1. A neural network device with a learning function, comprising: a network formed of a plurality of neurons interconnected by a plurality of synapses, each synapse having a synapse weight factor, said network having a plurality of output signals; comparison means for calculating an evaluation value according to a difference between each output signal of the network and a corresponding teacher signal; and inspection means for determining a manner of updating the synapse weight factor of said each synapse according to an evaluation value change between a present value and a previous value of the evaluation value calculated by the comparison means; wherein said each synapse includes: random number generation means for generating a randomly changing update control signal according to a random number; and synapse weight factor update means for updating a synapse weight factor of said each synapse as a learning with an update value specified by the update control signal generated by the random number generation means in the manner of updating determined by the inspection means.