Before revision:  By reconstructing the kernel functions for place cells, our model learns hexagon grid patterns that characterize the grid cells. The learned model is capable of near perfect path integral , and it is also capable of error correction  .
After revision:  By reconstructing the kernel functions for place cells, our model learns hexagonal grid response patterns that resemble the firing patterns observed from the grid cells in the brain. Furthermore, the learned model is capable of near perfect path integral , and it is also capable of error correction .