  When trying to gain better visibility into a machine learning model in order
to understand and mitigate the associated risks, a potentially valuable source
of evidence is: which training examples most contribute to a given behavior?
Influence functions aim to answer a counterfactual: how would the model's
parameters (and hence its outputs) change if a given sequence were added to the
training set? While influence functions have produced insights for small
models, they are difficult to scale to large language models (LLMs) due to the
difficulty of computing an inverse-Hessian-vector product (IHVP). We use the
Eigenvalue-corrected Kronecker-Factored Approximate Curvature (EK-FAC)
approximation to scale influence functions up to LLMs with up to 52 billion
parameters. In our experiments, EK-FAC achieves similar accuracy to traditional
influence function estimators despite the IHVP computation being orders of
magnitude faster. We investigate two algorithmic techniques to reduce the cost
of computing gradients of candidate training sequences: TF-IDF filtering and
query batching. We use influence functions to investigate the generalization
patterns of LLMs, including the sparsity of the influence patterns, increasing
abstraction with scale, math and programming abilities, cross-lingual
generalization, and role-playing behavior. Despite many apparently
sophisticated forms of generalization, we identify a surprising limitation:
influences decay to near-zero when the order of key phrases is flipped.
Overall, influence functions give us a powerful new tool for studying the
generalization properties of LLMs.
