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We introduce a new automaton on a word p, sequence of letters taken in an alphabet , that we call factor oracle. This automaton is acyclic, recognizes at least the factors of p, has m + 1 states and a linear number of transitions. We give an on-line construction to build it. We use this new structure in string matching algorithms that we conjecture optimal according to the experimental results. These algorithms are as e cient as the ones that already exist using less memory and being more easy to implement.

This paper proposes and evaluates the hybrid autoregressive transducer (HAT) model, a time-synchronous encoderdecoder model that preserves the modularity of conventional automatic speech recognition systems. The HAT model provides a way to measure the quality of the internal language model that can be used to decide whether inference with an external language model is beneficial or not. This article also presents a finite context version of the HAT model that addresses the exposure bias problem and significantly simplifies the overall training and inference. We evaluate our proposed model on a large-scale voice search task. Our experiments show significant improvements in WER compared to the state-of-the-art approaches .Index Terms-ASR, Encoder-decoder, Beam Search T t=1 P ( Y t =ỹ t |X). Finally P (Y |X) is calculated by marginalizing over the alignment posteriors with Eq 2.

Recent text and speech processing applications such as speech mining raise new and more general problems related to the construction of language models. We present and describe in detail several new and efficient algorithms to address these more general problems and report experimental results demonstrating their usefulness. We give an algorithm for computing efficiently the expected counts of any sequence in a word lattice output by a speech recognizer or any arbitrary weighted automaton; describe a new technique for creating exact representations of ¢-gram language models by weighted automata whose size is practical for offline use even for a vocabulary size of about 500,000 words and an ¢-gram order ¢ ¤ £ ¦ ¥ ; and present a simple and more general technique for constructing class-based language models that allows each class to represent an arbitrary weighted automaton. An efficient implementation of our algorithms and techniques has been incorporated in a general software library for language modeling, the GRM Library, that includes many other text and grammar processing functionalities.

We propose algorithms to train productionquality 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.

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