Unlike many other investigations on this topic, the present one considers the non-linear single-layer perceptron (SLP) as a process in which the weights of the perceptron are increasing, and the cost function of the sum of squares is changing gradually. During the backpropagation training, the decision boundary of of SLP becomes identical or close to that of seven statistical classifiers: (1) t...

We give a construction of quantum LDPC codes dimension $\Theta(\log N)$ and distance $\Theta(N/\log as the code length $N\to\infty$. Using product chain complexes this also provides family $\Omega(N^{1-\alpha/2}/\log $\Omega(N^\alpha \log N)$, where $0 \le \alpha < 1$. introduce study new operation called lifted product, which naturally generalizes operations for complexes. Moreover, simple byp...