> the ratio remains approximately 914x over TurboQuant, with compression improving rather than degrading as context length grows.

This line from the abstract got me really suspicious. Obviously a compression scheme that incorporates the entire sequence shouldn't get worse compared to a per element one as the length increases.

It is important to note that this paper is PURELY theoretical. I couldn't find much meat on the bone from a quick skim.

The single author, Gregory Magarshak, has only published one paper on arxiv before and appears to be a professor of business / music. I don't plan to give it more of a read hoping for something of value.

Me neither. There are no actual experiments / data, no peer reviews, and the innovation relies almost entirely on citations from the author’s other paper.

The author is not an ML researcher but rather an AI startup CTO / founder. Previously worked on “social operating systems” for the web, blockchain of course. And now an AI innovator. I’m suspicious. This was part of the author’s reply in another thread:

> When TurboQuant came out, I realized we can also go way below the Shannon limit in the same way, and take advantage of PLT. In fact, I'm working on publishing a paper that generalizes this to robotics (which needs to do cheap fast on-board inference "in the field"). I also believe this is how animals actually learn. In other words, over time they learn overall "sequences" of actions and then can check whether they are "good enough" to solve the problem, or whether to switch to a full analysis -- this corresponds to System 1 and 2 of Daniel Kahneman's "Thinking Fast and Slow".

Which doesn’t exactly inspire confidence and makes me wonder who they think their audience is. ML researchers or LinkedIn.

You're right, I'm not a well-known researcher, simply an entrepreneur who started to publish academic papers.

However, I do have a long history of diving deep into fields and building practical, open-source solutions to major problems I perceive in the fields.

15 years ago I started with social networks and PHP: https://github.com/Qbix http://laweekly.com/restoring-healthy-communities/

8 years ago I got into smart contracts on EVM, which was the SOTA at the time: https://github.com/Intercoin https://intercoin.org/applications

About a year and a half ago I started teaching a course on AI at a university not far from NYU where I studied... and that's what got me into this: https://vimeo.com/1063008765/c7ef3abcc5

I try to document everything on GitHub and popular articles, but only recently started publishing academic papers on arXiv and plan to actually start submitting them for real publications. While I build, I realized that I should start publishing any novel theoretical results that underpin my work.

I plan to publish actual code in a few weeks. To be fair, TurboQuant is also a purely theoretical paper. I just wanted to get this out and share.

> To be fair, TurboQuant is also a purely theoretical paper. I just wanted to get this out and share.

TurboQuant is not a purely theoretical paper. Section 4 "Experiments" (page 15) [0] has a bunch of figure based on actual GPU computations.

[0]: https://arxiv.org/abs/2504.19874

TurboQuant went through ICLR review, has multiple Google Research co-authors, open-source implementations, CUDA kernels, and LongBench benchmarks.

Contrast that with your paper: no experiments, no implementation, no empirical validation of any kind.

Did you try engaging with LLM researchers and get their feedback on your paper?

went through ICLR review: scores 4 4 6 10, serious? open-source implementations: where is the official code? CUDA kernels: where?

Since yesterday, I put up the source code btw:

https://github.com/Safebots/KV

the irritating thing about LLM generated papers like these is that they're wrong but are generated using LLMs that are capable enough to bury the absurd claim pretty deep in there.

Analyze it using an LLM. Claude was pretty ruthless about this one.

Yeah, for me Claude identified the phrase "this holds with probability 1 over random weight matrices since the null space has dimension"

Treating trained weights as random for the purpose of a proof is immediately discrediting for a paper to me.

"This holds for almost all matrices" is actually something you'd want to know if we're talking about probabilities, no?

sure but it seems spiritually wrong to use an LLM to debug a slop paper. Who knows, maybe claude generated it in the first place?

In fairness, real-world researchers are expert at selective emphasis too.

> The second layer, predictive delta coding, stores only the residual of each new KV vector from the model's own prediction of it

I don't understand this. The key and value vectors for any given layer + token are created by the model. By definition, they are exactly equal to the model's prediction of them!

Extreme KV cache compression is easy to get---you can get an infinite compression ratio by just regenerating the key and value vectors on every forward pass. The point of a KV cache is to reduce the amount of repeated computation during generation, though. Compression only helps if you have an efficient decompression algorithm.

The prediction being used is the model's prediction of the next token's KV vector, given all previous KV vectors. Because the model was trained on language, it has strong priors about what comes next. The residual, i.e the difference between the predicted next KV vector and the actual one -- is much smaller in entropy than the raw vector, for the same reason language model perplexity is low on fluent text.

What model is doing this prediction? The only way a transformer predicts the "next KV vector" is by sampling the next token and then running a forward pass with that token.

The predicted KV vector is the expected KV vector under the model's distribution over next tokens, i.e. a weighted average over the vocabulary, not an actual sampled token. So no forward pass with a sampled token is involved. Yes, the exact computation is expensive (one forward pass per vocabulary token), which the paper acknowledges, and the practical section covers top-k approximations that capture most of the probability mass cheaply. The entropy bound holds regardless of approximation scheme -- it's a statement about the theoretical floor. The residual is small whenever the model assigns high probability to the actual next token, which is exactly what low perplexity means.

> the practical section covers top-k approximations that capture most of the probability mass cheaply.

You say cheaply, but top-k with k=20 still means 20 forward passes for each position in the predicted KV cache vector, no? So to compute the residual at position i+1 you need another 20 passes?

It's late, perhaps I'm missing something.

A top-k approximation still requires k forward passes; that's k times as expensive as just computing the exact value. Unless you're doing a prefix-unconditional prediction, in which case you still likely need quite a large token -> vector dictionary, and particularly for inner layers a significant amount of information left in the residual.

the k forward passes for different candidate tokens share all their prefix computation -- the KV cache up to position i-1 is identical for all candidates, so you run one pass through the shared layers and then k cheap single-token extensions. At long context lengths the shared prefix dominates the cost. This is also structurally what speculative decoding already does, so the infrastructure largely exists.

Incredulous claims and unreviewed paper.

Attention really is all you need.

I think you mean incredible claims. You would be incredulous about them.

You're right, thanks for the correction

> The tokens stored in a KV cache are not arbitrary floating-point data -- they are samples from the exact formal language the model was trained on, and the model is by construction a near-optimal predictor of that language.

You can compress the KV cache to 0 bytes by just recomputing it every token. This observation is not worth an ArXiv paper though.

Very intersting. A compression strategy that uses the model itself as the dictionary.

Sounds like speculative decoding but for KV cache

Extraordinary claims! I don't follow the argument though.

Author here. Since starting to teach AI at IENYC, I started publishing my papers recently on arXiv, and considering submitting them to a journal.

This is based on my original "PLT" paper: Probablistic Language Tries (https://news.ycombinator.com/item?id=47743585). A "Trie" is basically a tree of prefixes. While working on https://safebots.ai I became obsessed with caching generated artifacts as a means to do a lot of things: extremely cheap inference, near-optimal compression, modeling decision trees for strategies, and so on.

The PLT model was about compression in general. My main insight there was that the LLM's own weights actually contain an incredibly detailed probability distribution of "the next token" in any sequence, which can therefore be very useful to supercharge statistical compression. Sequences which occur frequently in the domain of the model receive short codes. The other insight is that if we allowed lossy compression, we could compress well below the Shannon information limit, and just have an "overflow" bag for surprising sequences.

When TurboQuant came out, I realized we can also go way below the Shannon limit in the same way, and take advantage of PLT. In fact, I'm working on publishing a paper that generalizes this to robotics (which needs to do cheap fast on-board inference "in the field"). I also believe this is how animals actually learn. In other words, over time they learn overall "sequences" of actions and then can check whether they are "good enough" to solve the problem, or whether to switch to a full analysis -- this corresponds to System 1 and 2 of Daniel Kahneman's "Thinking Fast and Slow".

If you want more specific information, or see the code for a working prototype, you can write me at the email in the paper.

This is a compute memory trade, not compression vs. turobquant? Lemma 1 is something like, "forward pass is deterministic because it's deterministic" which means the input tokens were always the lower bound...which isn't caching? Smells tautological. What am I missing?

Well yeah, I just wrote it as a lemma, but it's basically close to tautological. Its only job is to formally ground the entropy argument that follows it. The interesting claim is what comes after: because KV vectors are deterministic functions of tokens, and because the model is a near-optimal predictor of its own distribution, the conditional entropy of each new KV vector given all previous ones is bounded by token-level perplexity. TurboQuant compresses against the marginal distribution of each vector in isolation -- that's the gap.

And yes, it's a compute/memory tradeoff, all caching is. The claim is just that the memory floor is much lower than anyone had formally established. Whether the compute cost of getting there is worth it is a fair open question the paper doesn't settle. But what if it is? Caching is the thread running through most of my work, and I intend to find out.

The reasoning around the 900000x claim isn't sound and violates way too many information density principles.

I was incredibly curious since I had a pet theory in my mind about something extremely similar, but arrived at a conclusion that the time complexity of such cache would end up being extremely slow.

This is like saying that you've achieved single token compression when you're passing a single token into a model and letting it regenerate the entire output since at the end of the day models are probabilistic stateless devices. At that point you don't have a cache and are just replaying the tokens or have a caching algorithm with a complexity similar to that of a model defeating the purpose of such cache.

I've never considered that arXiv had a problem, now I do.

No, the 914,000x in the paper is talking about the ratio between two entropy floors, it's not a claim about practical compression. The point is that per-vector quantization has been chasing the wrong theoretical limit: the sequential entropy bound is just fundamentally lower, by that factor, because KV vectors aren't independent samples!

On complexity, that's fair concern, and the paper doesn't fully resolve it. But the analogy to "replaying tokens through the model" isn't exactly right. The delta coding layer uses the model's own next-token prediction, which is already happening during normal autoregressive inference. You're not adding a forward pass, you're using the one already running and storing only the residual, which is much smaller than the raw vector -- precisely because the model is a good predictor of its own next state.

The trie index lookup is O(sequence length), not O(model forward pass). Whether that's fast enough in practice at scale is actually a legitimate open question and I'd be the first to admit the paper doesn't settle it. But the contribution here is simply establishing that the bound exists and is dramatically lower than what the field has been targeting. That's what I wanted to put out. The engineering question of how close you can get is the natural next step.

Your pet theory about time complexity sounds interesting actually, did you write it up anywhere?

Kahnemans book is considered outdated by modern neuroscience.

Dropping a grand theory of animal cognition into a defense of a KV cache compression bound is not something I was anticipating. I don’t think it’s a great argument.

At least some random pseudocrackpotery like that is points in the direction of it being a human. There's some strange human tendencies that AI just doesn't usually replicate

Can you show a working example/implementation of these theoretical improvements? Working code would also go far for replication.

this paper looks AI generated to me... I mean, there's no experiments to go along with it.

EGreg: Can we please have substantive code with reproducible results to go with each of your papers? It would go a long way in shutting up naysayers.