Comparing angles between population vectors of neural activity
They are not writing about &quot;after conditioning&quot; 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 &quot;out of plane&quot; 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 &quot;12 o'clock&quot;. The conditioned stimulus causes a response corresponding to &quot;3 o'clock&quot; before any training. As you do some conditioning training, pairing the US and CS, the CS response moves towards &quot;1 o'clock&quot;, beginning to resemble the US response. During extinction, we might expect the CS response to move back towards &quot;3 o'clock&quot;, maybe we'll find it at &quot;2 o'clock&quot;. This would represent rotation in the &quot;plane of the CS and US&quot; 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 &quot;new learning&quot;.