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What can memorization learning do?

Memorization learning (ML) is a method for supervised learning which reduces the training errors only. However, it does not guarantee good generalization capability in principle. This observation leads to two problems: 1) to clarify the reason why good generalization capability is obtainable by ML; and 2) to clarify to what extent memorization learning can be used. Ogawa (1995) introduced the concept of 'admissibility' and provided a clear answer to the first problem. In this paper, we solve the second problem when training examples are noiseless. It is theoretically shown that ML can provide the same generalization capability as any learning method in 'the family of projection learning' when proper training examples are chosen.