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Machine learning algorithms have been shown to be highly effective in solving optimization problems in a wide range of applications. Such algorithms typically use gradient descent with backpropagation and the chain rule. Hence, the backpropagation fails if intermediate gradients are zero for some functions in the computational graph, because it causes the gradients to collapse when multiplying with zero. Vector quantization is one of those challenging functions for machine learning algorithms, since it is a piece-wise constant function and its gradient is zero almost everywhere. A typical solution is to apply the straight through estimator which simply copies the gradients over the vector quantization function in the backpropagation. Other solutions are based on smooth or stochastic approximation. This study proposes a vector quantization technique called NSVQ, which approximates the vector quantization behavior by substituting a multiplicative noise so that it can be used for machine learning problems. Specifically, the vector quantization error is replaced by product of the original error and a normalized noise vector, the samples of which are drawn from a zero-mean, unit-variance normal distribution. We test our proposed NSVQ in three scenarios with various types of applications. Based on the experiments, the proposed NSVQ achieves more accuracy and faster convergence in comparison to the straight through estimator, exponential moving averages, and the MiniBatchKmeans approaches.

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Spectral envelope modeling is an instrumental part of speech and audio codecs, which can be used to enable efficient entropy coding of spectral components. Overall optimization of codecs, including envelope models, has however been difficult due to the complicated interactions between different modules of the codec. In this paper, we study an end-to-end optimization methodology to optimize all modules in a codec integrally with respect to each other while capturing all these complex interactions with a global loss function. For the quantization of the spectral envelope parameters with a fixed bitrate, we use multistage vector quantization which gives high quality, but yet has a computational complexity which can be realistically applied in embedded devices. The obtained results demonstrate benefits in terms of PESQ and PSNR in comparison to the 3GPP EVS, as well as our recently proposed PyAWNeS codecs.

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