Neural geometry in the human hippocampus enables generalization across spatial position and gaze
Assia Chericoni, Chad Diao, Xinyuan Yan, Taha S. Ismail, Elizabeth A. Mickiewicz, Melissa Franch, Ana G. Chavez, Danika L. Paulo, Vaishnav Krishnan, Mohamed Hegazy, Alica M. Goldman, Lu Lin, Gabriela Tantillo Sepulveda, Garrett P. Banks, Nisha Giridharan, Mohammed Hasen, Eleonora Bartoli, Nicole R. Provenza, Seng Bum Michael Yoo, Jay Hennig, Joshua Jacobs, Sameer A. Sheth, Benjamin Y. Hayden
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First, there were place cells. Those kept track of where you were in space, each one firing when you were in a particular location.
Then there were social place cells, and they kept track of where others people (rats or bats) were.
One kind of cell solves a problem.
Two kinds of cells solves two problems.
But as soon as you have two different groups of cells, well then you have a new problem. If one cell fires does that mean I am in the spot or that someone else is in their spot? How do you keep track of who the cell is talking about?
One solution is that one set of neurons represents where I am, and a different, disjoint set, responds to where you are. That’s a pretty good solution; it’s called a labelled line solution. There's no ambiguity about what the neuron means, the learning is easy, etc. But as we learn more and more about the brain, we are learning the brain basically never does anything resembling labelled lines, and when it does it only does it within a few synapses of the sensory structure.
But besides that empirical problem, there’s a serious theoretical problem. Labelled lines are GREAT for keeping information separate, but they are terrible for putting information together. (Makes sense, right?)
Wait, why do you want to put information together in a mapping system?
We are talking about the cognition of generalization. Imagine you are six and you are playing tag and you see another kid slid on some wet grass that looks dry. Now you know that you too will slip if you run on it, so you wisely avoid it. You take information from watching someone else and use it for you own navigation. Observational learning is hugely important and gives us substantial benefits as a species. And if we had a labelled line code, we could come up with a solution that involves some downstream decoder that combines information somehow, but that would be inefficient. But also…
In the modern era, maps are about so much more than location. Cognitive maps and real maps are thought to operate on the same principles, and generalization is definitely part of cognitive maps.
Modern theories of population codes offer a very simple elegant solution to this problem, one that doesn’t require the labelled line solution. And it's a solution that gives you both generalization and differentiation.
By the way, this is basically the same as what is known in the hippocampal literature as the problem of pattern completion and pattern separation. With generalization ≈ completion and differentiation ≈ separation.
But when do you want to generalize information about position? Imagine you are six and you are playing tag and you see another kid slid on some wet grass that looks dry. Now you know that you too will slip if you run on it, so you wisely avoid it. You take information from watching someone else and use it for you own navigation. Observational learning is hugely important and gives us substantial benefits as a species. And if we had a labelled line code, we could come up with a solution that involves some downstream decoder that combines information somehow, but that would be inefficient. But also…
Modern theories of population codes offer a very simple elegant solution to this problem, one that doesn’t require separate downstream populations. The problem being, you need generalization without sacrificing the ability to differentiate. This is also known in the hippocampal literature as the problem of pattern completion and pattern separation.
You can’t solve it with labelled line codes, but you can solve it with population codes. Basically, population codes create a high dimensional geometry, and then you can project that geometry in different directions depending on what you need it to do. You can project into onto a lower dimension that affords generalization or one that affords differentiation.
In our study, we looked at activity of single neurons in the human hippocampus as 21 people played a prey pursuit game. This is a game we developed a while ago, and recently used to study how people make control decisions. Here we used it to look a how they keep track of where things are in the virtual world.
These neurons aren’t place cells, as classically defined. (But perhaps as they are not classically defined). But they do have robust spatial information. (We detected it using a LN/GLM approach, which is much more general and makes fewer restrictive assumptions than the normal way people search for place cells).
We find that neurons keep track of where the self-avatar is and, a bit more weakly, where the prey is. If there are two prey, then the unattended prey is represented even more weakly (but is still tracked). And there’s a predator on some trials - that gets represented too. Oh yeah, and we also used eye tracking to track gaze and that gets tracked too.
And these things really don't have tuning surfaces that are neat and point-like. They have multiple lobes, often unattached. Is that bad? Maybe not. Maybe there's no reason for neurons to have tuning functions that are neat and elegant. Maybe it's actually a good thing for neurons to have complex, ugly, weird tuning curves.
Regardless of their shapes, it is theoretically possible for neurons to have entirely unrelated tuning curves for self and other (and gaze). That would sill give you complete differentiation (on the manifold even if not in the single neuron). That would be orthogonal axes, the high dimensional generalization of separate labelled line populations. But it still doesn't give you generalization.
Really what you need is axes that are partially orthogonalized. Axes that allow for differentiation or generalization based on the readout needs. That's what we find.
Look at these alignments - they are greater than zero (not totally orthogonal) but also smaller than 1 (not totally collinear). That intermediate value lets you have both generalization and differentiation.
Or in the classic hippocampal framing, it's a neurocomputational system that means you can have both pattern separation and pattern completion at the same time.
There’s a big debate in the hippocampal world about gaze. Some people think the human hippocampus does gaze and not navigation. We think it does both. (And a bunch of other things as well). And we think it keeps gaze and location separate using orthogonal subspaces, not labelled line codes. And enables generalization by subspace projection.
More broadly, these results point to geometry as a solution to the individuation problem. In social neuroscience there is a major concern with figuring out how we translate between individuals. That is, formally speaking, a generalization problem. And solutions generally take the form of special neurons - like mirror neurons - that enable generalization. But mirror nehrons are a bad solution! They solve the generalization problem but not the differentiation problem. So that solution leads to confusion between self and other. What we really need is a flexible solution, one that allows simultaneous separation and generalization. That’s where manifold solutions, including, semi-orthogonal subspaces, save the day. And that's going to be important not just for navigation but for other social domains as well. (We have another paper on this in language).