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Transformers are inherently succinct
This paper is being published at ICLR 2026 (top AI conference), and was selected as one of three outstanding papers.
- brandonb 4mo agoThis paper is being published at ICLR 2026 (top AI conference), and was selected as one of three outstanding papers.
- dang 4mo ago(We'll add that bit to the toptext as well. Thanks!)
- dang 4mo agoDiscussed (a bit) here: Transformers Are Inherently Succinct (2025) - https://news.ycombinator.com/item?id=48014197 https://news.ycombinator.com/item?id=48014197 - May 2026 (9 comments)
- lkm0 4mo agoI had no idea that LLMs (or the transformer architecture) were within reach of complexity theory. But if transformers "can be" exponentially more succinct than RNNs, doesn't that mean we're approaching optimality?
- thesz 4mo ago> doesn't that mean we're approaching optimality? No. Transformers are Markov chains [1]. Somewhere around this fascinating site [2] I read that stateful models have an advantage. Author provided an example, a state machine with two states A and B, where at state A transitions are to state A (output 0) and to state B (output 1) with equal probability and at state B the transition is always to state A and output is always 1. For this state machine just one bit of memory can make an optimal prediction that ones always go in pairs, whereas Markov chain will approximate this prediction and never reach optimality. [1] https://arxiv.org/abs/2410.02724 [2] https://bactra.org/
- pafoster 4mo agoMarkov chains are themselves a kind of state machine, namely a probabilistic deterministic finite automaton (PDFA), albeit where state is solely governed by the N most recent symbols. (Deterministic means that given a sequence, we can always infer the associated state transitions unambiguously). I believe the example in the reference you provide represents the more general case of PDFA, which is not representable as a finite order Markov processs.
- drdeca 4mo agoHuh? Any process on a computer by itself is also a Markov chain. If you include all the information the LLM uses to produce the next token as part of the state, then of course the LLM is a Markov chain. So would be any other process for sampling continuations of a text, with finite memory.
- deleted 4mo ago[deleted]
- hnsr 4mo agoI think that might have been the example given here: https://bactra.org/notebooks/nn-attention-and-transformers.html#just-markov https://bactra.org/notebooks/nn-attention-and-transformers.h...
- muvlon 4mo agoNo. We have an infinitely more succinct formalism, it's Turing machines. Succinctness is not necessarily a desirable property, it just says where on the capability-tractability tradeoff something is. Turing machines can express literally anything computable, but in exchange we can't use computers to reason about them in general (Rice's Theorem). Regexes are much more limited, they famously can't even recognize HTML, but we get to automatically prove things about them.
- measurablefunc 4mo agoWhat about the other direction? What languages are expressible w/ RNNs & LTLs that require exponential blowup for transformers?
- yorwba 4mo agoProposition 16. UHATs have polynomially bounded expansion over LTL. In particular, given an LTL formula φ, one can construct in polynomial time a UHAT T such that L(T) = L(φ). i.e. the blowup is only exponential in one direction.
- measurablefunc 4mo agoThat says every LTL formula can be compiled into UHAT w/ polynomial overhead. It doesn't say that all languages recognizable w/ UHATs necessarily do not have succinct recgonizers in LTLs or RNNs. Edit: Actually nevermind. If UHAT could be compiled into LTL w/ polynomial overhead then that would also work for the languages that have exponential overhead in LTL but since they don't there is a strict separation.
- aesthesia 4mo agoNot quite an answer to your question, but you might find this interesting. The Olmo Hybrid paper has some results on relative complexity of problems that can be solved by transformers and RNNs. They don't look at size, just solvability, and find that the sets of problems solvable by the two architectures are incomparable. They actually use these results to inform their architecture design, which includes both attention and state space layers. (Specifically, they choose gated delta-nets with negative eigenvalues, which they show have greater expressivity than those without.) https://arxiv.org/abs/2604.03444 https://arxiv.org/abs/2604.03444
- parasti 4mo agoPaper went over my head but is this in any way related to my experience of Claude Opus 4.8 using increasingly terse language with very short, overloaded words? Lately I've been having trouble parsing the things it writes about my own code, it's using the kind of compressed language that you see typically in git commit message subject lines but relentless, always on.
- AlotOfReading 4mo agoNo, this is in the same ballpark as ideas like big-O notation. The paper is saying that transformers can recognize a language with exponentially fewer symbols than other kinds of systems, i.e. they're more succinct. It's exactly as related to real models as computer science is to real computers.
- dontwannahearit 4mo agoNot just me then.
- nightshift1 4mo agoi noticed that with 4.7. i tried to add instructions in claude.md to unpack meaning when communicating to me but it did not work.
- 7e 4mo agoThat's a budget thing. Claude is suffering from huge demand and they're pulling out all the stops to try to keep the lights on: terse tokens, lobotomizing Claude six ways from Sunday, aggressive batching, the works.
- dfabulich 4mo agoThe last line of the abstract has the most important takeaway. > As a consequence of this succinctness, we show that basic verification problems for transformers, such as emptiness and equivalence, are provably intractable: specifically, EXPSPACE-complete. If you were hoping to formally prove the correctness of a large transformer, it turns out that you're going to need an exponentially larger amount of space to do your verification, more than you could possibly afford.
- ebiederm 4mo agoHow does it follow that there is no point in trying for formal correctness? In many problems there is an interesting subset that is quickly solvable even when the general case is not. SAT solvers in practice are quick on just about everything. SAT solvers being programs that solve the original NP-compete problem.
- thesz 4mo agoMy comment in the previous discussion of that paper: https://news.ycombinator.com/item?id=48014197 https://news.ycombinator.com/item?id=48014197 Authors used LTL (linear temporal logic) to express, basically, non-reduced non-ordered binary decision diagrams. Or just binary decision diagrams, BDDs. BDDs are almost guaranteed to have exponential size because they do not employ reduction (sharing of common expressions). Reduced BDDs are more succinct and reduced ordered BDDs are even more succinct. Also, transformers in the paper are constructed, not trained. Training any model to express some truth table is very hard. They also did not perform comparison with, say, Kolmogorov-Arnold representation, which is also universal approximator. So this paper is not as deep as one may think it is.
- nico 4mo agoThank you for the explanation, makes it a lot more digestible Just nit picking a bit: > Training any model to express some truth table is very hard What kind of models are you including here? Truth tables can be modeled in regular code very easily and reliably. And I’m sure there are many deterministic models that could do the same. Are you talking about LLMs in particular or a certain category/type of models?
- thesz 4mo ago> What kind of models are you including here? Logistic regression, non-linear logistic regression, simple neural networks, etc. Not the code as in "bunch of ifs" or decision trees. The truth tables? Predict zeroth bit in enwik9 from, say, bits of 64 previous bytes. Or multiply two 16 bit numbers and predict bit 16 of the multiplication result.
- dragontamer 4mo agoWhat? Reduced Ordered BDDs are likely not as succinct as an arbitrary BDD. The famous Hidden Weight Bit problem can be more succinctly expressed in arbitrary BDDs (changing the order and revisiting nodes), but are provably EXPSPACE in ROBDDs. ------- We study ROBDDs because they uniquely reduce to a canonical form. All functions have exactly one (!!!!) ROBDD. BDDs in general however are really arbitrary, as arbitrary as any codebase can basically get. That makes BDDs in general to difficult to study or do math upon. Results based on the studies of arbitrary BDDs do NOT apply to the simpler, easier to understand world of ROBDDs. And vice versa.
- jalospinoso 4mo ago[flagged]
- lee_ars 4mo ago"Why use lot word, when few word do trick?" —Optimus Prime
- Terr_ 4mo agoFoolish Autobots! Your so-called Matrix of Leadership is merely a bunch of weights!
- doug_durham 4mo agoThis is a truly important paper. It formalizes the intuition that many in the field have. We can stop wasting time doing formal analysis of LLMs. If you have a problem that requires formal verification, don't use an LLM. You can use an LLM to help you build such a system, but the LLM can't be the system.
- suddenlybananas 4mo agoI don't really see the relationship to your comment and the paper's content. Could you elaborate a little?
- dfabulich 4mo agoIt's the last line of the abstract. > As a consequence of this succinctness, we show that basic verification problems for transformers, such as emptiness and equivalence, are provably intractable: specifically, EXPSPACE-complete.
- platinumrad 4mo agoThat's saying you can't formally verify an LLM, not that LLMs can't be used in formal verification.
- deleted 4mo ago[deleted]
- nextos 4mo agoBut, if I have understood correctly on a quick read, they also claim transformers have pretty low expressive power. In particular, they claim they are limited to star-free subregular languages, whereas RNNs can recognize any regular language/simulate finite automata. This doesn't imply you can't get aid from a LLM to e.g. implement a function that has a formal specification (an application I think is very promising), but surely it has some profound implications on how much of a large system can be understood by a LLM at once, without supervision.
- deleted 4mo ago[deleted]
- dosisking 4mo agoWow, there's more than meets the eye
- spacebacon 4mo ago[dead]
- spacebacon 4mo agoFor the downvote. Computational semiotics is empirically proven. Read more.
- layer8 4mo agoYour comments are too succinct. Write more.
- spacebacon 4mo agoYou clearly have not read all of my words. Read more.
- sometimelurker 4mo agoreminds me of kolmogorov complexity