Neural computing studies on the essence and capacity of information processing with nonprogramming, adaptive and brain paradigm. Different areas in the brain perform different functionally significant tasks. Information geometry emerged from studies of the intrinsic structure of the manifold of probability distributions and is applicable to a wide variety of information systems. Information geometry provides a new tool for neural computing.

In 1985 Amari has presented information geometry for neural information processing[1]. Based on information geometry we have proposed neural field theory[8 ]. The research object of neural field theory is referred to try to understand the transformation mechanism, dynamical behaviour, capability and limitation of neural networks models, by the study of globally topological and geometrical structure on parameter spaces of neural networks models . The body of work is primarily devoted to investigate the global structure properties in the non-linear manifold by the set of all neural networks, the information processing mechanism about organizing and embedding submanifold by simple models into the manifold by general richer information systems. The research is also viewed to explore deeper theoretical foundation and new approach to develop the key concept and framework of neural information processing, and to pursue new breakthrough in the research of computation model for understanding of human-like recognition mechanism.

The basic ideas of information geometry for neural information processing can be described as follows: consider a neural networks set including modifiable parameters, such as weights and threshold, summarized in a vector form q = (q1, q2, ….qn ) , then the set of all the possible neural networks realized by changing q forms a n-dimension manifold N or submanifole embedding into more complex information processing manifold S, i.e. in many case, the set of a family of neural networks model can be represented by a finite dimension submanifold N, where parameter q play the role of a coordinate system in S. Under the framework of information geometry, for an adaptive system, one of the important problems we confront is to explore the new mathematical tools such as geometrical and topological structure on the parameter space that can be applied to describe the organization mechanism about how submanifold is embedded into a larger manifold, and provide an unifying approach to formulate the general principle about architecture-based learning by using the mechanism of embedding neural networks submanifold into the manifold by more richer information processing system. Neural field theory attempts to address the problem about geometrical and topological code mechanism by all information system. The goal of doing this is to study the optimal hybrid between field organization model and field action model with the architecture of simplical complexes on parameter space, It will give a new framework of neural information processing.