1_BrainGPS.md

Brain's GPS System

TODO: make biological firing patterns emerge from ANN

from brain_modules.systems.BrainGPS import BrainGPS, learn_path_integration_2d

Neural Computations

1. Head Direction Cells

   • Each cell corresponds to a preferred direction, its firing rate is max when the animal's head faces that direction
   • The cell population encodes any arbitrary direction as a vector
   • Computation: integrates angular velocity to get current allocentric head direction
   • Note: Head direction != head-body rotation. And we assume head direction = movement direction for simplicity

2. Grid Cells

   • Each cell's response forms a hexagonal grid, its firing rate is max when the animal goes to these grid points
   • Each cell in the population has different spatial frequency, essentially forming Fourier basis, the cell population encodes any arbitrary location as a vector
   • Computation: integrates the animal's linear velocity (with head direction info) to get current location
   • Note: The grids are internally generated via path integration, but are anchored to the environment when environmental cues are available

3. Place Cells

   • Each cell corresponds to a preferred location, its firing rate is max when the animal goes to that location
   • The cell population encodes an arbitrary location as a vector
   • Computation: decodes the location representation from grid cell population

PyTorch Replication

• Model: GRU (Gated Recurrent Unit) for sequence prediction (path integration)
  • Input: a sequence of (linear_velocity, angular_velocity) (animal's internal/egocentric knowledge)
  • Output: a sequence of (x, y, head_direction)