feed-forward neural networks
graph of states and failures
Incremental growth of chips integration level as well as errors through the chips development process increases the probability for rising of logical failures, when the correct logical function transforms to the any different logical function. Therefore, the development of the method for a technical diagnosis, consisting in definition of technical state for feed-forward neural networks through the testing, is very relevant task. Existing methods of suspected failures segregation are separated at two classes. The first class encapsulates the usage of constant failures model. The second class uses the logical failures model, which is more adequate to the transformation of the logical function. However, methods for the last class are very complex, because they use more common model of failures or the explicit diagnostic model or the states graph of a neural network.
Feed-forward neural networks (NN) have input-output poles, neurons and connections between them. As a model of NN, the correct logical net is used. The correct logical net is ranked (from 0 to n), neurons and poles are numbered. For showing the functioning rules and technical states of NN, the modified graph of states and failures (MGSF) of neurons is used. MGSF consist in nodes (describe input and output of neurons) and connections (describe technical states of neurons). The state of neuron contains four parameters: the neuron number, the input, the output and the sign of a failure (or a no-failure), for example, , where q – is neuron number, v – decimal number of input set, 0 – output value, the un-derline means a no-failure (an absence of the underline is a failure) . The MGSF is an explicit model of NN and directs the behavior of every neuron in NN under failures. Every set of states (with failures and no-failures) is displayed with a single path at the MGSF. The MGSF is visual and useful, but cumbersome at the same time. Therefore, the practical task is to build the expressions of suspected failures using the structure of the correct logical net. Let и are logical expressions for conditions to form k-th input set of correct poles or neurons for i-th rank and l-th output set of correct poles or neurons for i-th rank. Shortly, the algorithm is performed as follows:
Let i = 0, the expression corresponds the input set of NN with number ;
Using the functions of correct neurons and , it is necessary to build ;
For all neurons of NN, build every possible expression in the form of disjunction of terms. Every indication of expressions takes part in the term, and every term has the and the conjunction of signs of a failure and a no-failure of neurons at (i+1)-th rank.
The example of result for this algorithm: . The same results we obtain when build the single path at MGSF. The method of the suspected failures segregation is to build the expressions like , then concatenate them, exclude the terms when the repetition factor of failures is more then possible and the terms with no-logicality of suspected failures (no-logicality means different output value for the same input of neuron at the term, for example, ).