Probabilistic language models, e.g. those based on an LSTM, often face the problem of finding a high probability prediction from a sequence of random variables over a set of tokens. This is commonly addressed using a form of greedy decoding such as beam search, where a limited number of highest-likelihood paths (the beam width) of the decoder are kept, and at the end the maximum-likelihood path is chosen. In this work, we construct a quantum algorithm to find the globally optimal parse (i.e. for infinite beam width) with high constant success probability. When the input to the decoder is distributed as a power-law with exponent $k>0$, our algorithm has runtime $R^{n f(R,k)}$, where $R$ is the alphabet size, $n$ the input length; here $f<1/2$, and $f\rightarrow 0$ exponentially fast with increasing $k$, hence making our algorithm always more than quadratically faster than its classical counterpart. We further modify our procedure to recover a finite beam width variant, which enables an even stronger empirical speedup while still retaining higher accuracy than possible classically. Finally, we apply this quantum beam search decoder to Mozilla's implementation of Baidu's DeepSpeech neural net, which we show to exhibit such a power law word rank frequency.
Adaptive decoding of quantum LDPC codes through decoder disagreement
Centre for Computational Science, University College London（计算科学中心，伦敦大学学院）；Advanced Research Computing Centre, University College London（高级研究计算中心，伦敦大学学院）
Calibration-Conditioned FiLM Decoders for Low-Latency Decoding of Quantum Error Correction Evaluated on IBM Repetition-Code Experiments
Pacific Northwest National Laboratory（太平洋西北国家实验室）；Fordham University（福特汉姆大学）；Lehigh University（勒海大学）；University of Washington（华盛顿大学）；University of California San Diego（加州大学圣地亚哥分校）
