Research On High Dimensional Space Function Fitting Algorithm Based On Grid Cell

Mammals are able to form internal representations of their environments.Place cells found in the hippocampus fire stingily only at a couple of locations of the environment.One synapse away from the hippocampus,grid cells in medial entorhinal cortex discharge bountifully at many locations of the environment,expressing periodic triangular grid firing maps in two-dimensional open field maze.In this study,we investigate the functional advantage of grid codes in the hippocampal-entorhinal circuit from the perspective of model learning.We build neural network models to learn the mapping from space to an abstract variable,which could be used in cognitive processes such as decision-making or motor control.The network using grid code as spatial input achieves better learning accuracy with fewer number of cells than the radial basis function network,which assumes place cell inputs.Our result shows that grid representations constitute better spatial representation in the task of model learning,and may help associative cortex better read out the information held in memory circuits.Based on the above theory,this paper presents a grid cell-based high-dimensional space function fitting algorithm,the main contribution is as follows:(1)Firstly,it introduces the purpose and significance of this subject in basic theoretical research and practical application,then investigates the current research status of brain science at home and abroad in detail,and analyzes the advantages and disadvantages of traditional intensive learning.(2)A new neural network model named grid cell neural network is proposed according to the regular triangular periodic discharge pattern of grid cells.The network can fit the function in three-dimensional space.The fitting results show that the grid cell neural network can fit the function in three-dimensional space with fewer cells than the RBF neural network with the same fitting accuracy.(3)Combining the grid cell neural network with the random projiection,the combined network can fit the functions in the high-dimensional space.The fitting results show that the grid cell neural network can fit the function in high-dimensional space with fewer cells than the RBF neural network with the same fitting accuracy.(4)The new reinforcement learning algorithm(referred to as GQL)is combined with the grid cell neural network and Q-Learning.For the mouse to find the food path planning problem,the grid cell neural network can be used more than the RBF neural network The small number of cells in the learning environment action value function,more suitable for solving the problem of large-scale path planning environment,mitigated the dimension of disaster learning in intensive learning.