[HN Gopher] How Animals Map 3D Spaces Surprises Brain Researchers
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How Animals Map 3D Spaces Surprises Brain Researchers
Author : jonbaer
Score : 74 points
Date : 2021-10-15 11:04 UTC (11 hours ago)
(HTM) web link (www.quantamagazine.org)
(TXT) w3m dump (www.quantamagazine.org)
| MR4D wrote:
| How birds can fly into a tree at speed, and land on a branch
| without poking an eye out (or anything else) several times per
| day is amazing to me.
|
| "Bird-brain" may be an insult to people, but I'd bet their 3-D
| processing capabilities blow away an RTX 3090 - especially when
| considering power use and heat.
|
| We have a lot left to learn from them.
| qq4 wrote:
| Birds are also much smaller than you and I. Bugs, fish, humans
| etc can all navigate a complex environment at speed.
| hypertele-Xii wrote:
| And yet you'd be hard-pressed to find a single human on the
| planet willing to trade their brain in for a GPU.
| crazysim wrote:
| Pretty sure there are a bunch on Mechanical Turk. Slow
| though.
| trhway wrote:
| You actually describe the NVDA's next major revenue source.
| Initially of course it will be just a co-processor to the
| wet-ware, and with time it will start to beat it in
| computational power, features, ... Upgradeability and cloud
| connectivity of course are among its advantages from the
| start.
| trhway wrote:
| the trick i observed crows doing - somewhat similar to the
| opening of the Cobra maneuvers - they come about a foot below
| branch or whatever their landing target is and by quickly
| angling up they extinguish their horizontal speed by trading it
| for that foot of the height - ie. they get 0 horizontal speed
| right over the branch. Thus they avoid the overwise would be
| needed horizontal speed slowdown in the level flight and
| associated stall risk.
| clairity wrote:
| also amazing are gibbons. they literally fly through 3d tree-
| space using branches that flex generously, making the split-
| second routing calculations they're making seem unbelievable.
| [deleted]
| doodlebugging wrote:
| After reading this article I have decided that the researchers
| earlier conclusions about how the rats keep track of their
| environment is suffering from a serious defect introduced by the
| researchers at the start.
|
| Their earlier work involved studying rat and bat navigation in
| unnatural environments - a "2D" space which was really a 3D space
| constrained to be along a single level. This forced or even
| allowed the rat brains to dumb things down to a situation where
| they had no need or opportunity to consider things outside that
| unnaturally limited space and so their brains naturally optimized
| for that simplistic situation.
|
| You have dumbed down their environment to the point where you
| have established a minimal ability that they need to master in
| order to function and navigate that environment.
|
| Then when you discover that their memory encodes navigational
| information from this dumbed-down, unnatural environment in a
| regularized grid, this should be no surprise. They are minimizing
| the energy required to thrive in that environment.
|
| Once you allow them to navigate in a more natural environment you
| should expect to see this regular grid disappear since their
| options for reaching a destination are no longer constrained to a
| single path along most of the route to their destination. Their
| brains will have to incorporate many more clues to guide their
| route selection and those clues could be time-varying as in the
| case where they are tracking the source of an odor as they search
| for food so they will need to monitor air flow and direction,
| odor intensity, potential obstacles between themselves and the
| source, alternate routes which present themselves as they move
| through space, threat detection from predators or bait traps,
| etc. In short, there so many variables that will need to be
| evaluated once you remove the flat plane constraints that led to
| their grid discovery that it should be no surprise to discover
| that a more complex environment uses different optimizations,
| some of which are encoded in a regularized notation and others,
| probably situational events on the path-picking decision tree,
| are more random.
| exporectomy wrote:
| > you should expect to see this regular grid disappear since
| their options for reaching a destination are no longer
| constrained to a single path along most of the route to their
| destination.
|
| That's a post hoc rationalization. All those complicating
| factors can exist in 2D too. Are you predicting that the 2D
| hexagonal structure will also be lost in a 2D environment with
| odors/etc., and this conclusion about it being 2D vs 3D is
| false?
| bckr wrote:
| I think it's important to see all of these situations. The very
| fact that the brain optimizes its maps based on constrained
| environments is awesome. Also, the technology had to be built
| to do the previous 2d studies, which then bootstrapped the 3d
| studies. Knowing that under certain circumstances the neural
| maps had a very "clean architecture" may have saved a lot of
| time and effort once these more random 3d structures were being
| analyzed.
| doodlebugging wrote:
| I agree. This is awesome work and is a great starting point.
| The regular gridding to me indicates that the rats learned
| the routes and found them easy and maybe even boring so after
| a point, they were not challenged intellectually in the
| navigation. Once their environment was modified, the rats
| began to engage more of their brain to learn and manage the
| choices that each situation required.
|
| I just thought it was funny that the researchers were
| surprised to see such a large difference in how rats handle
| complexity when we know going in that rats are pretty
| intelligent. Those rats probably know each researcher, have
| favorites, remember routes, and get bored with those tasks
| like we would be. It becomes muscle memory for them so they
| go through the motions to get the treat they know is waiting.
| jjoonathan wrote:
| Ruthless problem reduction and minimization is good
| experimental design. "Let's, like, let all the variables vary,
| man" is a recipe for failing to learn anything at all, rather
| than learning one small piece of a bigger puzzle.
| doodlebugging wrote:
| It is a lot like programming. Start off defining the
| algorithm to handle the general case and refine it until it
| works with no issues. Then add in edge cases so that you tune
| it to handle more real-world situations. That is the way to
| build a solid, fail-safe code base. If you truly understand
| the problem you can eventually code enough to handle any
| real-world scenario. Don't be surprised if the code looks
| hairy and nothing like the original though.
|
| In their case, they started with a generalized "2D" simple
| case and concluded after study that a real-world scenario
| would look very similar or would be a neat permutation of
| their original grid-optimized discovery. They found instead
| that they had discovered that the rat brains optimized their
| navigation to the difficulty of the task and that once you
| add enough difficulty, the brains spread the computational
| resources in a different optimization in order to handle the
| newfound complexity. Patterns were still detectable but they
| did not follow the original hexagonal grid optimization
| discovered in the initial tests.
|
| This is, as you say, a process of learning one small piece of
| a bigger puzzle. In this case, they found that the complexity
| of the puzzle is higher than the initial guess they made
| after collating and analyzing all the data from the simple
| experiments. Useful things were learned but I was attempting
| to note that they have apparently made assumptions based on a
| very simple case that turned out not to be entirely accurate
| and that they appear to be surprised by that instead of
| accepting that the simplicity of the tasks used to generate
| the data may have biased the results. No doubt they will
| continue to add complexity and learn new things, and win more
| awards for their pioneering work.
| TheCoreh wrote:
| Reading the article I couldn't stop thinking: Isn't 3D space
| perhaps being mapped by a "crumpled" 2D space filling surface?
|
| Real world environments are rarely really 3D, and a 2D surface is
| perhaps the sweet spot in complexity/degrees of freedom for most
| practical cases? This would explain why 3D mazes are so much more
| disorienting than 2D mazes, for example.
| JabavuAdams wrote:
| Sorry if I'm Mx-splaining -- I don't know your background, but
| I'm interested in/working on this stuff.
|
| Your crumpled space-filling surface makes me think of
| manifolds.
|
| Machine-learning researchers often speak loosely of e.g. the
| "manifold"* of possible images of naturalistic scenes embedded
| within the space of all possible images. The networks are
| presumably learning a lower-dimensional representation of the
| world than the dimension of all possible combinations of sense
| impressions. If you have a 100 pixel by 100 pixel image and
| each pixel can have 256 intensity levels, then that's 256 to
| the power of ten thousand possible distinct images. If each
| image is a point in an abstract space of all possible images,
| then that space has 256 to the ten thousand dimensions. But the
| vast, vast, vast majority of the volume of that space
| corresponds to images that just look like static to humans. So
| the thinking is that we internally represent images as some
| learned non-linear transformation to a much lower dimensional
| set of features that actually correspond to stuff we experience
| / see.
|
| A really simple canonical example is the Swiss Roll dataset.
| You only need two parameters (numbers) to specify it fully, but
| you can embed it (nonlinearly) in a 3D space.
| http://people.cs.uchicago.edu/~dinoj/manifold/swissroll.html
|
| In terms of neuroscience, there are competing ideas (as
| always). There's a body of work that tries to show that as we
| learn, the brain encodes our high-dimensional sense-impressions
| in the lowest possible (most efficient) internal
| representations. However, some recent work seems to imply that
| instead the brain uses as high a dimension as possible, but up
| to some limit that demarcates the transition between being
| differentiable and not differentiable. They found a beautiful
| power-law:
| https://www.biorxiv.org/content/10.1101/374090v1.full
|
| * When ML researchers speak of such a manifold, it's kind of
| loosey-goosey because a set that includes isolated points that
| don't have a continuous region around them aren't actually
| manifolds. In contrast, in the computer graphics and meshing
| literature people speak of non-manifold geometry which is
| isolated points and lines that you can't triangulate with 2d or
| 3d elements. I.e. 1d or 0d elements.
| whatshisface wrote:
| > _When ML researchers speak of such a manifold, it 's kind
| of loosey-goosey because a set that includes isolated points
| that don't have a continuous region around them aren't
| actually manifolds._
|
| So they mean "subset" when they say "manifold?"
| JabavuAdams wrote:
| I suppose so, but they really are trying to convey that all
| the points lie close to some lower-dimensional crumpled
| surface. So a subset that was e.g. just a lattice in the
| high-dimensional space wouldn't fit this mental image.
|
| E.g. Generate 3d points that are on a 2d plane +- some
| small random offset normal to the plane. If the points are
| isolated, without each having a local neighbourhood, it's
| not technically a manifold. But, you could describe the
| data-set as lying on or near a plane to within some
| tolerance.
|
| So they're trying to describe something that is much more
| specific / strongly constrained than an arbitrary subset,
| but it doesn't meet the very stringent (and frankly
| idealized) requirements of a manifold. I wonder whether
| there is a math-object to describe this?
|
| EDIT> Maybe it's just a matter of saying "close to some
| lower-dimensional manifold", rather than "on a lower-
| dimensional manifold."
| whatshisface wrote:
| > _I wonder whether there is a math-object to describe
| this?_
|
| Here is how I would phrase it: there is a probability
| distribution in the higher-dimensional space that
| expresses P(this image | given that it's a natural
| image). The level sets of the probability distribution
| are manifolds.
| TheCoreh wrote:
| > Sorry if I'm Mx-splaining -- I don't know your background
|
| Not at all! All of this is far more advanced than my
| knowledge on the topic, and very interesting! Thanks for
| sharing
|
| That idea of representing in the highest dimensionality
| possible, with some constraint is also very interesting. In
| that case perhaps the 3D space is being represented in a
| higher dimensional form that makes it more convenient for
| some neural processing purpose (e.g. just like we use
| homogenous coordinates) The 2D-2D case is then just a happy
| coincidence where the highest representation that makes sense
| maps 1 to 1 with the actual data.
| JabavuAdams wrote:
| We should be careful to distinguish between the
| dimensionality of the physical space, the dimensionality of
| image data coming in from the retina, and the
| dimensionality of the navigational representation.
|
| Going back to the image example, a 100x100 pixel image is
| 2D in that it can be shown on a screen, or printed on a
| page, or laid flat on a plane. But the (abstract) space of
| all possible images is #intensities_per_pixel to the
| 100x100 = 10000 power.
|
| It's abstract in that each point in this space is not a
| location in the external world, but specifies one
| particular image. If you're familiar with phase spaces or
| configuration spaces from physics, it's like that.
|
| The other thing is that we don't seem to have direct access
| to a 2d or 3d position-tracker sense. So instead, we have
| to build up some internal representation for navigation,
| based on our senses which as outlined for images are much
| higher-dimensional than the physically allowable positions
| in the world they're sensing. Robotics SLAM is one
| approach.
|
| Then finally, there's the dimensionality of the neural
| representation itself. Let's say that your internal
| navigation map is represented by the firing-pattern of a
| population of neurons (i.e. more than one). Define a time-
| step, say one millisecond. For simplicity, consider each
| neuron to just be have an "activity" in the range 0.0 to
| 1.0 per time-step by e.g. counting the number of spikes
| emitted per time-step and dividing by some number to get
| things in a nice range. So now you can represent the
| activity of a neuron by one number per timestep. If you
| have a population of 100 neurons, then that's a 100 number
| string. But ... you can also think of it as a point in a
| 100 dimensional space. Each point is one particular pattern
| of neural activations. The entire space is all of the
| possible patterns of neural activations. Again, this is not
| a space in the sense of physical positions in the world or
| in the brain. It's an abstract space. But all the vector
| space math works.
|
| SO we're perceiving 3D by means of retinas that take way
| more than 3 measurements at an instant, and maybe our brain
| is finding correlations so that it can represent these in a
| distributed way in << input_dimensions, but >
| world_dimensions.
| pharke wrote:
| So are the hexagonal latices for 2D grid cells just an artifact
| of whatever sphere packing[0] algorithm the neurons are using?
|
| [0]https://en.wikipedia.org/wiki/Sphere_packing
| JabavuAdams wrote:
| I love sphere packing, but we don't know that neurons do sphere
| packing. Check out Shimada et. al. Bubble Mesh for some fun
| sphere-packing algos.
| pharke wrote:
| I find this paragraph from the article intriguing
|
| > But the grid cells' firing wasn't entirely random either.
| Instead, there was local order: For each grid cell, the
| places where it fired weren't arranged in a perfect periodic
| lattice, but the distances between them were too regular to
| be merely a matter of chance. Rather than the neat stack of
| oranges, the researchers were seeing something similar but
| less orderly, more like marbles filling a box. "They're
| always stuck in some local minimum, such that there is not a
| lattice," Ulanovsky said. "On the other hand, the local
| distances there are fixed, because all the [marbles] are sort
| of touching their neighbors."
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