To show Qnet's ability to map one set of numbers to another set, a problem is presented where a 1000 random numbers will be used to predict 2 random numbers at the target nodes. Obviously, one set of truly random numbers cannot be used to predict another set of random numbers. A neural network, however, can memorize the training set and map the random inputs to the random outputs for all cases presented to it (assuming the network size is large enough to memorize the total number of cases). To monitor network learning in this example we will use a test set. If the model behaves as expected, the network will memorize the training set cases, but show no ability to learn the test set. This example is designed to show the importance of test sets, especially when relationships between the inputs and output targets are not well defined or understood.

This example uses a set of 8 training patterns and 4 test patterns. Each pattern contains 1000 random values for inputs and 2 random values for output (all inputs and targets normalized between 0. and 1.). The network is fully connected with three layers containing 1000 input nodes, 3 hidden nodes and 2 output nodes. The training data is contained in the file Random.dat. Two network input files, RandomMapping.net and RandomMappingTrained.net, are available for examination.

The trained network easily mapped the input random numbers to the output random numbers. The network memorized the training set for the 8 training cases presented to it. This memorization, however, produces no constructive learning. The relationships developed during training are valid only for the training set. No predictive capabilities are ever seen in the test set. The figure below shows that while training points were nearly perfect, the test points appear randomly scattered. Memorization learning is fine for models where table look-up type functionality is desired. Problems that require some type of predictive capability do not benefit from training set memorization. Incorporating a test set is the best way to monitor training memorization.