  A key goal of current mechanistic interpretability research in NLP is to find
linear features (also called "feature vectors") for transformers: directions in
activation space corresponding to concepts that are used by a given model in
its computation. Present state-of-the-art methods for finding linear features
require large amounts of labelled data -- both laborious to acquire and
computationally expensive to utilize. In this work, we introduce a novel
method, called "observable propagation" (in short: ObProp), for finding linear
features used by transformer language models in computing a given task -- using
almost no data. Our paradigm centers on the concept of "observables", linear
functionals corresponding to given tasks. We then introduce a mathematical
theory for the analysis of feature vectors, including a similarity metric
between feature vectors called the coupling coefficient which estimates the
degree to which one feature's output correlates with another's. We use ObProp
to perform extensive qualitative investigations into several tasks, including
gendered occupational bias, political party prediction, and programming
language detection. Our results suggest that ObProp surpasses traditional
approaches for finding feature vectors in the low-data regime, and that ObProp
can be used to better understand the mechanisms responsible for bias in large
language models.
