alt Hacker NewsIsn’t big-endian vs little-endian a trivial example of how you can represent the same mathematical object (integers) in mutually-incompatible ways?
Maybe I’m missing the detail on how complex the mapping function can be before we say the representations are incompatible.
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js8 • today at 6:11 PM
Big vs little endian are equivalent up to rotation, which includes permutations.
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.
Yes, the mapping function is the thing you're missing.
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.