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%24 neurons%2C even when the input features are emph{themselves in superposition}. We generalize this construction to arbitrary sparse boolean circuits of low depth%2C and then construct ``error correction'' layers that allow deep fully-connected networks of width %24d%24 to emulate circuits of width %24tilde{O}(d^{1.5})%24 and emph{any} polynomial depth. We conclude by providing some potential applications of our work for interpreting neural networks that implement computation in superposition.?quality=80&w=800)
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