4 ms·

The "platonic representation hypothesis" crowd can't stop winning. Potentially useful for things like innate mathematical operation primitives. A major part of

The "platonic representation hypothesis" crowd can't stop winning. 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.

LeCompteSftware 6mo ago
"using periodic features with dominant periods at T=2, 5, 10" seems inconsistent with "platonic representation" and more consistent with "specific patterns noticed in commonly-used human symbolic representations of numbers." Edit: to be clear I think these patterns are real and meaningful, but only loosely connected to a platonic representation of the number concept.
- brentd 6mo ago
  Regardless of whether the convergence is superficial or not, I am interested especially in what this could mean for future compression of weights. Quantization of models is currently very dumb (per my limited understanding). Could exploitable patterns make it smarter?
  - ACCount37 6mo ago
    That's more of a "quantization-aware training" thing, really.
    - brentd 6mo ago
      [dead]
- ACCount37 6mo ago
  Is it an actual counterargument? 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.
  - convolvatron 6mo ago
    you're right, its just that 'platonic' is an argument that numbers exist in the universe as objects in and of themselves, completely independent of human reality. if we don't assume this, that numbers are a system that humans created (formalism), then sure, we can be happy that llms are picking common representations that map well into our subjective notions of what numbers are.
    - LeCompteSftware 6mo ago
      FWIW it's objectively false that numbers are a system humans created. That's almost certainly true for symbolic numbers and therefore large numbers ( > 20). But pretty much every bird and mammal is capable of quantitative reasoning; a classic experiment is training a rat to press a lever X times when it hears X tones, or training a pigeon to always pick the pile with fewer rocks even if the rocks are much larger (i.e. ruling out the possibility of simpler geometric heuristics). Even bees seem to understand counting: an experiment set up 5 identical human-created (clearly artificial) landmarks pointing to a big vat of yummy sugar water. When the experimenters moved the landmarks closer together, the bees undershot the vat, and likewise overshot when the landmarks were moved further apart. 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.
causal 6mo ago
You seem to be going off the title which is plainly incorrect and not what the paper says. The paper demonstrates HOW different models can learn similar representations due to "data, architecture, optimizer, and tokenizer". "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.
- dnautics 6mo ago
  > latter implying some immutable law of the universe I think the implications is slightly weaker -- it implies some immutable law of training datasets?
- NooneAtAll3 6mo ago
  I don't understand your argument "How X happens" still implies that X happens, just adds additional explanation on top
  - causal 6mo ago
    "How" = it can happen Without "How" = it will happen
FrustratedMonky 6mo ago
Same with images maybe? 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?'
- ACCount37 6mo ago
  "Subjective experience" is "subjective" enough to be basically a useless term for any practical purpose. Can't measure it really, so we're stuck doing philosophy rather than science. And that's an awful place to be in. 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.
  - snaking0776 6mo ago
    As someone actively researching in the neuroscience field these ideas are increasingly questionable. They do do a decent job of job of predicting neural data depending on your definition and if you compare them to hand built sets of features but we’re actually not even sure that will stay true. Especially in vision we already know that as models have scaled up they actually diverge more from humans and use quite different strategies. If you want them to act like humans or better reflect neural data you have to actively shape the training process to make that happen. There’s less we know about the language side of things currently though as that part of the field hasn’t yet really figured out exactly what they’re looking at yet because we generally know less about language in the brain vs vision. I think most vision scientists are on board with the idea that these things have really been diverging and have to be coerced to be useful. Language it’s more up in the air but there’s a growing wave of papers lately that seem to call the human LLM alignment idea into question. Personally I think the platonic representation idea is just a function of the convergence of training methods, data, and architectures all of these different labs are using. If you look at biological brains across species and even individuals within a species you see an incredible variety of strategies and representations that it seems ridiculous to me that anyone would suggest that there’s some base way to represent reality that is shared across everyone and every species. Here’s some articles that may be of interest if you’re curious: [1] https://arxiv.org/pdf/2211.04533 https://arxiv.org/pdf/2211.04533 [2] https://www.nature.com/articles/s41586-025-09631-6 https://www.nature.com/articles/s41586-025-09631-6 [3] https://www.biorxiv.org/content/10.1101/2025.03.09.642245v1 https://www.biorxiv.org/content/10.1101/2025.03.09.642245v1
deleted 6mo ago
[deleted]
jeremie_strand 6mo ago
[dead]

LeCompteSftware 6mo ago

"using periodic features with dominant periods at T=2, 5, 10" seems inconsistent with "platonic representation" and more consistent with "specific patterns noticed in commonly-used human symbolic representations of numbers." Edit: to be clear I think these patterns are real and meaningful, but only loosely connected to a platonic representation of the number concept.

brentd 6mo ago
Regardless of whether the convergence is superficial or not, I am interested especially in what this could mean for future compression of weights. Quantization of models is currently very dumb (per my limited understanding). Could exploitable patterns make it smarter?
- ACCount37 6mo ago
  That's more of a "quantization-aware training" thing, really.
  - brentd 6mo ago
    [dead]
ACCount37 6mo ago
Is it an actual counterargument? 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.
- convolvatron 6mo ago
  you're right, its just that 'platonic' is an argument that numbers exist in the universe as objects in and of themselves, completely independent of human reality. if we don't assume this, that numbers are a system that humans created (formalism), then sure, we can be happy that llms are picking common representations that map well into our subjective notions of what numbers are.
  - LeCompteSftware 6mo ago
    FWIW it's objectively false that numbers are a system humans created. That's almost certainly true for symbolic numbers and therefore large numbers ( > 20). But pretty much every bird and mammal is capable of quantitative reasoning; a classic experiment is training a rat to press a lever X times when it hears X tones, or training a pigeon to always pick the pile with fewer rocks even if the rocks are much larger (i.e. ruling out the possibility of simpler geometric heuristics). Even bees seem to understand counting: an experiment set up 5 identical human-created (clearly artificial) landmarks pointing to a big vat of yummy sugar water. When the experimenters moved the landmarks closer together, the bees undershot the vat, and likewise overshot when the landmarks were moved further apart. 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.

causal 6mo ago

You seem to be going off the title which is plainly incorrect and not what the paper says. The paper demonstrates HOW different models can learn similar representations due to "data, architecture, optimizer, and tokenizer". "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.

dnautics 6mo ago
> latter implying some immutable law of the universe I think the implications is slightly weaker -- it implies some immutable law of training datasets?
NooneAtAll3 6mo ago
I don't understand your argument "How X happens" still implies that X happens, just adds additional explanation on top
- causal 6mo ago
  "How" = it can happen Without "How" = it will happen

FrustratedMonky 6mo ago

Same with images maybe? 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?'

ACCount37 6mo ago
"Subjective experience" is "subjective" enough to be basically a useless term for any practical purpose. Can't measure it really, so we're stuck doing philosophy rather than science. And that's an awful place to be in. 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.
- snaking0776 6mo ago
  As someone actively researching in the neuroscience field these ideas are increasingly questionable. They do do a decent job of job of predicting neural data depending on your definition and if you compare them to hand built sets of features but we’re actually not even sure that will stay true. Especially in vision we already know that as models have scaled up they actually diverge more from humans and use quite different strategies. If you want them to act like humans or better reflect neural data you have to actively shape the training process to make that happen. There’s less we know about the language side of things currently though as that part of the field hasn’t yet really figured out exactly what they’re looking at yet because we generally know less about language in the brain vs vision. I think most vision scientists are on board with the idea that these things have really been diverging and have to be coerced to be useful. Language it’s more up in the air but there’s a growing wave of papers lately that seem to call the human LLM alignment idea into question. Personally I think the platonic representation idea is just a function of the convergence of training methods, data, and architectures all of these different labs are using. If you look at biological brains across species and even individuals within a species you see an incredible variety of strategies and representations that it seems ridiculous to me that anyone would suggest that there’s some base way to represent reality that is shared across everyone and every species. Here’s some articles that may be of interest if you’re curious: [1] https://arxiv.org/pdf/2211.04533 https://arxiv.org/pdf/2211.04533 [2] https://www.nature.com/articles/s41586-025-09631-6 https://www.nature.com/articles/s41586-025-09631-6 [3] https://www.biorxiv.org/content/10.1101/2025.03.09.642245v1 https://www.biorxiv.org/content/10.1101/2025.03.09.642245v1

deleted 6mo ago

[deleted]

jeremie_strand 6mo ago

[dead]