Different language models learn similar number representations
arxiv.org
arxiv.org
What about through the lens of the Norvig-Chomsky debate?
In this case, Chomsky's LAD almost certainly relies on Baldwin-effect structure to get around the paucity of stimuli, and the LLMs are just getting to "the same place" through sheer masses of data.
I really don't think this is evidence for "universal grammar" in any sense. It is evidence that we are all using the same very specific grammar for very specific cultural reasons.
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.
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.
You just don't "learn reality" by getting good at representations. You can learn a data set. You can learn a statistical regularity in things such as human languages. You can analyze the concept spaces of LLM's and compare them numerically. I agree with that.
What the hell does "learning an objective shared reality" mean?
This reminds me of EY saying that a solomonoff inductor would learn all of physics in a few days of a 1920x1080 data stream. Either it's false (because it needs to do empirical testing itself), or it's true, but only if you presuppose the idea that it has a perfect model of all the interactions of the world and can decide between all theories a priori... so then why are we even asking if it's a "perfect learner"? It already has a model for all possible interactions already, there's nothing out of distribution. You might argue, "Well, which model is the correct one?" That's the wrong question already - empirical data is often about learning what you didn't know that you didn't know, not just learning about in-distribution unknowns.
I just get an ick because I associate people talking about this hypothesis as if "LLM's converge on shared objective reality => they are super smart and objective, unlike humans". LLM's can be smart. They can even be smarter than humans. It's also true that empiricism is king.
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.
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.
And of course similar findings have been reproduced etc etc. The important thing to note is how strange and artificial these experiments must seem for the animals involved - maybe not the bees - so e.g. it seems unlikely that a rat evolved to push a lever X times, it is much more plausible that in some sense the rat figured it out. At least in birds and mammals there seems to be a very specific center of the brain responsible for coordinating quantitative sensory information with quantitative motor output, handling the 1-1 mapping fundamental to counting. More broadly, it seems quite plausible that animals which have to raise an indeterminate number of live young would need a robust sense of small-number quantitative reasoning.
It is an interesting question as to whether this is some cognitive trick that evolved 200m years ago and humans are just utterly beholden to it. But I think it requires jumping through less hoops to conclude that the human theory of numbers is pointing to a real law of the universe. It's a consequence of conservation of mass/energy: if you have 5 apples and 5 oranges, you can match each apple to a unique orange and vice versa. If you're not able to do that, someone destroyed an apple or added an orange, etc. It is this naive intuitive sense of numbers that we think of as the "platonic concept" and we share it with animals. It seems to be inconsistent and flaky in SOTA reasoning LLMs. I don't think it's true that LLMs have stumbled into a meaningful platonic representation of numbers. Like an artificial neural network, they've just found a bunch of suggestive and interesting correlations. This research shows the correlations are real! But let's not overinflate them.
I don't think this is a correct formulation of the platonic representation argument:
different models converge on similar representations because they are exposed to the same reality
Trying to drag an operational definition of "actual understanding" out of anyone doing this song and dance might as well be pulling teeth. People were trying to make the case for decades, and there's still no ActualUnderstandingBench to actually measure things with.
We don't know how to demonstrate actual understanding, but we sure can demonstrate a lack of it. When it comes to abstract concepts like "three" or even "more," LLMs have a clear lack of understanding. Birds and mammals do not.
"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?
"How X happens" still implies that X happens, just adds additional explanation on top
Without "How" = it will happen
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.
[1] https://arxiv.org/pdf/2211.04533 [2] https://www.nature.com/articles/s41586-025-09631-6 [3] https://www.biorxiv.org/content/10.1101/2025.03.09.642245v1
If you could brain scan a human, and identify a shape of the network that corresponds to an emotion, and then could identify that in the ANN, could we say the ANN is experiencing an emotion.
I think its loosely referred to as "neural correlate".
I'm assuming what you are talking about with Convergence, would be these "neural correlate". And no reason we couldn't move beyond images to 'feelings'.
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.
It's still used for numbers between 70-99 in French, which is maddening when trying to copy down a phone number as a non-native speaker.