The Brain’s Ability to Perceive Space Expands Like the Universe

Summary: Time spent in a novel environment causes neural representations to grow in a surprising way.

Source: Salk Institute

Young children sometimes believe that the moon is following them, or that they can reach out and touch it. It appears to be much closer than is proportional to its true distance. As we move about our daily lives, we tend to think that we navigate space in a linear way.

But Salk scientists have discovered that time spent exploring an environment causes neural representations to grow in surprising ways.

The findings, published in Nature Neuroscience on December 29, 2022, show that neurons in the hippocampus essential for spatial navigation, memory, and planning represent space in a manner that conforms to a nonlinear hyperbolic geometry—a three-dimensional expanse that grows outward exponentially. (In other words, it’s shaped like the interior of an expanding hourglass.)

The researchers also found that the size of that space grows with time spent in a place. And the size is increasing in a logarithmic fashion that matches the maximal possible increase in information being processed by the brain.

This discovery provides valuable methods for analyzing data on neurocognitive disorders involving learning and memory, such as Alzheimer’s disease.

“Our study demonstrates that the brain does not always act in a linear manner. Instead, neural networks function along an expanding curve, which can be analyzed and understood using hyperbolic geometry and information theory,” says Salk Professor Tatyana Sharpee, holder of the Edwin K. Hunter Chair, who led the study.

“It is exciting to see that neural responses in this area of the brain formed a map that expanded with experience based on the amount of time devoted in a given place. The effect even held for miniscule deviations in time when animal ran more slowly or faster through the environment.”

Sharpee’s lab uses advanced computational approaches to better understand how the brain works. They recently pioneered the use of hyperbolic geometry to better understand biological signals like smell molecules, as well as the perception of smell.

In the current study, the scientists found that hyperbolic geometry guides neural responses as well. Hyperbolic maps of sensory molecules and events are perceived with hyperbolic neural maps.

This is a drawing of an hour glass
New experiences are absorbed into neural representations over time, symbolized here by a hyperboloid hourglass. Credit: Salk Institute

The space representations dynamically expanded in correlation with the amount of time the rat spent exploring each environment. And, when a rat moved more slowly through an environment, it gained more information about the space, which caused the neural representations to grow even more.

“The findings provide a novel perspective on how neural representations can be altered with experience,” says Huanqiu Zhang, a graduate student in Sharpee’s lab.

“The geometric principles identified in our study can also guide future endeavors in understanding neural activity in various brain systems.”

“You would think that hyperbolic geometry only applies on a cosmic scale, but that is not true,” says Sharpee.

“Our brains work much slower than the speed of light, which could be a reason that hyperbolic effects are observed on graspable spaces instead of astronomical ones. Next, we would like to learn more about how these dynamic hyperbolic representations in the brain grow, interact, and communicate with one another.”

Other authors include P. Dylan Rich of Princeton University and Albert K. Lee of the Janelia Research Campus at the Howard Hughes Medical Institute.

About this spatial perception research news

Author: Press Office
Source: Salk Institute
Contact: Press Office – Salk Institute
Image: The image is credited to Salk Institute

Original Research: Open access.
Hippocampal spatial representations exhibit a hyperbolic geometry that expands with experience” by Huanqiu Zhang et al. Nature Neuroscience


Hippocampal spatial representations exhibit a hyperbolic geometry that expands with experience

Daily experience suggests that we perceive distances near us linearly. However, the actual geometry of spatial representation in the brain is unknown.

Here we report that neurons in the CA1 region of rat hippocampus that mediate spatial perception represent space according to a non-linear hyperbolic geometry. This geometry uses an exponential scale and yields greater positional information than a linear scale.

We found that the size of the representation matches the optimal predictions for the number of CA1 neurons. The representations also dynamically expanded proportional to the logarithm of time that the animal spent exploring the environment, in correspondence with the maximal mutual information that can be received. The dynamic changes tracked even small variations due to changes in the running speed of the animal.

These results demonstrate how neural circuits achieve efficient representations using dynamic hyperbolic geometry.

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  1. Might this be relevant to the perceived passage of time? Would spending time in novel places expand the perception of passage of time?

  2. Clarification: Not that the representation of the brain=map is 2-dimensional, but rather that the Poincare disk is a 2-dimensional analog of this kind of representation. The brain-map would be a “Poincare sphere”, I suppose. The point being that it is not so much that the “brain expands to infinity” (although that does sound cool!), but that “infinity” is hyperbolically projected onto a finite map.

  3. Or think of it 2-dimensionally, as a Poincare disk, with the self’s point of origin at the center. Then everything is included, out to infinity, but projected onto a finite disk, so we then conceive it, not as the brain-map expanding exponentially, but as the information shrinking exponentially, becoming exponentially “less important” the closer it gets to the edge of the disk, which is the same as saying the further it gets away from the center, approaching infinity.

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