influence functions

Influence functions are an analytical technique that works backward from a model's output to score how much each of the countless documents it read during training contributed to that particular answer.

Think of it like tracing back which class or which reference book actually helped a student who did well on an exam solve a particular problem. Just as this kind of tracing requires knowing exactly what the student studied, this technique only works if you know exactly which documents the model was trained on. The problem is that most AI models only release their finished outputs and never disclose the list of materials used in training. So there are very few models this technique can actually be applied to.

Conversely, if a model discloses its full training data and intermediate process, this technique can really show its power. By calculating the influence of each individual document and then aggregating them by category—literature, technical documents, conversational text, and so on—you can draw something like a map showing which type of writing produced which capability in the model.

In articles, it appears as a tool for calculating the relationship between a model's answers and its training documents, as in phrases like "the method the research team used is a technique called influence functions." It's easy to misunderstand this as directly inspecting the model's internal weights or architecture, but it's actually a method for statistically estimating how the answer would have changed if a specific document had been excluded from training.