I am reading this paper on fear conditioning, where the following is given:

  • The n-dimensional population vector (activity of n neurons) evoked by the conditioned stimulus (CS+, auditory tone) before conditioning
  • The n-dimensional population vector (activity of n neurons) for the CS+ after conditioning

The authors write that: "[After conditioning] the CS+ population vector rotated out of the plane defined by the US [unconditioned stimulus] and the initial CS+". They conclude that this out-of-plane rotation corresponds to "new learning".

My question: Why is out-of-plane-rotation of neural activity vectors equated with a new representation/new learning?


They are not writing about "after conditioning" as you write, but, importantly, after extinction.

What they observe is that, during learning, the response to the conditioned stimulus (CS+) becomes more similar to the response to the US. In the n-dimensional space in which a population response lives, you can describe this as the population vector evoked by CS+ pointing closer to same direction as the population vector from the US.

We expect that during extinction, the CS+ vector will become different from the US compared to at the peak of conditioning. There are two general possibilities for how that could happen. The first possibility (perhaps the simplest one to expect) is that with extinction the CS+ vector returns to where it was initially, before the conditioned stimulus was paired with the US. You could describe this as merely forgetting what has been learned: responses to the US and CS go back to how they were before conditioning and it's as if nothing was ever learned.

However, that's not what these authors observe:

During within-session extinction, the CS+ representation did not revert and gained no more similarity to its initial representation before learning

Although they do observe that with extinction the CS+ vector moves away from the US, it doesn't move back towards the old response, it points in a new direction that is further both from the US response and from the original CS response. That can be described as an "out of plane" rotation, not towards either of the other vectors.

In case it's hard to think about these things in N-dimensional space, we can think of a more familiar situation in our own 3-dimensional world.

Let's say the US causes a response corresponding to "12 o'clock". The conditioned stimulus causes a response corresponding to "3 o'clock" before any training. As you do some conditioning training, pairing the US and CS, the CS response moves towards "1 o'clock", beginning to resemble the US response. During extinction, we might expect the CS response to move back towards "3 o'clock", maybe we'll find it at "2 o'clock". This would represent rotation in the "plane of the CS and US" made by the clock. Instead, the hand points out away from the wall, so it is further from both the original US at 12 and original CS at 3. That's the "new learning".

  • $\begingroup$ Thanks for the fast response! Right - extinction in particular. I think my point is a bit deeper: I understand that extinction is considered new learning, and hence the representation of the CS+ should not convert to its original form. I still don't see, however, why out-of-plane-rotation is "new learning". My understanding would be that previously inactive neurons would display activity now, as you describe the rotation would be into a new plane not defined by the original orthonormal vectors. Right? This seems to me a mathematical property, however, and very removed from behavioral learning? $\endgroup$
    – Pugl
    Mar 3 '21 at 23:13
  • $\begingroup$ ..2/2 like, how do we know this mathematical out-of-plane-rotation is in any way physiologically meaningfull? What is the typical argument made for such an interpretation? $\endgroup$
    – Pugl
    Mar 3 '21 at 23:14
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    $\begingroup$ @Pugl Maybe you're thinking about it too deeply. It's just a geometric interpretation for the extincted CS+ response not returning to the original CS+ response. "New learning" just means that the CS, post-extinction, produces a response that is similar neither to the US nor to the original CS. That's it. It's evidence against a hypothesis that extinction means the response returns to how it was originally before learning. $\endgroup$
    – Bryan Krause
    Mar 3 '21 at 23:17
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    $\begingroup$ @Pugl Another way to say it (sorry if I'm getting exhaustive) is that during learning of the CS-US association, the population response stays in the plane of the clock. It moves really just in one dimension defined by the plane of the initial CS and US responses, like the minute hand on a clock. Extinction moves the response in a different direction to that plane, into new territory not observed during the initial learning process. $\endgroup$
    – Bryan Krause
    Mar 3 '21 at 23:22
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    $\begingroup$ @Pugl Not sure what you mean by "they described in-plane rotation based on newly active cells". Might be worth another question. Also important that you have some grasp on what these vectors and planes are. Easiest to think about is with just 3 neurons, the population vector would be given by the activity of those three neurons on the X, Y, and Z dimensions. So if only X is active, you'd have a vector right along the X-axis. If only X and Y are active, you'd have vector pointing somewhere along the XY plane, but with no magnitude in the Z direction. Etc. $\endgroup$
    – Bryan Krause
    Mar 3 '21 at 23:27

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