper are released at https://anonymous.4open.science/r/Shuttle-Between-Instructions-Parameters