This is a great development for KV cache compression. I did notice a missing citation in the related works regarding the core mathematical mechanism, though. The foundational technique of applying a geometric rotation prior to extreme quantization, specifically for managing the high-dimensional geometry and enabling proper bias correction, was introduced in our NeurIPS 2021 paper, "DRIVE" (https://proceedings.neurips.cc/paper/2021/hash/0397758f8990c...). We used this exact rotational approach and a similar bias correction mechanism to achieve optimal distributed mean estimation. I also presented this work and subsequent papers in a private invited talk at Google shortly after publication. Given the strong theoretical overlap with the mechanisms in TurboQuant and PolarQuant, I hope to see this prior art acknowledged in the upcoming camera-ready versions.
In this context, the rotation is for spreading energy and ensuring predictable coordinate distributions rather than diagonalization; it makes coordinate-wise quantization much more computationally efficient, though it throws away learnable structure.
ah ok, so intuitively it's like minimizing the error when replacing the values with a well-known distribution. So all you need to carry along is the rotation and the assumption that there is some amount of loss.
But if they read your paper enough that they invited you to a talk, that probably means they were far enough along to independently inventing it they were going to do so anyway, and wanted to chat with someone who was also doing the thing they were already doing. Good ideas tend to reveal themselves to anyone who is aware of the problem.
To be clear, I am not claiming they stole an idea. They have made significant independent research. However, a specific part regarding the treatment of rotation with bias correction relates to prior work, and it would be appropriate to have that recognized.
I just today learned about Multi-Head Latent Attention, which is also sort of a way of compressing the KV cache. Can someone explain how this new development relates to MHLA?
Multi-Head Latent attention is a redesigned attention mechanism that produces lower-dimensional KV-cache entries. Vector quantization can store KV-cache entries using a small number of bits per dimension while ensuring that the resulting attention scores don't change too much. So MLA needs to be part of the model from the beginning of training, whereas VQ can be retrofitted afterwards, and you could also combine the two.
Can someone ELI5 these two concepts please, which make no sense to me:
> "TurboQuant starts by randomly rotating the data vectors. This clever step simplifies the data's geometry"
I don't understand how taking a series of data and applying a random rotation could mathemetically lead every time to "simpler" geometry.
If I throw a bunch of shapes on the ground, tightly packed and touching each other, then rotate all of them, you can't guarantee that the new conglomerate shape is any more/less "simple" than before, right?
> "Johnson-Lindenstrauss Transform to shrink complex, high-dimensional data while preserving the essential distances and relationships between data points. It reduces each resulting vector number to a single sign bit (+1 or -1)."
How can a boolean value preserve all of the relational and positional information between data points?
Other people have answered here but the real answer is that deep neural networks don't learn isotropic distributions of activations.
What happens is that you get very spikey activations, there are so called "outlier" activations. A easy to read paper that tells you about this is SmoothQuant [0]. Another source from Anthropic and the Mechanistic Interperability people is calling these "privileged basis" [1].
Now based on the weight symmetries of a typical transformer, these actually don't need to exist. Weight symmetries means the ways you can change the weights without actually affecting the mathematical function, there are a broad class of these because the linear algebra has a lot of redundancies in it.
But the behaviour of the Adam optimizer is such that you do end up w/ these things because it sort of more quickly optimizes to produce them. This comes from the fact it is an elementwise dynamic learning rate (and probably partly to do with the epsilon).
They are saying that models should be invariant to data's orientation - and only sensitive to the distance between vectors. This has a pretty significant effect on reducing the set of possible models, and may stabilize the optimization.
In simple terms, large ML models like LLMs often learn trivial rules such as "if the 21st decimal place of the 5th dimension in the embedding vector is 5 - then the image is of a cat." Learning such a memorization function is usually not what we are trying to do, and there are a variety of techniques to avoid these trivial solutions and "smooth" the optimization geometry.
The whole goal of quantisation is to put the data into 'bins' so that it can easily be 'packed' so that you can represent it using less bits (less information). You can think of it like rounding essentially (3.14159 -> 3). Now, sometimes within data, the distribution will be non-ideal for separating it out into bins (let's say that our rounding rules are simple -- we simply use a floor function so 2.45 maps to 2 and 6.4543 maps to 6 etc...) and our bins simply map to the floor -- if we had a set of numbers which look like this: [3.11, 4.43, 5.78, 12.33, 34.32], they would simply map to [3, 4, 5, 12, 34]. Now, we have one huge outlier in our data (34) so to create bins for those sets of numbers, we would need 6 bits of information (2 to the power of 6 = 64), but this is mostly due to the fact that we have one huge outlier (34.32). To get rid of this -- the algorithms applies a random rotation matrix which 'distorts' the original data so that it is more evenly distributed among the possible bins which are assigned to the data set. In linear algebra, a rotation matrix is an orthogonal matrix. When you multiply your vector by this matrix, you aren't changing the "amount" of data (the length of the vector remains the same), but you are recalculating every single number in that vector as a weighted sum of the originals. According to the Central Limit Theorem, when you sum up many random things, the result always starts looking like a bell curve. This is the magic TurboQuant relies on: they don't know what your data looks like, but they know that after the rotation, the data must look like a Beta Distribution and they use this fact to transform the original data into a more 'tightly packed' distribution which allows them to more efficiently pack (or quantise) the information. If most of the transformed data is huddled together into a predictable Bell curve shape, you can pack your bins tightly around that shape leading to much higher precision with fewer needed bits to store it. For example, after applying a rotation matrix, our original transform [3.11, 4.43, 5.78, 12.33, 34.32] might get mapped to something like [8.12, 8.65, 9.25, 10.53, 12.86] and we can crate bins which both are more accurate and need less bits in order to hold our original data set. To create the most optimal bins -- the Lloyd-Max algorithm is used. This algorithm is the gold standard for 1D quantisation. Its goal is to find the best places to put your "boundaries" (where you cut the data) and your "reconstruction values" (the number you store) to minimise the Mean Squared Error (MSE). After applying this, you have your 'rounded' values (or quantized data), but there is still an error value which is missing from our data set: and this is where the residual bit comes in. That bit doesn't represent the original data (or vector) - it simply represents our 'bias' after we apply the above algorithms. It's basically like a '1-bit note' which allows you to perfectly cancel out all the bias terms which our above quantisation algorithm produces to make the 'interactions' (or inner products) when we multiply our values together extremely accurate again even after transforming our original data. Does this make sense?
They are not doing random rotation, simplification here means they are aligning the outliers. If you threw a bunch of shapes on the ground they are picking up one that rolled away and putting it with the others.
>How can a boolean value preserve all of the relational and positional information between data points?
They aren't reducing entire vector to a bollean only each of its dimensions.
He even attempts to improve on the paper by replacing the random rotation operation which is O(d^2), by a Subsampled Randomized Hadamard Transform which can be computed in O(d*log d).
Hopefully Johnson–Lindenstrauss lemma applies in the same way for SRHTransformed vectors as they do for randomly rotated vectors and the independence of the distribution laws of the coordinates remains and therefore the quantization of each coordinates independently is still theoretically sound.
For some reason I thought the implementation would be way more complicated than that. I obviously lack the domain knowledge to tackle something like this, but it looks straight forward.
It is AI generated. Or was written by someone a bit far from the technical advances IMHO. The Johnson-Lindenstrauss Lemma is a very specific and powerful concept, when in the article the QLJ explanation is vacuous. A knowledgeable human would not have left the reader wanting for how that relates to the Lemma.
“ TurboQuant, QJL, and PolarQuant are more than just practical engineering solutions; they’re fundamental algorithmic contributions backed by strong theoretical proofs. These methods don't just work well in real-world applications; they are provably efficient and operate near theoretical lower bounds.”
Only because people are lazy, and don't bother with a simple post-processing step: attach a bunch of documents or text snippets written by a human (whether yourself or, say, some respected but stylistically boring author), and ask the LLM to match style/tone.
I also instinctively reacted to that fragment, but at this point I think this is overreacting to a single expression. It's not just a normal thing to say in English, it's something people have been saying for a long time before LLMs existed.
> Redefining AI efficiency with extreme compression
"Redefine" is a favorite word of AI. Honestly no need to read further.
> the key-value cache, a high-speed "digital cheat sheet" that stores frequently used information under simple labels
No competent engineer would describe a cache as a "cheat sheet". Cheat sheets are static, but caches dynamically update during execution. Students don't rewrite their cheat sheets during the test, do they? LLMs love their inaccurate metaphors.
> QJL: The zero-overhead, 1-bit trick
> It reduces each resulting vector number to a single sign bit (+1 or -1). This algorithm essentially creates a high-speed shorthand that requires zero memory overhead.
Why does it keep emphasizing zero overhead? Why is storing a single bit a "trick?" Either there's currently an epidemic of algorithms that use more than one bit to store a bit, or the AI is shoving in extra plausible-sounding words to pad things out. You decide which is more likely.
It's 1:30am and I can't sleep, and I still regret wasting my time on this slop.
I say you're fixating on the wrong signal here. "Redefine" and "cheat sheet" are normal words people frequently use, and I see worse metaphors in human-written text routinely.
It's the structure and rhythm at the sentence and paragraph levels that's the current tell, as SOTA LLMs all seem to overuse clarification constructs like "it's not X, it's Y" and "it's X, an Y and a Z", and "it's X, it's essentially doing Y".
Thing is, I actually struggle to find what's so off-putting about these, given that they're usually used correctly. So far, the best hypothesis I have for what makes AI text stand out is that LLM output is too good. Most text written by real humans (including my own) is shit, with the best of us caring about communicating clearly, and most people not even that; nobody spends time refining the style and rhythm, unless they're writing a poem. You don't expect a blog post or a random Internet article (much less a HN comment) to be written in the same style as a NYT bestseller book for general audience - but LLMs do that naturally, they write text better at paragraph level than most people ever could, which stands out as jarring.
> Either there's currently an epidemic of algorithms that use more than one bit to store a bit, or the AI is shoving in extra plausible-sounding words to pad things out. You decide which is more likely.
Or, those things matter to authors and possibly the audience. Which is reasonable, because LLMs made the world suddenly hit hard against global capacity constraints in compute, memory, and power; between that and edge devices/local use, everyone who pays attention is interested in LLM efficiency.
LLM prose is very bland and smooth, in the same way that bland white factory bread is bland and smooth. It also typically uses a lot of words to convey very simple ideas, simply because the data is typically based on a small prompt that it tries to decompress. LLMs are capable of very good data transformation and good writing, but not when they are asked to write an article based on a single sentence.
"The X Trick" or "The Y Dilemma" or similar snowclones in a header is also a big AI thing. Humans use this construction too, but LLMs love it out of all proportion. I call it The Ludlum Delusion (since that's how every Robert Ludlum book is titled).
There is also the possibility that the article when through the hands of the company's communication department which has writers that probably write at LLM level.
Compression research keeps producing surprisingly practical results. The interesting parallel in image formats — AVIF and JPEG XL both came from video codec research (AV1 and JPEG committee respectively), and the compression gains translated almost directly. Makes me wonder how much of the current AI quantization work will eventually land in production inference the same way.
Is this a tradeoff between GPU-computation-expense vs accuracy? ie: you could quantize into segments or grids on the unit circle/sphere/etc, but that's too expensive so it's better to just quantize to a Cartesian grid because the GPU can decompress cheaper?
I am guessing as Google is vertically integrated and "actually pays" for AI infra (compared to OpenAI & Anthropic that receives hardware as partnerships) they have a more urgent incentive to reduce model sizes. Also, Google and Apple will be the first to gain from running model on-device
It seems like most breakthroughs I see are for efficiency? What are the most importsnt breakthroughs from the past two or three years for intelligence?
If you think of it from the point of view of the universal approximation theorem, it's all efficiency optimisation. We know that it works if we do it incredibly inefficiently.
Every architecture improvement is essentially a way to achieve the capability of a single fully-connected hidden layer network n wide. With fewer parameters.
Given these architectures usually still contain fully connected layers, unless they've done something really wrong, they should still be able to do anything if you make the entire thing large enough.
That means a large enough [insert model architecture] will be able to approximate any function to arbitrary precision. As long as the efficiency gains with the architecture are retained as the scale increases they should be able to get there quicker.
Most breakthroughs that are published are for efficiency because most breakthroughs that are published are for open source.'
All the foundation model breakthroughs are hoarded by the labs doing the pretraining. That being said, RL reasoning training is the obvious and largest breakthrough for intelligence in recent years.
With all the floating around of AI researchers though, I kind of wonder how "secret" all these secrets are. I'm sure they have internal siloing, but even still, big players seem to regularly defect to other labs. On top of this, all the labs seem to be pretty neck and neck, with no one clearly pulling ahead across the board.
> What are the most importsnt breakthroughs from the past two or three years for intelligence?
The most important one in that timeframe was clearly reasoning/RLVR (reinforcement learning with verifiable rewards), which was pioneered by OpenAI's Q* aka Strawberry aka o1.
That overview is frustratingly high-level. I know what a vector is, a bit, and yet that compression description is crazy uninformative. And that PolarQuant visualization is.. Very abstract.
“””
For the full technical explanation with equations, proofs, and PyTorch pseudocode, see the companion post: TurboQuant: Near-Optimal Vector Quantization Without Looking at Your Data.“
Yeah that's odd. It seems like you'd want an n-1 dimensional grid on the surface of the unit sphere rather than an n dimensional grid within which the sphere resides.
Looking at the paper (https://arxiv.org/abs/2504.19874) they cite earlier work that does exactly that. They object that grid projection and binary search perform exceptionally poorly on the GPU.
I don't think they're using a regular grid as depicted on the linked page. Equation 4 from the paper is how they compute centroids for the MSE optimal quantizer.
Why specify MSE optimal you ask? Yeah so it turns out there's actually two quantization steps, a detail also omitted from the linked page. They apply QJL quantization to the residual of the grid quantized data.
My description is almost certainly missing key details; I'm not great at math and this is sufficiently dense to be a slog.
1. Efficient recursive transform of kv embeddings into polar coordinates
2. Quantize resulting angles without the need for explicit normalization. This saves memory via key insight: angles follow a distribution and have analytical form.
The way I understand it, it's a way of compressing vectors by switching from their per-component representation to polar coordinates representation, where the nearby vectors are clumped together to a single line, allowing to describe them by different lengths
The gap between how this is described in the paper vs the blog post is pretty wide. Would be nice to see more accessible writing from research teams — not everyone reading is a ML engineer
Agreed. The practical implications are often
more interesting than the math anyway — smaller
models running locally means you can afford to
run multiple models in parallel for cross-validation,
which changes how you approach tasks like code
analysis or bug detection.
"TurboQuant proved it can quantize the key-value cache to just 3 bits without requiring training or fine-tuning and causing any compromise in model accuracy" -- what do each 3 bits correspond to? Hardly individual keys or values, since it would limit each of them to 8 different vectors.
If in short, for many inference tasks the bottleneck is memory bandwidth. Suppose you have a machine with a memory bandwidth of 256 GB/s, and let's say you want to do inference for 4B model (model with 4 billion parameters). If you will load the model in BF16 format (16 bits), each forward pass (i.e. each token generated) will require roughly ~8 GB of memory bandwidth. So, 256/8 = 32 t/s, and that's the generation speed you will be strictly capped at even if your processing power is measured in exaFLOPS. But let's say now that you have decided to instead quantize the model and then run the quantized version. Suppose you have made a Q4_K_M version (4 bits + some weights will take more). Now each of your forward passes will take roughly 2-3 GB (rough approximations, reality is different) of memory bandwith (actually, it will be around 2 GB), and even in the worst case 256/3 = 85.3, while 256/2 = 128 t/s. Quants can reduce quality of the model and lower it's performance, but in most modern quantization methods those losses are usually negligible (although, of course, they're still present). So, as you can see, it can be concluded that quantization "widens" (it's not removing it fully) memory bottleneck while still preserving (not always though) acceptable quality.
(Sorry for my terrible English, it's not my native language)
So let’s start with a really simple decoder transformer with a single layer and single attention head, and train it to predict the next token in a sequence of text. To predict the next token you need a few things: a query for the very last token in the sequence, and a key and value for every prior token. You take your query and compute a dot product with every prior key (two large vectors in, scaler attention score out). That scaler attention score first goes through softmax, and then becomes the weight you use to compute a weighted average of your values, new value goes through the mlp, mlp output is projected into the logits from which you sample your next token (that’s the general idea at least skipped a few steps).
The last query in the sequence will be new for every new token you predict, but the set of prior keys and values stay the same, ie keys and values are reusable. The key value cache gets bigger and bigger for each new token you add to the sequence, and that’s where compression comes in. You have to store the keys and values in vram, and you’d like to keep the size down by not storing the raw uncompressed tensors. To make this work well your compression needs two things: it needs to be fast so that you can compress and decompress on the fly, and it needs to play well with softmax attention. Prior attempts at compression usually suck at one or the other, either the speed to decompress is too slow and your token/s takes a hit, or you lose important precision and the model output quality suffers. The claim in the paper is that they’ve made progress on both.
So limiting max context length also reduces VRAM needs a bit? If cache is 20% of total, 1/10th of context as a limit would mean 18% total memory reduction.
Aren’t polar coordinates still n-1 + 1 for radius for n-dim vector? If so I understand that angles can be quantized better but when radius r is big the error is large for highly quantized angles right? What am I missing?
What they're saying is that the error for a vector increases with r, which is true.
Trivially, with r=0, the error is 0, regardless of how heavily the direction is quantized. Larger r means larger absolute error in the reconstructed vector.
Yes, the important part is that the normalized error does not increase with the dimension of the vector (which does happen when using biased quantizers)
It is expected that bigger vectors have proportionally bigger error, nothing can be done by the quantizer about that.
Nah, those are completely different beasts. DeepSeek's MLA solves the KV cache issue via low-rank projection - they literally squeeze the matrix through a latent vector at train time. TurboQuant is just Post-Training Quantization where they mathematically compress existing weights and activations using polar coordinates
This sounds great! TurboQuant does KV cache compression using quantization via rotations, and ParoQuant [1] does weight compression using quantization via rotations! So we can get 4-bit weights that match bf16 precision, the KV cache goes down to 3 bits per key. This brings larger models and long contexts into the range of "possibly runnable" on beefy consumer hardware.
Pied Piper vibes. As far as I can tell, this algorithm is hardly compatible with modern GPU architectures. My guess is that’s why the paper reports accuracy-vs-space, but conveniently avoids reporting inference wall-clock time. The baseline numbers also look seriously underreported. “several orders of magnitude” speedups for vector search? Really? anyone has actually reproduced these results?
Efficient execution on the GPU appears to have been one of the specific aims of the authors. Table 2 of their paper shows real world performance that would appear at a glance to be compatible with inference.
This is not an LLM inference result. Table 2 is the part I find most questionable. Claiming orders-of-magnitude improvements in vector search over standard methods is an extraordinary claim. If it actually held up in practice, I would have expected to see independent reproductions or real-world adoption by now. It’s been about a year since the paper came out, and I haven’t seen much of either. That doesn’t prove the claim is false, but it certainly doesn’t inspire confidence.
Classic academic move. If the authors show accuracy-vs-space charts but hide end-to-end latency, it usually means their code is slower in practice than vanilla fp16 without any compression. Polar coordinates are absolute poison for parallel GPU compute
So storing the diagonal as a matrix and the new bases is more compact?
But if they read your paper enough that they invited you to a talk, that probably means they were far enough along to independently inventing it they were going to do so anyway, and wanted to chat with someone who was also doing the thing they were already doing. Good ideas tend to reveal themselves to anyone who is aware of the problem.
That's more than a stretch. They likely invented them because someone thought the abstract sounded interesting, or something like that.
If I throw a bunch of shapes on the ground, tightly packed and touching each other, then rotate all of them, you can't guarantee that the new conglomerate shape is any more/less "simple" than before, right?
How can a boolean value preserve all of the relational and positional information between data points?What happens is that you get very spikey activations, there are so called "outlier" activations. A easy to read paper that tells you about this is SmoothQuant [0]. Another source from Anthropic and the Mechanistic Interperability people is calling these "privileged basis" [1].
Now based on the weight symmetries of a typical transformer, these actually don't need to exist. Weight symmetries means the ways you can change the weights without actually affecting the mathematical function, there are a broad class of these because the linear algebra has a lot of redundancies in it.
But the behaviour of the Adam optimizer is such that you do end up w/ these things because it sort of more quickly optimizes to produce them. This comes from the fact it is an elementwise dynamic learning rate (and probably partly to do with the epsilon).
[0] https://arxiv.org/pdf/2211.10438 [1] https://transformer-circuits.pub/2023/privileged-basis/index...
In simple terms, large ML models like LLMs often learn trivial rules such as "if the 21st decimal place of the 5th dimension in the embedding vector is 5 - then the image is of a cat." Learning such a memorization function is usually not what we are trying to do, and there are a variety of techniques to avoid these trivial solutions and "smooth" the optimization geometry.
>How can a boolean value preserve all of the relational and positional information between data points?
They aren't reducing entire vector to a bollean only each of its dimensions.
Hopefully Johnson–Lindenstrauss lemma applies in the same way for SRHTransformed vectors as they do for randomly rotated vectors and the independence of the distribution laws of the coordinates remains and therefore the quantization of each coordinates independently is still theoretically sound.
https://github.com/tonbistudio/turboquant-pytorch
“ TurboQuant, QJL, and PolarQuant are more than just practical engineering solutions; they’re fundamental algorithmic contributions backed by strong theoretical proofs. These methods don't just work well in real-world applications; they are provably efficient and operate near theoretical lower bounds.”
There goes another bit of my writing style that will get mistaken for an LLM.
It reads like a pop science article while at the same time being way too technical to be a pop science article.
Turing test ain't dead yet.
Only because people are lazy, and don't bother with a simple post-processing step: attach a bunch of documents or text snippets written by a human (whether yourself or, say, some respected but stylistically boring author), and ask the LLM to match style/tone.
> Redefining AI efficiency with extreme compression
"Redefine" is a favorite word of AI. Honestly no need to read further.
> the key-value cache, a high-speed "digital cheat sheet" that stores frequently used information under simple labels
No competent engineer would describe a cache as a "cheat sheet". Cheat sheets are static, but caches dynamically update during execution. Students don't rewrite their cheat sheets during the test, do they? LLMs love their inaccurate metaphors.
> QJL: The zero-overhead, 1-bit trick
> It reduces each resulting vector number to a single sign bit (+1 or -1). This algorithm essentially creates a high-speed shorthand that requires zero memory overhead.
Why does it keep emphasizing zero overhead? Why is storing a single bit a "trick?" Either there's currently an epidemic of algorithms that use more than one bit to store a bit, or the AI is shoving in extra plausible-sounding words to pad things out. You decide which is more likely.
It's 1:30am and I can't sleep, and I still regret wasting my time on this slop.
It's the structure and rhythm at the sentence and paragraph levels that's the current tell, as SOTA LLMs all seem to overuse clarification constructs like "it's not X, it's Y" and "it's X, an Y and a Z", and "it's X, it's essentially doing Y".
Thing is, I actually struggle to find what's so off-putting about these, given that they're usually used correctly. So far, the best hypothesis I have for what makes AI text stand out is that LLM output is too good. Most text written by real humans (including my own) is shit, with the best of us caring about communicating clearly, and most people not even that; nobody spends time refining the style and rhythm, unless they're writing a poem. You don't expect a blog post or a random Internet article (much less a HN comment) to be written in the same style as a NYT bestseller book for general audience - but LLMs do that naturally, they write text better at paragraph level than most people ever could, which stands out as jarring.
> Either there's currently an epidemic of algorithms that use more than one bit to store a bit, or the AI is shoving in extra plausible-sounding words to pad things out. You decide which is more likely.
Or, those things matter to authors and possibly the audience. Which is reasonable, because LLMs made the world suddenly hit hard against global capacity constraints in compute, memory, and power; between that and edge devices/local use, everyone who pays attention is interested in LLM efficiency.
Every architecture improvement is essentially a way to achieve the capability of a single fully-connected hidden layer network n wide. With fewer parameters.
Given these architectures usually still contain fully connected layers, unless they've done something really wrong, they should still be able to do anything if you make the entire thing large enough.
That means a large enough [insert model architecture] will be able to approximate any function to arbitrary precision. As long as the efficiency gains with the architecture are retained as the scale increases they should be able to get there quicker.
All the foundation model breakthroughs are hoarded by the labs doing the pretraining. That being said, RL reasoning training is the obvious and largest breakthrough for intelligence in recent years.
The most important one in that timeframe was clearly reasoning/RLVR (reinforcement learning with verifiable rewards), which was pioneered by OpenAI's Q* aka Strawberry aka o1.
Is is something like pattern based compression where the algorithm finds repeating patterns and creates an index of those common symbols or numbers?
“”” For the full technical explanation with equations, proofs, and PyTorch pseudocode, see the companion post: TurboQuant: Near-Optimal Vector Quantization Without Looking at Your Data.“
Looking at the paper (https://arxiv.org/abs/2504.19874) they cite earlier work that does exactly that. They object that grid projection and binary search perform exceptionally poorly on the GPU.
I don't think they're using a regular grid as depicted on the linked page. Equation 4 from the paper is how they compute centroids for the MSE optimal quantizer.
Why specify MSE optimal you ask? Yeah so it turns out there's actually two quantization steps, a detail also omitted from the linked page. They apply QJL quantization to the residual of the grid quantized data.
My description is almost certainly missing key details; I'm not great at math and this is sufficiently dense to be a slog.
Does this mean I would be able to run 500b model on my 48gb macbook without loosing quality?
https://mesuvash.github.io/blog/2026/turboquant-interactive/
(Sorry for my terrible English, it's not my native language)
The last query in the sequence will be new for every new token you predict, but the set of prior keys and values stay the same, ie keys and values are reusable. The key value cache gets bigger and bigger for each new token you add to the sequence, and that’s where compression comes in. You have to store the keys and values in vram, and you’d like to keep the size down by not storing the raw uncompressed tensors. To make this work well your compression needs two things: it needs to be fast so that you can compress and decompress on the fly, and it needs to play well with softmax attention. Prior attempts at compression usually suck at one or the other, either the speed to decompress is too slow and your token/s takes a hit, or you lose important precision and the model output quality suffers. The claim in the paper is that they’ve made progress on both.
Trivially, with r=0, the error is 0, regardless of how heavily the direction is quantized. Larger r means larger absolute error in the reconstructed vector.
It is expected that bigger vectors have proportionally bigger error, nothing can be done by the quantizer about that.
[1] https://github.com/z-lab/paroquant