When it comes to representational similarity analysis, we're trying to isolate the representations from the "coordinate systems" they sit in. If you take an image, and make a second image by rotating it 90 degrees and mirroring it, then, for the purposes of platonic representation hypothesis, they're the same image. Once you get past the "coordinate transform", the similarity between the first representation space and the 90-deg+mirror replica of it is total.

A mapping function between LE and BE can be constructed easily, and it's going to be lossless both ways. Which means that those two representations are fully compatible.

Now, INT16 and FP16? Those are far less compatible representations. There will be an overlap subspace where lossless conversion between the two is trivial, but this compatibility window will be relatively narrow.

But it's actually much weaker condition than it looks, because, for example, lot of representations of boolean circuits are equivalent up to linear transformations over Z_2^n.

Anyway, if they truly proven such a theorem you won't find "incompatible" representations of the same thing.

You're making a mistake there - focusing on the tip of the iceberg without considering what lies beneath it.

The bulk of what the human brain does isn't "decide whether skub is good or bad". The foundation that the human cognition is built upon is vast, and mostly invisible from the inside. You don't get to see the feature matching operators of your visual cortex, or the patterns that decide whether a sound is "soft" or "sharp". And a lot of those foundational features are assembled by biological development programs spun up all the way from DNA.

On that level, when it comes to the bulk of neural circuits and the processes implemented by them, the representations within a "Pro Skub" and an "Anti Skub" guy might easily be 90%+ compatible. The two people who had vastly different life experiences, worldviews and opinions would be more alike to two different LLMs fine tuned from the same base model than they would be to two different architectures trained on completely different datasets.