@misc{Krawczak_Maciej_Automatyka,_2002, author={Krawczak, Maciej}, copyright={Creative Commons Attribution BY 4.0 license}, address={Warszawa}, journal={Książka = Book}, howpublished={online}, year={2002}, publisher={Instytut Badań Systemowych. Polska Akademia Nauk}, publisher={Systems Research Institute. Polish Academy of Sciences}, language={eng}, abstract={In the artificial neural networks literature Little attention has been given to consideration of neural networks from the point of view of graph theory. Examination of neural networks as flow graphs gives very interesting and new properties of the neural networks' learning process. The approach is based on tools used in electric circuits when Kirchhoff s laws may not be valid. The analysis leads to the proper equations of the backpropagation algorithm, but in a much simpler manner. The graph methodology incorporates the reciprocal graphs in which signals flow in opposite directions. Neural networks in which signals flow in opposite direction are called the adjoint neural networks.}, type={Text}, title={Automatyka, sterowanie, zarządzanie : książka jubileuszowa z okazji 70-lecia urodzin profesora Kazimierza Mańczaka * Odwrotne wielowarstwowe sieci neuronowe}, URL={http://www.rcin.org.pl/Content/206693/PDF/KS-2002-01-P10.pdf}, }