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Discussion (27 Comments)Read Original on HackerNews
What about through the lens of the Norvig-Chomsky debate?
Which will be true of many human curated corpuses. But it will also be similar to, for natural data as well. Such as the lengths of random rivers, or the brightness of random stars.
The law was first discovered because logarithm books tended to wear out at the front first. That turned out to because most numbers had a small leading digit, and therefore the pages at the front were being looked up more often.
This proves a decimal system is correct. Base twelve numeral systems are clearly unnatural and inefficient.
What would using base 12 in our natural language mean? Number names needed to be based on 12, not 10. Thirteen, twenty-seven, our numbers have base 10 embedded in their naming.
Potentially useful for things like innate mathematical operation primitives. A major part of what makes it hard to imbue LLMs with better circuits is that we don't know how to connect them to the model internally, in a way that the model can learn to leverage.
Having an "in" on broadly compatible representations might make things like this easier to pull off.
"How Different Language Models Learn Similar Number Representations" (actual title) is distinctly different from "Different Language Models Learn Similar Number Representations" - the latter implying some immutable law of the universe.
I think the implications is slightly weaker -- it implies some immutable law of training datasets?
Saw similar study comparing brain scans of person looking at image, to neural network capturing an image. And were very 'similar'. Similar enough to make you go 'hmmmm, those look a lot a like, could a Neural Net have a subjective experience?'
That particular landmine aside, there are some works showing that neural networks and human brain might converge to vaguely compatible representations. Visual cortex is a common culprit, partially explained by ANN heritage perhaps - a lot of early ANN work was trying to emulate what was gleaned from the visual cortex. But it doesn't stop there. CNNs with their strong locality bias are cortex-alike, but pure ViTs also converge to similar representations to CNNs. There are also similarities found between audio transformers and auditory cortex, and a lot more findings like it.
We don't know how deep the representational similarity between ANNs and BNNs runs, but we see glimpses of it every once in a while. The overlap is certainly not zero.
Platonic representation hypothesis might go very far, in practice.
Edit: to be clear I think these patterns are real and meaningful, but only loosely connected to a platonic representation of the number concept.
The "platonic representation" argument is "different models converge on similar representations because they are exposed to the same reality", and "how humans represent things" is a significant part of reality they're exposed to.
I'm partial to the "evolved low k-complexity priors are nature's own pre-training" hypothesis of where the sample efficiency in biological brains comes from.