A Quantum Search Decoder for Natural Language Processing

TL;DR

This paper introduces a quantum algorithm for decoding language models that finds globally optimal predictions more efficiently than classical methods, especially for power-law distributed inputs, and demonstrates practical speedups in speech recognition.

Contribution

It develops a quantum decoding algorithm that surpasses classical beam search in speed and accuracy, particularly for power-law distributed language data.

Findings

Quantum decoder achieves more than quadratic speedup over classical methods.

Modified quantum algorithm performs well with finite beam width, maintaining high accuracy.

Application to speech recognition shows the model's power-law distribution enables practical quantum speedups.

Abstract

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.