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Support region of μ-law logarithmic quantizers for Laplacian source applied in neural networks

机译:用于神经网络的Laplacian源的μ-Law对数量化器的支撑区域

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摘要

The main aim of the paper is to provide effective and accurate solutions for the calculation of the support region of the mu-law logarithmic companding quantizers. A new solution for the starting point of iterative methods will be proposed, that provides very accurate value of the support region (being the main parameter needed for the design of the quantizer) only after one iteration of the iterative method. Based on this new starting point, an accurate closed-form approximate expression for the calculation of the support region will be derived, as one of the main contributions of the paper. To significantly simplify implementation of the mu-law companding quantizer, piecewise linearization is performed. A new linearization method is presented, based on the optimization of the last segments. Derivation of an accurate closed-form formula for the support region of the linearized quantizer is done, as an important contribution. The obtained linearized mu-law companding quantizer is very simple to design (due to closed-form formulas) and to implement (due to linearization), providing at the same time very high performance (due to optimization of the last segments). Due to these and other advantages (robustness, adjustability to the statistical distribution of the input signal), the proposed quantizer can be used in many topical applications, such as in receivers of 5G wireless systems or in neural networks for quantization of weights and activations. The paper provides an application of the designed quantizers for quantization of weights of a neural network, showing significant decreasing of the bit-rate compared to the standard full-precision representation (from 32 bits to just 5 bits), with the same prediction accuracy of the network.
机译:本文的主要目的是为计算MU-LAME对数的支持区提供有效和准确的解决方案。将提出用于迭代方法的起点的新解决方案,仅在迭代方法的一次迭代之后,提供了支持区域的非常准确的支持区域值(作为量化器设计所需的主参数)。基于该新起点,将导出用于计算支撑区域的准确闭合近似表达式,作为纸张的主要贡献之一。为了显着简化MU-Law的实施方式,进行分段线性化。基于最后一个段的优化,提出了一种新的线性化方法。作为一个重要的贡献,完成了用于线性化量化器的支撑区域的精确闭合式公式的衍生。所获得的线性化的MU-LAME体积化器非常简单地设计(由于闭合形式的公式)并实现(由于线性化),同时提供非常高的性能(由于最后段的优化而产生)。由于这些和其他优点(鲁棒性,对输入信号的统计分布的统计分布),所提出的量化器可以在许多局部应用中使用,例如在5G无线系统的接收器或神经网络中用于量化权重和激活。本文提供了设计量化器的应用,用于量化神经网络的权重,显示与标准的全精度表示(从32位到仅5位)相比的比特率的显着降低,具有相同的预测精度网络。

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