Our 3D visualization relies havily on photons doing the heavy lifting of traversing 3D space in straight lines, people get, you know, accustomed to it.
In fact how we see things is frozen by physics, not brains - they are just accommodated to reality
There are no such utility particles doing any heavy lifting in 4D, so nothing to accommodate to.
I think the idea is that the geometry of straight lines in 4D should be similar enough to picture using the same mental abilities.
How we see is frozen by not only physics, but also biology. We can't actually see in 3D, only in the 2D of our retinae (and the embedded 2D of light-exposed surfaces). That's true for both 3D and 4D objects. I suppose fish, with their electroreceptive abilities, might be the only animals that can sorta "see" in true, volumetric 3D.
biology plays the role, certainly, but nature was trying to capture a model for 3D physical interactions first of all, physics first. And final choice of two 2D sensors is explicitly optimal and minimally effective for 3D - so it can not be similarly descriptive for 4D, just not fair to expect results on same level imho.
For meaningful 4D perception on similar level our body need three volumetric sensors, separated, to define volume with 4D direction
Interesting research, but it is still fascinates me why AI devs of current SOTAs ignore possibility to add numbers as first-grade citizens to AI. like for example suggested here: https://huggingface.co/papers/2502.09741
clean separation matter, it’s really strange to force models to mimic numbers and math via incredibly unfit token-mangling stuff, imho
They definitely does not aware of soviet reality that “roof over head” usually is not in the place where human want to live, same with job. if student after university decided (not by student, by state distributing workforce) to go work at city on polar circle - that means that student will go live and work here, without sunlight for the rest of his life! not joking, personal story with soviet collapse as happy ending (moved to normal place after that)
regarding “math with tokens”: There was paper with tokenization that has specific tokens for int numbers, where token value = number. model learned to work with numbers as numbers and with tokens for everything else... it was good at math. can’t find a link, was on hugginface papers
Shouldn't production models already do this? They already tend to use tokenizers with complex rules to deal with a lot of input that would otherwise be tokenized in a suboptimal way. I recall a bug in an inference engine (maybe llama.cpp?) because of an implementation difference in their regex engine compared to the model trainer. Which means that the tokenizer used regex-based rules to chop up the input.
in paper mentioned “number” is a single sort-of “token” with numeric value, so network dealing with numbers like real numbers, separately from char representation. All the math happens directly on “number value”. In majority of current models numbers are handled like sequences of chars
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