  This study presents a neural network which uses filters based on logistic
mapping (LogNNet). LogNNet has a feedforward network structure, but possesses
the properties of reservoir neural networks. The input weight matrix, set by a
recurrent logistic mapping, forms the kernels that transform the input space to
the higher-dimensional feature space. The most effective recognition of a
handwritten digit from MNIST-10 occurs under chaotic behavior of the logistic
map. The correlation of classification accuracy with the value of the Lyapunov
exponent was obtained. An advantage of LogNNet implementation on IoT devices is
the significant savings in memory used. At the same time, LogNNet has a simple
algorithm and performance indicators comparable to those of the best
resource-efficient algorithms available at the moment. The presented network
architecture uses an array of weights with a total memory size from 1 to 29 kB
and achieves a classification accuracy of 80.3-96.3%. Memory is saved due to
the processor, which sequentially calculates the required weight coefficients
during the network operation using the analytical equation of the logistic
mapping. The proposed neural network can be used in implementations of
artificial intelligence based on constrained devices with limited memory, which
are integral blocks for creating ambient intelligence in modern IoT
environments. From a research perspective, LogNNet can contribute to the
understanding of the fundamental issues of the influence of chaos on the
behavior of reservoir-type neural networks.
