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Implementation of signal processing operations by transforms with random coefficients for neuronal systems modelling

机译：通过对神经元系统建模的随机系数变换实现信号处理操作

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This work investigates signal processing networks in which randomness is an inherent feature like in biological neuronal networks. Signal processing operations are usually performed with algorithms requiring high-precision and order. It is thus interesting to investigate how signal processing operations could be realized in systems with inherent randomness which is apparent in neuronal networks. We are studying possible implementation of convolution and correlation operations based on generalized transform approach with rectangular matrices generated by random sequences. Conditions are formulated and illustrated how correlation and convolution operators can be computed with such matrices. We show next that increasing the size of matrices allows to decrease the precision of operations and to introduce substantial quantization and thresholding. The use of random matrices provides also for strong robustness to noise resulting from unreliable operation. We show also that the nonlinearity due to the quantization and thresholding leads naturally to the decorrelation of transformation vectors which might be useful for associative storage.
机译：这项工作研究了信号处理网络，其中像生物神经元网络一样，随机性是其固有特征。信号处理操作通常使用需要高精度和高阶的算法来执行。因此，有趣的是研究如何在具有固有随机性的系统中实现信号处理操作，这在神经元网络中是显而易见的。我们正在研究基于广义变换方法的卷积和相关运算的可能实现，该方法具有由随机序列生成的矩形矩阵。公式化了条件，并说明了如何使用此类矩阵计算相关和卷积运算符。接下来，我们表明增加矩阵的大小会降低运算的精度，并引入大量的量化和阈值处理。随机矩阵的使用还提供了对由于不可靠操作导致的噪声的强大鲁棒性。我们还表明，归因于量化和阈值的非线性自然导致转换向量的去相关，这可能对关联存储有用。

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