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