Error postback correction method

The correction method with the error signal return transmission is a stochastic method of perceptron training, which is necessary in order to guarantee convergence in variable relationships for more than one layer. The method was proposed by Rosenblatt for a perceptron with variable SA bonds and can be used for binary multilayer perceptrons . It is an alternative to the method of back propagation of error , but in contrast to it guarantees the process of convergence (achievement of a solution).

Algorithm

An error is set for each R-element. $E_{r}=R^{*}-r^{*}$ ${\ displaystyle E_ {r} = R ^ {*} - r ^ {*}}$ where $R^{*}$ ${\ displaystyle R ^ {*}}$ - required, and $r^{*}$ ${\ displaystyle r ^ {*}}$ - achieved reaction.
For each A-element $a$ $i$ {\ displaystyle a_ {i}} The error is calculated as follows:
- initially $E_{i}=0$ ${\ displaystyle E_ {i} = 0}$ ;
- If the item $a_{i}$ ${\ displaystyle a_ {i}}$ active and communication $c_{ir}$ ${\ displaystyle c_ {ir}}$ ( ${\textstyle c_{ir}=a_{i}\cdot w_{ir}}$ ${\ textstyle c_ {ir} = a_ {i} \ cdot w_ {ir}}$ or in general case ${\textstyle c_{ir}=f(w_{ir},a_{i})}$ ${\ textstyle c_ {ir} = f (w_ {ir}, a_ {i})}$ ) ends on an R-element with a nonzero error $E_{r}$ ${\ displaystyle E_ {r}}$ different in sign from bond weight $w_{ir}$ ${\ displaystyle w_ {ir}}$ then with probability $p_{1}$ ${\ displaystyle p_ {1}}$ to $E_{i}$ ${\ displaystyle E_ {i}}$ a correction equal to -1 should be added;
- If the item $a_{i}$ ${\ displaystyle a_ {i}}$ inactive and communication $c_{ir}$ ${\ displaystyle c_ {ir}}$ ends on an R-element with a non-zero error $E_{r}$ ${\ displaystyle E_ {r}}$ , does not differ (coincides) in sign from the weight of the bond $w_{ir}$ ${\ displaystyle w_ {ir}}$ then with probability $p_{2}$ ${\ displaystyle p_ {2}}$ to $E_{i}$ ${\ displaystyle E_ {i}}$ a correction equal to +1 should be added;
- If the item $a_{i}$ ${\ displaystyle a_ {i}}$ inactive and communication $c_{ir}$ ${\ displaystyle c_ {ir}}$ ends on an R-element with a non-zero error $E_{r}$ ${\ displaystyle E_ {r}}$ different in sign from bond weight $w_{ir}$ ${\ displaystyle w_ {ir}}$ (or $w_{ir}=0$ ${\ displaystyle w_ {ir} = 0}$ ), then with probability $p_{3}$ ${\ displaystyle p_ {3}}$ to $E_{i}$ ${\ displaystyle E_ {i}}$ a correction equal to +1 should be added;
- Under all other conditions $E_{i}$ ${\ displaystyle E_ {i}}$ does not change.
If a $E_{i}\not =0$ ${\ displaystyle E_ {i} \ not = 0}$ , then to all active connections ending in an A or R element, we add a correction $\eta$ ${\ displaystyle \ eta}$ with a sign matching the sign $E_{i}$ ${\ displaystyle E_ {i}}$ , i.e. $\Delta w_{ij}=a_{i}^{*}sign(E_{i})\varepsilon$ ${\ displaystyle \ Delta w_ {ij} = a_ {i} ^ {*} sign (E_ {i}) \ varepsilon}$ where $\varepsilon$ ${\ displaystyle \ varepsilon}$ - absolute value $\eta$ ${\ displaystyle \ eta}$ (usually a unit).

In most cases, the best characteristics can be obtained if the probabilities are chosen according to the following condition $p_{1}>p_{2}>p_{3}$ ${\ displaystyle p_ {1}> p_ {2}> p_ {3}}$ .

Literature

Rosenblatt, F. Principles of Neurodynamics: Perceptrons and Theory of Brain Mechanisms = Principles of Neurodynamic: Perceptrons and the Theory of Brain Mechanisms. - M .: Mir, 1965 .-- 480 p.

Lakhmi C. Jain; NM Martin Fusion of Neural Networks, Fuzzy Systems and Genetic Algorithms: Industrial Applications. - CRC Press, CRC Press LLC, 1998

Error postback correction method

Algorithm

Literature

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