The noisy broadcast model was first studied in [Gallager, TranInf'88] where an @math -character input is distributed among @math processors, so that each processor receives one input bit. Computation proceeds in rounds, where in each round each processor broadcasts a single character, and each reception is corrupted independently at random with some probability @math . [Gallager, TranInf'88] gave an algorithm for all processors to learn the input in @math rounds with high probability. Later, a matching lower bound of @math was given in [Goyal, Kindler, Saks; SICOMP'08]. We study a relaxed version of this model where each reception is erased and replaced with a ?' independently with probability @math . In this relaxed model, we break past the lower bound of [Goyal, Kindler, Saks; SICOMP'08] and obtain an @math -round algorithm for all processors to learn the input with high probability. We also show an @math -round algorithm for the same problem when the alphabet size is @math .
Recently, a work by Efremenko, Kol, and Saxena @cite_16 showed that under a model where the processors can adaptively choose which processor will speak in each round, the lower bound of @cite_3 breaks down.
@cite_16 @cite_3
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Suppose that n processors are arranged in a ring and can communicate only with their immediate neighbors. It is shown that any probabilistic algorithm for 3 coloring the ring must take at least @math rounds, otherwise the probability that all processors are colored legally is less than @math . A similar time bound holds for selecting a maximal independent set. The bound is tight (up to a constant factor) in light of the deterministic algorithms of Cole and Vishkin [Inform, and Control, 70 (1986), pp. 32–53] and extends the lower bound for deterministic algorithms of Linial [Proc. 28th IEEE Foundations of Computer Science Symposium, 1987, pp. 331–335]. A new type of End-to-End system for text-dependent speaker verification is presented in this paper. Previously, using the phonetically discriminative speaker discriminative DNNs as feature extractors for speaker verification has shown promising results. The extracted frame-level (DNN bottleneck, posterior or d-vector) features are equally weighted and aggregated to compute an utterance-level speaker representation (d-vector or i-vector). In this work we use speaker discriminative CNNs to extract the noise-robust frame-level features. These features are smartly combined to form an utterance-level speaker vector through an attention mechanism. The proposed attention model takes the speaker discriminative information and the phonetic information to learn the weights. The whole system, including the CNN and attention model, is joint optimized using an end-to-end criterion. The training algorithm imitates exactly the evaluation process --- directly mapping a test utterance and a few target speaker utterances into a single verification score. The algorithm can automatically select the most similar impostor for each target speaker to train the network. We demonstrated the effectiveness of the proposed end-to-end system on Windows @math "Hey Cortana" speaker verification task. Attention-based encoder-decoder architectures such as Listen, Attend, and Spell (LAS), subsume the acoustic, pronunciation and language model components of a traditional automatic speech recognition (ASR) system into a single neural network. In previous work, we have shown that such architectures are comparable to state-of-theart ASR systems on dictation tasks, but it was not clear if such architectures would be practical for more challenging tasks such as voice search. In this work, we explore a variety of structural and optimization improvements to our LAS model which significantly improve performance. On the structural side, we show that word piece models can be used instead of graphemes. We also introduce a multi-head attention architecture, which offers improvements over the commonly-used single-head attention. On the optimization side, we explore synchronous training, scheduled sampling, label smoothing, and minimum word error rate optimization, which are all shown to improve accuracy. We present results with a unidirectional LSTM encoder for streaming recognition. On a 12, 500 hour voice search task, we find that the proposed changes improve the WER from 9.2 to 5.6 , while the best conventional system achieves 6.7 ; on a dictation task our model achieves a WER of 4.1 compared to 5 for the conventional system. Attentional, RNN-based encoder-decoder models for abstractive summarization have achieved good performance on short input and output sequences. For longer documents and summaries however these models often include repetitive and incoherent phrases. We introduce a neural network model with a novel intra-attention that attends over the input and continuously generated output separately, and a new training method that combines standard supervised word prediction and reinforcement learning (RL). Models trained only with supervised learning often exhibit "exposure bias" - they assume ground truth is provided at each step during training. However, when standard word prediction is combined with the global sequence prediction training of RL the resulting summaries become more readable. We evaluate this model on the CNN Daily Mail and New York Times datasets. Our model obtains a 41.16 ROUGE-1 score on the CNN Daily Mail dataset, an improvement over previous state-of-the-art models. Human evaluation also shows that our model produces higher quality summaries.