When the brain remembers the stimuli received from the eyes, ears, nose, tongue, and skin as information, it refers to the past memories and associates with what new input information is.For example, when I see an apple that I bite, I associate it with an apple, and when I see a lemon, I associate it with sour and keep it as a new memory.

　Thirty-one years ago, Professor Tsuda began researching associative memory with a neural circuit model that simulated the network structure of neurons (nerve cells) in the neocortex.We propose a mathematical model in which a state (pseudo-attractor) on the way to memory temporarily stays in the neural circuit, and finally becomes an ordered memory while moving back and forth between multiple neurons in a chaotic state. Then, a numerical simulation was carried out.However, it could not be proved due to errors such as finiteness of infinite decimal numbers and rounding.This time, the mathematical model has been proved to be correct by a mathematical method that guarantees that the true solution is within the error.

　Professor Tsuda presented a mathematical model linked to a mathematical model of associative memory when he was a doctoral student at Kyoto University.This is to change to an orderly state by adding noise to the chaotic state, which was proved mathematically in 2017 by mathematicians at the University of Pisa, Italy.Two mathematically proven models are expected to be useful in future brain science research and AI (artificial intelligence) research.

Paper information:
1987[Progress of Theoretical Physics] Memory Dynamics in Asynchronous Neural Networks (PDF)
2018[Mathematics] Chaotic Itinerancy in Random Dynamical System Related to Associative Memory Models (PDF)