The vision of k2 is to be able to seamlessly integrate Finite State Automaton (FSA) and Finite State Transducer (FST) algorithms into autograd-based machine learning toolkits like PyTorch and TensorFlow. For speech recognition applications, this should make it easy to interpolate and combine various training objectives such as cross-entropy, CTC and MMI and to jointly optimize a speech recognition system with multiple decoding passes including lattice rescoring and confidence estimation. We hope k2 will have many other applications as well.