  Fine-tuning on generalized tasks such as instruction following, code
generation, and mathematics has been shown to enhance language models'
performance on a range of tasks. Nevertheless, explanations of how such
fine-tuning influences the internal computations in these models remain
elusive. We study how fine-tuning affects the internal mechanisms implemented
in language models. As a case study, we explore the property of entity
tracking, a crucial facet of language comprehension, where models fine-tuned on
mathematics have substantial performance gains. We identify the mechanism that
enables entity tracking and show that (i) in both the original model and its
fine-tuned versions primarily the same circuit implements entity tracking. In
fact, the entity tracking circuit of the original model on the fine-tuned
versions performs better than the full original model. (ii) The circuits of all
the models implement roughly the same functionality: Entity tracking is
performed by tracking the position of the correct entity in both the original
model and its fine-tuned versions. (iii) Performance boost in the fine-tuned
models is primarily attributed to its improved ability to handle the augmented
positional information. To uncover these findings, we employ: Patch Patching,
DCM, which automatically detects model components responsible for specific
semantics, and CMAP, a new approach for patching activations across models to
reveal improved mechanisms. Our findings suggest that fine-tuning enhances,
rather than fundamentally alters, the mechanistic operation of the model.
