Mechanistic interpretability strives to explain model behavior in terms of bottom-up primitives. The leading paradigm is to express hidden states as a sparse linear combination of basis vectors, called features. However, this only identifies which text sequences (exemplars) activate which features; the actual interpretation of features requires subjective inspection of these exemplars. This paper advocates for a different solution: rule-based descriptions that match token patterns in the input and correspondingly increase or decrease the likelihood of specific output tokens. Specifically, we extract rule-based descriptions of SAE features trained on the outputs of attention layers. While prior work treats the attention layers as an opaque box, we describe how it may naturally be expressed in terms of interactions between input and output features, of which we study three types: (1) skip-gram rules of the form "[Canadian city]... speaks --> English", (2) absence rules of the form "[Montreal]... speaks -/-> English," and (3) counting rules that toggle only when the count of a word exceeds a certain value or the count of another word. Absence and counting rules are not readily discovered by inspection of exemplars, where manual and automatic descriptions often identify misleading or incomplete explanations. We then describe a simple approach to extract these types of rules automatically from a transformer, and apply it to GPT-2 small. We find that a majority of features may be described well with around 100 skip-gram rules, though absence rules are abundant even as early as the first layer (in over a fourth of features). We also isolate a few examples of counting rules. This paper lays the groundwork for future research into rule-based descriptions of features by defining them, showing how they may be extracted, and providing a preliminary taxonomy of some of the behaviors they represent.