Grid Cells: The next building block in Artificial Intelligence research?

Current Machine Learning research has made huge progress in the past 20 years thanks to Deep Learning. We have computers we can talk to, powerful image recognition, and (almost) self-driving cars. Almost of these technologies are built on artificial neural networks , which in turn use perceptrons, a very simplified model of neurons.

What we can do with these building blocks seem to be reaching a plateau.

The ultimate goal in building these AI systems is to create generalized intelligence. Our systems still fall apart on slight variations of data. Like if we teach a computer to recognize pictures of a house, but then if we add more doors to the house, it may fail to recognize the picture as a house.

The human mind has many types of neurons that we could try to more accurately emulate to create intelligent systems.

For example there are glial cells which are cells surrounding neurons to support and maintain them. The estimates of neurons to glial cells are estimated from anywhere from 1:1 to 1:10! They have also been recently shown to contribute to memory and learning.

There is growing evidence among neuroscientists that grid cells may be a (the?) key to human level intelligence. The discovery of grid cells in 2005 led to a noble peace prize to Edvard Moser and May-Britt Moser in 2014. Grid cells fire in way that makes a map like representation of the environment that the organism is traversing. What makes them different from place cells is that the firing pattern of these cells stay the same regardless of their environment. That means they make generalized maps across all information they receive, some kind of universal mapping system, including potentially cognitive and conceptual maps.

Grid cells are located in the Entorhinal Cortex (EC), which is located in the Medial Temporal Lobe. The EC is known as the main interface between the hippocampus system and neocortex. These 3 systems are increasingly thought to contain the core of human intelligence. The EC has many other cell types such as border cells, which fire at bounders and object vector cells, which fire at specific distances and directions to objects. Grid cells do make up the majority of the EC.

This neocortex-EC-hippocampus combination seem to be so central to human level intelligence, that many famous AI and intelligence researchers have focused on this area. CEO and cofounder of DeepMind, Demis Hassibis focused his PhD research on the hippocampus and strongly believes that the key to unlocking AGI is through studying the human brain and combining machine learning research with neuroscience research. Jeff Hawkins of palm pilot fame has focused his research on the neocortex and believes the neocortex has grid-cell like properties.

The grid cells map looks like graphing paper, except instead of squares, they are shaped like triangles forming hexagons. We don’t know exactly why they are hexagonal shaped, but there are a few hypotheses around being the most efficient structure. There seem to be 3 parameters that describe grid cells:

  1. spacing, the distance between the fields
  2. the orientation of the axes
  3. the spatial phase, the x-y location of the grids

Orienting and spacing grid cells are usually clumped together, while spatial phasing cells seem to be randomly distributed. There are some grid cells that function as head direction cells at the same time.

Many mammals have been tested for grid cells and were found, so it is safe to assume that all mammals have grid cells just like they all have a neocortex.

These maps all work in a 2D space. The grid cells will still fire if the animal’s eyes are closed, which means that the grid cells are firing based off location information that it is maintaining in realtime. There have been studies with bats to understand if grid cells can represent 3D spaces, but so far the evidence is inconclusive. There have been multiple maps found (at least 4) composing of different length arrangements of the grid cells described above. It is hypothesized that by having multiple maps stored in the EC, the combination of firing maps allows us to find and retrieve specific memories from the hippocampus. When I think of this system, I imagine multiple maps stacked on each other that are moving and by having certain neurons firing, it opens the path to a specific memory. Without having the coordinates for all of these maps, the specific memory is essentially lost. These multiple maps provide a form of a multi-scale periodic representation. I suspect that this multi-scale periodic representation may be the building block for generalization, abstraction, and time.

Studying grid cells and almost all cell types in the EC are a lot easier for neuroscientist to study compared to many other neurons. When doing neuroscience experiments, directly linking stimulus to firing output makes it easier to study, but most neurons are taking lots of abstract inputs from other parts of the brain where we don’t know what those inputs mean. On the other hand, grid cells are already high up in the cognitive processing pipeline and can be directly measured against the outside world by observing how the organism moves. Its one of the only systems we can directly measure these high level cognitive functions from outside.

Costantinescu et al. have done experimentation where they contrived a 2D “bird space” and used fMRI to measure human brains as they were thinking about this “bird space”. The evidence suggests that these same grid cells can be used to organize abstract knowledge.

Grid cells seem to store some form of abstract mapping that allows concepts to be stored in a structured way AND constrain them so that when they need to be retrieved and compared with other objects, it can do so in a direct and quick manner. One paper I read theorizes that this stored representation is like a plan that can be used similar to transitive learning (if A is greater than B and A is greater than C, then A is greater than C). There is a lot of research going on know to understand how the conceptual mapping of grid cells works and how to implement this algorithm into ANNs.

In the paper “What is a Cognitive Map? Organizing Knowledge for Flexible Behavior“, Behrans et al. hypothesize that the EC made up predominately of grid cells is a system of transition functions to learn and find generalized structures. The cells embed the relationships in structures. They also state that for this cognitive map to work, the sensory stimuli must be separate from the structure representations and that these structure representations must be explicitly represented. For example, you may learn that to navigate a vehicle on a road, you want to have control of your direction (steering wheel) , acceleration (gas pedal), and stopping (break pedal). If you go play a video game for driving cars, you will want to make sure you have access to the same basic controls. If you ride a motorcycle, you need the same controls. If you go to ride a bike, you need similar maneuvers. [The exact details and sensory stimulus changes, but the structure remains the same]. Another way said, the structural knowledge transfers across domains. So the EC is storing structural abstractions. By storing these structural abstractions, the mind can use them for quick lookups, acting as a filter for all the thousands of actions one could take. For example, if you are assembling a new electric toy, your mind can pull up how to turn a screw driver and insert batteries and can skip pulling up instructions for pouring a glass of water. In the vision system, it is thought that all objects are composed of smaller parts that the vision neurons see. For example a box would be composed of lines, edges, and corners. Similarly, it is thought that structural abstractions are compositional and made up of smaller structures.

There are several computational models that been built to test out using grid cells in computation. This is an exciting direction that may lead to computers that can generalize like humans.

Further grid cell research

Speech from Edward Moser while recieving his Nobel Peace prize for discovering grid cells: https://www.nobelprize.org/prizes/medicine/2014/edvard-moser/lecture/

What I am trying to learn:

Do I see a way to represent generalizable knowledge.

How does this hexagonal grid system work as we know it

how do the experiments actually working

TODO:

finish memorizing every paper on grid cells

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