This is the hardest project I've worked on: extensive methods development, painstaking piloting, writing two grants, intensive data collection, and a LOT of thinking. It needed a huge dose of patience as we carried its burden over many years. A bit like Frodo carrying the ring.

Therefore, at least in highly trained subjects, lPFC learned task-tailored representations that recapitulated the structure of the task, showing that lPFC representations are shaped by representation learning.

On the other hand, in the flat task, a global axis encoded the response-relevant, XOR categories abstractly. Category-specific local geometries were high-dimensional, retaining stimulus information that was not strictly required for readout.

In the hierarchy task, the global axis abstractly encoded higher-level context, while low-dimensional, context-specific local geometries compressed context-irrelevant information & abstractly encoded context-relevant response-relevant category.

Using a series of decoding analyses, we comprehensively worked out the detailed local structure within each cluster in both tasks.

Nevertheless, lPFC representational geometry for each task was highly tailored to its structure. In each task, clustering created subspaces along a global axis - context subspaces in the hierarchy task, and response category subspaces in the flat task.

Across both tasks, inputs were encoded on manifolds of intermediate dimensionality, with at least some non-linear mixing of inputs. These representations did not differ in their overall separability, or degree of non-linear mixing.

With decoding analyses, across both task structures, we found lPFC coding diverse task-relevant information. On the other hand, primary auditory cortex showed obligatory coding of only auditory information, whether or not it was task-relevant.

As we have previously shown, lPFC representations are hard to study with fMRI, with poor pattern reliability and small effects. Haley tackled this head-on with deep sampling, heroically collecting 200+ minutes of fMRI data on each task from 20 subjects.

One task used a categorization rule for mapping inputs to outputs. The other used a flat, XOR structure. We yoked & counterbalanced inputs and output across the two tasks, focusing the comparison on the structure of input-output mappings.

One account, popularized by Mattia Rigotti & Stefano Fusi, is that lPFC non-linearly mixes inputs, projecting them on a high-dim, task-agnostic manifold from which any task mapping can be read out without any representation learning.