Abstract: The single shortest path algorithm is undefined for weighted finite-state automata over non-idempotent semirings because such semirings do not guarantee the existence of a shortest path. However, in non-idempotent semirings admitting an order satisfying a monotonicity condition (such as the plus-times or log semirings), the shortest string is well-defined. We describe an algorithm which finds the shortest string for a weighted non-deterministic automaton over such semirings using the backwards shortest distance of an equivalent deterministic automaton (DFA) as a heuristic for A* search performed over a companion idempotent semiring, which is proven to return the shortest string. There may be exponentially more states in the DFA, but the proposed algorithm needs to visit only a small fraction of them if determinization is performed “on the fly”.

In finite-state language processing pipelines, a lexicon is often a key component. It needs to be comprehensive to ensure accuracy, reducing out-of-vocabulary misses. However, in memory-constrained environments (e.g., mobile phones), the size of the component automata must be kept small. Indeed, a delicate balance between comprehensiveness, speed, and memory must be struck to conform to device requirements while providing a good user experience.In this paper, we describe a compression scheme for lexicons when represented as finite-state transducers. We efficiently encode the graph of the transducer while storing transition labels separately. The graph encoding scheme is based on the LOUDS (Level Order Unary Degree Sequence) tree representation, which has constant time tree traversal for queries while being information-theoretically optimal in space. We find that our encoding is near the theoretical lower bound for such graphs and substantially outperforms more traditional representations in space while remaining competitive in latency benchmarks.

We propose algorithms to train production-quality n-gram language models using federated learning. Federated learning is a distributed computation platform that can be used to train global models for portable devices such as smart phones. Federated learning is especially relevant for applications handling privacy-sensitive data, such as virtual keyboards, because training is performed without the users’ data ever leaving their devices. While the principles of federated learning are fairly generic, its methodology assumes that the underlying models are neural networks. However, virtual keyboards are typically powered by n-gram language models for latency reasons. We propose to train a recurrent neural network language model using the decentralized FederatedAveraging algorithm and to approximate this federated model server-side with an n-gram model that can be deployed to devices for fast inference. Our technical contributions include ways of handling large vocabularies, algorithms to correct capitalization errors in user data, and efficient finite state transducer algorithms to convert word language models to word-piece language models and vice versa. The n-gram language models trained with federated learning are compared to n-grams trained with traditional server-based algorithms using A/B tests on tens of millions of users of a virtual keyboard. Results are presented for two languages, American English and Brazilian Portuguese. This work demonstrates that high-quality n-gram language models can be trained directly on client mobile devices without sensitive training data ever leaving the devices.