This paper describes how new learning methods may make it possible for a large‐scale, hierarchical neural network to recognize most Japanese handwritten characters. This is a very large and complex task, as the Japanese character set consists of about 3000 categories which can be written in many different ways. Such a difficult task can lead a neural network to converge very slowly and to yield recognition rates that are uneven between categories. To address these problems we here propose five learning methods as modifications of the conventional back‐propagation learning rule. These methods produce fast convergence, even recognition rates over all categories, and adequate recognition of test samples. We also describe how a large‐scale neural network can be built by dividing the recognition task into several subtasks, with networks for each subtask, and then integrating these subnetworks in a large network with a hierarchical structure. In a hierarchical network, the upper level network directly integrates outputs from each lower level network. Application of that network to handwritten Japanese character recognition has resulted in poor recognition, because lower level networks do not know about unknown input patterns, and the direct integration of ambiguous outputs from many lower level networks confuses the upper level network. We propose a new integration method which provides each subnetwork with more information as to how close an input pattern is to the categories of that subnetwork. This method resulted in high recognition performance for character recognition. We here described the above methods, and report the performance of our implementation of a neural network for the recognition of 71 Hiragana characters, and describe our implementation of this network on a hypercube concurrent computer.

W e derive an operator solution for the fermion in the chiral Schwinger model with a Wess-Zumino term and study the quantum structure o f the model in a manifestly covariant operator formalism. The U(1), gauge symmetry restored by the inclusion o f the Wess-Zumino term gets spontaneously broken and the gauge field becomes massive. The left-handed fermion is found to be confined. The right-handed fermion, on the other hand, remains a massless free field in spite o f the fact that the left-and right-handed sectors o f the model are coupled through the anomaly. This massless fermion is interpreted as the Nambu-Goldstone mode associated with the spontaneous breakdown o f the global U(1), symmetry.

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We solve a generalization of the chiral Schwinger model with a Wess-Zumino term in a covariant operator formalism. The model is essentially specified by two parameters (o,a), where o measures the relative strength of the right-and left-handed gauge couplings (eR and e,) while a parametrizes the anomaly ambiguity. The fermion operator is constructed from the asymptotic boson fields in bosonized versions of the model. The model yields a sensible quantum theory in some restricted domain of o and a. The gauge symmetry restored by the inclusion of the Wess-Zumino term gets spontaneously broken and the gauge field becomes massive. The fermion is confined as long as eReL#O. The model has a dual structure such that the model specified by ( o , a ) is equivalent to the model specified by another set (of= -0, a ' = a +2 sin2u). This duality, in particular, reveals the equivalence of the Schwinger model and (a gauge-invariant version of) the axial Schwinger model.