A live algorithm describes an ideal autonomous performance system able to engage in performance with abilities analogous, if not identical, to a human musician. This paper proposes five attributes of a live algorithm: adaptability, empowerment, intimacy, opacity and unimagined music. These attributes are explored in NN Music, a performer-machine system for Max/MSP that fosters listening and learning. Live improvisation is encoded statistically to train a feed-forward neural network, mapped to stochastic processes for musical output. Through adaptation, mappings are learnt and covertly assigned, to be revisited by both player and machine as a performance develops.