A big problem with some of these supervised* interpretability approaches is that they can find spurious structure. (There are lots of ways to make the model do what you want; which is roughly what Hewitt and Liang 2019 showed). This paper draws a contrast to a previous method, DAS (distributed alignment search) on page 20. These and related methods rest on theories of causal abstraction, which are great in theory, but harder in practice. DAS, for example, has faced numerous recent criticisms (Makelov 2024, Meloux 2025, Sutter 2025, Grant 2026, Kumon 2026). My favorite is the quite approachable Meloux et al.; Sutter 2025 is also really good, but relies on a sort of real number argument that allows a lossless encoding of every input.
My forthcoming paper at EMNLP offers an alternative that instead grounds the notion of representation in a very simple notion of the effect it has on model learning/behavior when you adversarially perturb it. For example, if I tell a model that in the context "I saw a duck quacking" it should replace 'duck' with 'glam', how much does it desire to replace 'duck' with 'glam' in "I need to duck out of the meeting" vs. "At the park a duck protected her ducklings." This method turns out to work quite well, and as we use only a single example, avoids the need for supervision.
The linked paper argues that their method, DISCOVER, is not supervised in the same way as DAS, since it does not directly optimize for causal effect. I have only skimmed this, but I am not so sure it might not suffer from a similar issue. They're still supervising to align representations with their underlying hypothesis, even if they don't directly supervise for causal outcomes.
Refs
- Hewitt and Liang 2019. Designing and interpreting probes with control tasks
- Kumon and Yanaka, 2026. Fine-grained analysis of shared syntactic mechanisms
- Meloux et al., 2025. Everything everywhere all at once
- Rozner and Shain 2026. Perturbation: A simple and efficient adversarial tracer for representation learning in LMs. https://arxiv.org/abs/2603.23821
- Sutter et al. 2025. The nonlinear representation dilemma
(1) they are claiming to produce apparently bijective closed-form symbolic representations/approximations of, among other things, LLMs. Is evaluating these closed-form representations more computationally efficient? The implications of that are potentially huge. It would be essentially analytic distillation. Fable on a chip and not a data center would be important — and disruptive - in many ways.
(2) Unsupervised, and even supervised, symbolic approaches to problem solving break down due to combinatorial explosion, among other things. This could potentially allow us to treat LLM training and inference as a search algorithm for novel symbolic approaches to solving new classes of complex problems hitherto unreachable through other approaches. If that works, I suspect it’s a feedback loop, too - the learnings from one representation push advances in the other. This would also increase the economic value of large training runs, since the model itself is now valuable, not just its inference.
(3) Per the above, can this push LLM design to greater capabilities?
The relationship between this and Anthropic’s J-space observation is also interesting. This is much, much deeper and more directly actionable, though.
EDIT: I ran my questions through Sonnet — yes, I appreciate the irony — and it was none too sanguine about questions (1) and (2), but thought (3) was reasonable. In any case, this is quite the paper. On reflection, I do think that the apparent reliance on very simple symbolic representations and tasks is underwhelming. But the approach is impressive. And obviously this is still early days, and the value of building a bridge between the very fuzzy LLM models and the rigorous, mechanically provable models would be enormous.
The math and core experimentation here is beyond my abilities, but what I think I understand is that there are possible deeper patterns of representation that exist in LLMs that are distillations of core conceptual relations in grammar that we can get our heads around in a mathematical sense rather than apparent layer-smeared noise that somehow, un-interpretably (in a meaningful sense), resolve to correct grammar/inferences.
That's pretty cool. I hope I've got that kinda-right.
I haven't read this in depth yet, though I plan to. If this general line of research is interesting to you, I'd recommend checking out some of the lines of research it touches upon--they're really rich and fascinating, and some are pretty approachable mathematically even if ML research papers aren't usually your thing. The related works section here seems pretty well stocked, but mechanistic interpretability is a pretty interesting peephole into this general vein: https://transformer-circuits.pub/
Sounds reasonable... That the model is sometimes learning a lossy vector representation of something symbolic in nature... Sure, a NN can approximate a function?
They say this holds in... Some examples they found?
Imagine a box of balls. They have size, weight, colour, density… etc. These properties, each a measure, are dimensions and they are orthogonal to each other. Taken together are multi-dimensional.
Now take a set of words. They have "sizeness", "weightness", "colorness" and "densityness"...and "pythonness" and "haskellness" and even "adjectiveness" and "verbness" and so on and so forth...You can readily see that this can encode arbitrary patters (like language grammer or program syntax)
Training identifies these dimensions in the training data and links it with each word/token. Then given a stream of such tokens, each with its own set of dimensions (which can be huge), and LLM predicts the dimensions that the next token is most likely to have...
This is nonsense. The human mind cannot visualize more than 3 dimensions. It can perfectly comprehend any number of dimensions as long as they are represented in a vector space. In fact, that's what linear algebra does.
Yes. It's worth pointing out that anything with n distinct parameters is just a point in n-dimensional space. We're so used to handling so many dimensions that nobody ever bats an eye until someone brings up the magic word "dimensions". It's quite intuitive actually.
The trivial example that comes to mind is the character customization sliders in many video games.
Too shallow of a dismissal, and you don't determine what everyone else takes seriously.
It's been several years now of LLMs only appeasing those with low expectations and inexperience. Unless the only goal was generating boilerplate or really sloppy proofs of concept, LLMs are a waste time for everyone else. This argument is so over already. We're all just hoping for a soft landing when the hangover really kicks in.
You are disconnected from reality. The whole industry is already completely dominated by LLMs generating code. Bury your head in the sand all you want. This is not about low expectations or inexperience at all. Your condescending tone doesn't make you look smarter, it makes you look like an Amish who expects the industrial revolution is temporary and soon people will come to their senses and stop using all this nonsense industrial technology.
Doesn't that say more about the massive crumb tray nobody ever bothered to empty at the bottom of mathematics?
I'm sure someone will point out something like the 4-color theorem as a counterargument. Where is that kind of theorem proving in this generation of AI? We seem to have hit a dead end rather quickly.
They're borderline useless and certainly potentially inadvertently malicious for writing, customer service, speech to text, writing large amounts of complex code, therapy, medical diagnostics... the list goes on
Sounds like you're part of the problem?
It's really a serious problem just eroding the fabric of society in real-time. Being complacent in it or believing in the promise is just wholly foolish and bad for everyone.
this is an obvious result. for example, this guy has been writing on substack about this for at least a year or two (with code snippets) explaining the phenomenon of grokking and the ghostbasin.com concept - https://richardaragon.substack.com/
their algorithm is even named "DISCOVER" so they set out to discover the connective tissue of why the universe has invariants like math, and lo it was discovered.
i guess good job for having credentials & publishing the math so people 2years behind the curve can learn from your tenure?
yes. large matrices can gradient descend to understand arbitrary symbolic logic.
ENGLISH IS INSUFFICIENT but it is at least a few decades of math proofs & progress :) welcome to the future Slackernews
It's like Neo says "You get used to it, though. Your brain does the translating. I don't even see the code." He was referring to something like a K, Q, V vector at the time I believe.
"Vectors seem inadequate for capturing the structure of language, logic, and other cognitive domains, yet neural networks achieve impressive performance in these areas". Missing the forest for the trees? Aren't neural networks modeled after biological systems? Our brains are obviously able to contain symbolic structure despite not having a "symbol processing unit".
People really overstate the relationship between ANNs and the brain, they have very different mechanisms and only have a similarity if you squint at 100000 feet. ANNs don't have neurotransmitters or even action potentials.
I hate that whole intro - the first four sentences - so much. It’s nothing but unsupported assumptions. Basically, a strawman that they can do battle with in the paper. Not an auspicious start.
My forthcoming paper at EMNLP offers an alternative that instead grounds the notion of representation in a very simple notion of the effect it has on model learning/behavior when you adversarially perturb it. For example, if I tell a model that in the context "I saw a duck quacking" it should replace 'duck' with 'glam', how much does it desire to replace 'duck' with 'glam' in "I need to duck out of the meeting" vs. "At the park a duck protected her ducklings." This method turns out to work quite well, and as we use only a single example, avoids the need for supervision.
The linked paper argues that their method, DISCOVER, is not supervised in the same way as DAS, since it does not directly optimize for causal effect. I have only skimmed this, but I am not so sure it might not suffer from a similar issue. They're still supervising to align representations with their underlying hypothesis, even if they don't directly supervise for causal outcomes.
Refs
- Hewitt and Liang 2019. Designing and interpreting probes with control tasks
- Kumon and Yanaka, 2026. Fine-grained analysis of shared syntactic mechanisms
- Meloux et al., 2025. Everything everywhere all at once
- Rozner and Shain 2026. Perturbation: A simple and efficient adversarial tracer for representation learning in LMs. https://arxiv.org/abs/2603.23821
- Sutter et al. 2025. The nonlinear representation dilemma
(1) they are claiming to produce apparently bijective closed-form symbolic representations/approximations of, among other things, LLMs. Is evaluating these closed-form representations more computationally efficient? The implications of that are potentially huge. It would be essentially analytic distillation. Fable on a chip and not a data center would be important — and disruptive - in many ways.
(2) Unsupervised, and even supervised, symbolic approaches to problem solving break down due to combinatorial explosion, among other things. This could potentially allow us to treat LLM training and inference as a search algorithm for novel symbolic approaches to solving new classes of complex problems hitherto unreachable through other approaches. If that works, I suspect it’s a feedback loop, too - the learnings from one representation push advances in the other. This would also increase the economic value of large training runs, since the model itself is now valuable, not just its inference.
(3) Per the above, can this push LLM design to greater capabilities?
The relationship between this and Anthropic’s J-space observation is also interesting. This is much, much deeper and more directly actionable, though.
EDIT: I ran my questions through Sonnet — yes, I appreciate the irony — and it was none too sanguine about questions (1) and (2), but thought (3) was reasonable. In any case, this is quite the paper. On reflection, I do think that the apparent reliance on very simple symbolic representations and tasks is underwhelming. But the approach is impressive. And obviously this is still early days, and the value of building a bridge between the very fuzzy LLM models and the rigorous, mechanically provable models would be enormous.
That's pretty cool. I hope I've got that kinda-right.
They say this holds in... Some examples they found?
I don't enough about this area
Just going from 2D to 3D creates massive new positional potential (e.g. surface of the earth, vs. the atmosphere above earth...).
Now imagine 1,000 dimensions.
Training identifies these dimensions in the training data and links it with each word/token. Then given a stream of such tokens, each with its own set of dimensions (which can be huge), and LLM predicts the dimensions that the next token is most likely to have...
The trivial example that comes to mind is the character customization sliders in many video games.
That is why the scam works, because investors are humans...
Seeing LLMs for what they really are will also make it clear they are fundamentally unfit for a lot of tasks they are currently marketed for...
It's been several years now of LLMs only appeasing those with low expectations and inexperience. Unless the only goal was generating boilerplate or really sloppy proofs of concept, LLMs are a waste time for everyone else. This argument is so over already. We're all just hoping for a soft landing when the hangover really kicks in.
Maybe you forgot that important tidbit?
People are using them because they're being shoved down their throats and they're complacent.
Software quality, maintainability, exploitability, morale, competency are all at all-time lows and just worsening.
It's really bad to defend this.
I'm sure someone will point out something like the 4-color theorem as a counterargument. Where is that kind of theorem proving in this generation of AI? We seem to have hit a dead end rather quickly.
They're borderline useless and certainly potentially inadvertently malicious for writing, customer service, speech to text, writing large amounts of complex code, therapy, medical diagnostics... the list goes on
Sounds like you're part of the problem?
It's really a serious problem just eroding the fabric of society in real-time. Being complacent in it or believing in the promise is just wholly foolish and bad for everyone.
their algorithm is even named "DISCOVER" so they set out to discover the connective tissue of why the universe has invariants like math, and lo it was discovered.
i guess good job for having credentials & publishing the math so people 2years behind the curve can learn from your tenure?
yes. large matrices can gradient descend to understand arbitrary symbolic logic.
ENGLISH IS INSUFFICIENT but it is at least a few decades of math proofs & progress :) welcome to the future Slackernews