Package: k2
k2The 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.One of the key algorithms that we have implemented is
pruned composition of a generic FSA with a "dense" FSA (i.e. one that
corresponds to log-probs of symbols at the output of a neural network).  This
can be used as a fast implementation of decoding for ASR, and for CTC and
LF-MMI training.  This won't give a direct advantage in terms of Word Error Rate when
compared with existing technology; but the point is to do this in a much more
general and extensible framework to allow further development of ASR technology.ImplementationA few key points on our implementation strategy.Most of the code is in C++ and CUDA.  We implement a templated classRagged,
which is quite like TensorFlow'sRaggedTensor(actually we came up with the
design independently, and were later told that TensorFlow was using the same
ideas).  Despite a close similarity at the level of data structures, the
design is quite different from TensorFlow and PyTorch.  Most of the time we
don't use composition of simple operations, but rely on C++11 lambdas defined
directly in the C++ implementations of algorithms.  The code in these lambdas operate
directly on data pointers and, if the backend is CUDA, they can run in parallel
for each element of a tensor.  (The C++ and CUDA code is mixed together and the
CUDA kernels get instantiated via templates).It is difficult to adequately describe what we are doing with theseRaggedobjects without going in detail through the code.  The algorithms look very
different from the way you would code them on CPU because of the need to avoid
sequential processing.  We are using coding patterns that make the most
expensive parts of the computations "embarrassingly parallelizable"; the only
somewhat nontrivial CUDA operations are generally reduction-type operations
such as exclusive-prefix-sum, for which we use NVidia'scublibrary.  Our
design is not too specific to the NVidia hardware and the bulk of the code we
write is fairly normal-looking C++; the nontrivial CUDA programming is mostly
done via the cub library, parts of which we wrap with our own convenient
interface.The Finite State Automaton object is then implemented as a Ragged tensor templated
on a specific data type (a struct representing an arc in the automaton).AutogradIf you look at the code as it exists now, you won't find any references to
autograd.  The design is quite different to TensorFlow and PyTorch (which is
why we didn't simply extend one of those toolkits).  Instead of making autograd
come from the bottom up (by making individual operations differentiable) we are
implementing it from the top down, which is much more efficient in this case
(and will tend to have better roundoff properties).An example: suppose we are finding the best path of an FSA, and we need
derivatives.  We implement this by keeping track of, for each arc in the output
best-path, which input arc it corresponds to.  (For more complex algorithms an arc
in the output might correspond to a sum of probabilities of a list of input arcs).
We can make this compatible with PyTorch/TensorFlow autograd at the Python level,
by, for example, defining a Function class in PyTorch that remembers this relationship
between the arcs and does the appropriate (sparse) operations to propagate back the
derivatives w.r.t. the weights.Current state of the codeWe have wrapped all the C++ code to Python withpybind11and have finished the integration withPyTorch.We are currently writing speech recognition recipes using k2, which are hosted in a
separate repository. Please seehttps://github.com/k2-fsa/icefall.Plans after initial releaseWe are currently trying to make k2 ready for production use (see the branchv2.0-pre).Quick startWant to try it out without installing anything? We have setup aGoogle Colab.
You can find more Colab notebooks using k2 in speech recognition athttps://icefall.readthedocs.io/en/latest/recipes/librispeech/conformer_ctc.html.