The goal of circuit discovery is to decompose a monolithic neural network into tiny modular subnetworks which are interpretable in the sense that each does an identifiable subtask.
We develop a practical method for composing arbitrarily many circuits into a single model.
We propose a greedy, density-scaled composition algorithm that overcomes limitations of previous attempts to compose circuits by naive union, then generalize it to $N$ circuits via CircuitTree, a new data structure built on a $Θ(N\log N)$ tree-compose schedule.
We compose circuits pruned from HuBERT for classifying individual phonemes into a syllable classifier, a capability none of the 39 phoneme circuits has individually.
Chaining CircuitTrees into a hierarchy-of-circuits pipeline, we transcribe open syllables at 64.8\% accuracy, within 1.2 points of a 66.0\% ceiling that shares no circuitry at all, with 99.5\% of circuit components shared.