It is thought that enormous neurons in the brain mutually communicate using their spike activities through complicated neural networks so that the brain works as a parallel information processor. From this point of view, the information processing principle of the brain is completely different from that of conventional von Neumann-type computers.

A neuroidal net is a network of neuroids each of which is a threshold element augmented with a state and a timing mechanism. This network model was introduced by L. G. Valiant as a mathematical model of the human brain. On neuroidal nets, we can specify any learning processes on the underlying threshold circuit. A learning process on a neuroidal net consists of updating of the weights of the edges and threshold values of the neuroids in the net according to the specified learning algorithm given a initial circuit and training samples.

Thus, in order to represent a brain function by using neuroidal net, we have to design an initial circuit and a learning algorithm on it corresponding to the brain function. To achieve this goal, it is useful to consider the neural circuit of the real brain especially when we design the initial circuit.

## Learning and generation of sequence information on neuroidal nets

Actions in our behavior are basically conducted sequentially one by one. This raises a question of how sequential actions are generated from parallel computation of the brain, which remains to be solved. One of examples of the information processing of temporal sequences by the brain is the generation of voluntary movement. When we try to drink water in a glass on the table, we will extend our hand toward the glass, grasp it, bring it to our mouth and decline the glass to drink water. Unless we conduct all the component actions in this order, we cannot achieve the purpose of drinking water. As can be seen in this example, it is necessary for the brain to elicit motor commands for component actions in an adequate order when we wish to achieve a particular purpose. The underlying mechanism for such information processing by the brain is a long-standing target of research, known as “”the serial order of motor behavior problem””.

We adopt the neuroidal net model as a mathematical model of the human brain. Then, based on the neural circuit related to the generation of voluntary movement and consideration of computational mechanisms for temporal sequence generation, we construct an initial circuit, and also design a learning algorithm to learn sequence informations of component actions. Furthermore, we describe the behavior of the neuroidal model on our neuroidal net simulator.

Tetsuro Nishino, Shigeru Tanaka, and Masanori Tsujikura :Learning and generation of sequence information on neuroidal nets(in preparation).

## Optimality Theoretic LFGs on Neuroidal Nets

In order to construct a neuroidal net model of a brain function, such as the language recognition or the language acquisition, we need to design an initial circuit and a learning algorithm corresponding to the brain function. To achieve this goal, it is useful to consider linguistic theories especially when we design the initial circuit.

In this study, we will construct a network model for the optimality theoretic LFG (OT LFG for short) as an initial circuit, and design algorithms, which are executed on the circuit, for (1) the language recognition, and (2) the acquisition of some ranking information for CON (i.e. constraints in OT Theory).

Our Goal is to construct a neuroidal network model for the language processing based on OT LFG theory, which is a dynamic, parallel, and brain-like model of the language processing.

Tetsuro Nishino : Optimality Theoretic LFGs on Neuroidal Nets – — A Network Model for the Language Processing — (presented at AILA’99, in preparation).

## Related Papers

- Tetsuro Nishino : Attribute Grammars and Lexical-Functional Grammars, Proceedings of International Computer Science Conference ’88, Hong Kong, December 19-21, pp.426-433 (1988).
- Tetsuro Nishino : Mathematical Analysis of Lexical-Functional Grammars – Complexity, Parsability, and Learnability -, Proceedings of Seoul International Conference on Natural Language Processing, November 22-25, 1990.
- Tetsuro Nishino : Mathematical Analysis of Lexical-Functional Grammars – Complexity, Parsability, and Learnability -, Language Research, Vol.27, No.1, pp.119-141 (1991).
- Tetsuro Nishino : Relating Attribute Grammars and Lexical-Functional Grammars, Information Sciences, Vol.66, pp.1-22 (1992).
- Tetsuro Nishino : The Emptiness Problem for Lexical-Functional Grammars is Undecidable, IEICE Transactions on Information and Systems, Vol.E77-D, No.6, pp.720-722 (1994).