If you squint your eyes it's a fixed iteration ODE solver. I'd love to see a generalization on this and the Universal Transformer metioned re-envisioned as flow-matching/optimal transport models.
One of the core ideas behind LLMs is that language is not a discrete space, but instead a multidimensional vector field where you can easily interpolate as needed. It's one of the reasons LLMs readily make up words that don't exist when translating text for example.
This makes me think it would be nice to see some kinda child of modern transformer architecture and neural ODEs. There was such interesting work a few years ago on how neural ode/pdes could be seen as a sort of continuous limit of layer depth. Maybe models could learn cool stuff if the embeddings were somehow dynamical model solutions or something.
Does the training process ensure that all the intermediate steps remain interepretable, even on larger models? Not that we end up with some alien gibberish in all but the final step.
Training doesn’t encourage the intermediate steps to be interpretable. But they are still in the same token vocabulary space, so you could decode them. But they’ll probably be wrong.
token vocabulary space is a hull around human communication (emoji, mathematical symbols, unicode scripts, ...), inside that there's lots of unused representation space that an AI could use to represent internal state.
So this seems to be bad idea from an safety/oversight perspective.
What is a bad idea? Allowing reasoning to happen in continuous space instead of discrete token space? This paper can be seen as a variant of the Coconut models (continuous chain of thought). Continuous reasoning is certainly more efficient when it works. Lack of interpret ability makes certain safety systems harder to enforce. Is that your point?
Yes. Coconut has the same issue. See also: a joint statement by researchers from several labs about CoT monitorability: https://arxiv.org/abs/2507.11473
It's hard to know which way this will go. Discrete/text reasoning has many advantages. Safety as you note. Interpretability, which is closely related. Interoperability - e.g. the fact that you can switch models mid-discussion in Cursor and the new model understands the previous model's CoT just fine, or the ability to use reasoning traces from a larger model to train a smaller model to reason.
Continuous latent reasoning is a big hassle, but wins on efficiency, and in some situations I'm sure people will decide that benefit is worth the hassle. Because efficiency is fighting physics, which is hard to argue with on small devices with batteries. So my guess is that we'll see some of each approach in the future - with most cloud stuff being discrete, and a few highly-tuned edge applications being continuous.
Safety is a multi-faceted problem. I think it's easy to over-index on it because the impacts can be so huge. But there are so many different ways to approach the problem, and we must not rely on any one of them. It's like cyber-security - you need to use defense in depth. And sometimes it makes sense to sacrifice one kind of protection in order to get some convenience. e.g. if you decide to use continuous reasoning, that probably means you need to write a custom classifier to detect mal-intent rather than relying on an off-the-shelf LLM to analyze the reasoning trace. So I wouldn't ever take a position like "nobody should ever use continuous reasoning because it's too dangerous" - it just means that kind of safety protection needs to be applied differently.
If you squint your eyes it's a fixed iteration ODE solver. I'd love to see a generalization on this and the Universal Transformer metioned re-envisioned as flow-matching/optimal transport models.
How would flow matching work? In language we have inputs and outputs but it's not clear what the intermediate points are since it's a discrete space.
One of the core ideas behind LLMs is that language is not a discrete space, but instead a multidimensional vector field where you can easily interpolate as needed. It's one of the reasons LLMs readily make up words that don't exist when translating text for example.
Not the input and output though, which is the important part for flow matching modeling. Unless you're proposing flow matching over the latent space?
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This makes me think it would be nice to see some kinda child of modern transformer architecture and neural ODEs. There was such interesting work a few years ago on how neural ode/pdes could be seen as a sort of continuous limit of layer depth. Maybe models could learn cool stuff if the embeddings were somehow dynamical model solutions or something.
Does the training process ensure that all the intermediate steps remain interepretable, even on larger models? Not that we end up with some alien gibberish in all but the final step.
Training doesn’t encourage the intermediate steps to be interpretable. But they are still in the same token vocabulary space, so you could decode them. But they’ll probably be wrong.
token vocabulary space is a hull around human communication (emoji, mathematical symbols, unicode scripts, ...), inside that there's lots of unused representation space that an AI could use to represent internal state. So this seems to be bad idea from an safety/oversight perspective.
https://openai.com/index/chain-of-thought-monitoring/
What is a bad idea? Allowing reasoning to happen in continuous space instead of discrete token space? This paper can be seen as a variant of the Coconut models (continuous chain of thought). Continuous reasoning is certainly more efficient when it works. Lack of interpret ability makes certain safety systems harder to enforce. Is that your point?
Yes. Coconut has the same issue. See also: a joint statement by researchers from several labs about CoT monitorability: https://arxiv.org/abs/2507.11473
Interesting. Thanks for the reference!
It's hard to know which way this will go. Discrete/text reasoning has many advantages. Safety as you note. Interpretability, which is closely related. Interoperability - e.g. the fact that you can switch models mid-discussion in Cursor and the new model understands the previous model's CoT just fine, or the ability to use reasoning traces from a larger model to train a smaller model to reason.
Continuous latent reasoning is a big hassle, but wins on efficiency, and in some situations I'm sure people will decide that benefit is worth the hassle. Because efficiency is fighting physics, which is hard to argue with on small devices with batteries. So my guess is that we'll see some of each approach in the future - with most cloud stuff being discrete, and a few highly-tuned edge applications being continuous.
Safety is a multi-faceted problem. I think it's easy to over-index on it because the impacts can be so huge. But there are so many different ways to approach the problem, and we must not rely on any one of them. It's like cyber-security - you need to use defense in depth. And sometimes it makes sense to sacrifice one kind of protection in order to get some convenience. e.g. if you decide to use continuous reasoning, that probably means you need to write a custom classifier to detect mal-intent rather than relying on an off-the-shelf LLM to analyze the reasoning trace. So I wouldn't ever take a position like "nobody should ever use continuous reasoning because it's too dangerous" - it just means that kind of safety protection needs to be applied differently.
so it's:
output = layers(layers(layers(layers(input))))
instead of the classical:
output = layer4(layer3(layer2(layer1(input))))
Yeah if layers() is a shortcut for layer4(layer3(layer2(layer1(input)))). But sometimes it’s only
output = layers(input)
Or
output = layers(layers(input))
Depends on how difficult the token is.
Or more like,
That’s closer still. But even closer would be:
Except the accumulation of the stop probabilities isn’t linear like that - it’s more like a weighted coin model.