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Sequence-discriminative training of deep neural networks (DNNs) is investigated on a 300 hour American English conversational telephone speech task. Different sequencediscriminative criteria -maximum mutual information (MMI), minimum phone error (MPE), state-level minimum Bayes risk (sMBR), and boosted MMI -are compared. Two different heuristics are investigated to improve the performance of the DNNs trained using sequence-based criteria -lattices are regenerated after the first iteration of training; and, for MMI and BMMI, the frames where the numerator and denominator hypotheses are disjoint are removed from the gradient computation. Starting from a competitive DNN baseline trained using cross-entropy, different sequence-discriminative criteria are shown to lower word error rates by 8-9% relative, on average. Little difference is noticed between the different sequencebased criteria that are investigated. The experiments are done using the open-source Kaldi toolkit, which makes it possible for the wider community to reproduce these results.

We describe a lattice generation method that is exact, i.e. it satisfies all the natural properties we would want from a lattice of alternative transcriptions of an utterance. This method does not introduce substantial overhead above one-best decoding. Our method is most directly applicable when using WFST decoders where the WFST is "fully expanded", i.e. where the arcs correspond to HMM transitions. It outputs lattices that include HMM-state-level alignments as well as word labels. The general idea is to create a state-level lattice during decoding, and to do a special form of determinization that retains only the best-scoring path for each word sequence. This special determinization algorithm is a solution to the following problem: Given a WFST A, compute a WFST B that, for each input-symbolsequence of A, contains just the lowest-cost path through A.

We demonstrate the chaotic behavior of timelike, null, and spacelike geodesics in nonhomogeneous vacuum pp-wave solutions by analytic and fractal methods. This seems to be the first known example of a chaotic motion in exact radiative spacetime.