"This is what's happening to the parameters of models when they're quantized down to sizes that are possible to run on your laptop. Instead of floats, small integers are what get stored and loaded into memory. When the time comes to use the quantized values, to generate an answer to a question for example, the values are dequantized on the fly. You might think this sounds slower, but we'll see later on that this actually ends up being faster as well as smaller."
I thought that most GPUs supported floating point math in these quantized formats, like they can natively do math on an float4 number (that's maybe packed, 2 float4s into a single byte, or more probably 16 float4s in an 8 byte array or maybe something even bigger)
Am I getting this wrong - is it instead the GPU pulls in the quantized numbers and then converts them back into 32-bit or 64-bit float to actually run through the ALUs on the GPU? (and the memory bandwidth savings make up for the extra work to convert them back into 32 bit numbers once you get them onto the GPU?)
Or is it some weird hybrid, like there is native support for float8 and Bfloat16, but if you want to use float2 you have to convert it to float4 or something the hardware can work with.
I am confused what actually happens in the vectorized ADD and MULT instructions in the GPU with these quantized numbers.
The hardware situation is way better than you think, and quantization is a huge part of why.
Take Qwen 3.5 27B, which is a solid coding model. At FP16 it needs 54GB of VRAM. Nobody's running that on consumer hardware. At Q4_K_M quantization, it needs 16GB. A used RTX 3090 has 24GB and goes for about $900. That model runs locally with room for context.
For 14B coding models at Q4, you're looking at about 10GB. A used RTX 3060 12GB handles that for under $270.
The gap between "needs a datacenter" and "runs on my desk" is almost entirely quantization. A 27B model at Q4 loses surprisingly little quality for most coding tasks. It's not free, but it's not an RTX 7090 either. A used 3090 is probably the most recommended card in the local LLM community right now, and for good reason.
One thing from practical experience - the quality gap between model sizes shows up in a way benchmarks don't capture. I have a system where a smaller model generates plans and a larger model can override them. On any single output they look comparable. The difference shows up 3-4 steps later — small model makes a decision that sounds reasonable but compounds into a bad plan. Perplexity won't catch that, KL divergence won't either. They both measure one prediction at a time.
Leading to my question: Ok keeping a zero and a minus-zero does make sense for some limits calculations...
But when all you have is 4 bits, is this not quite wasteful? Would using the bits for eg. a 2.5 not improve the model?
I read the entire thing top-to-bottom, as a visual learner this is superb.
One nitpick -- in the "asymmetric quantification" code, shouldn't "zero" be called "midpoint" or similar? Or is "zero" an accepted mathematics term in this domain?
“Zero point” is how I saw it referred to in the literature, so that’s what I went with. I personally prefer to think of it as an offset, but I try to stick with terms folks are likely to see in the wild.
Sam's previous posts are well worth digging up too. This one is outstanding, but they're all good. I really enjoyed this and learned a lot.
I'm a bit envious of his job. Learning to teach others, and building out such cool interactive, visual documents to do it? He makes it look easier than it is, of course. A lot of effort and imagination went into this, and I'm sure it wasn't a walk in the park. Still, it seems so gratifying.
This is beautifully written and visualised, well done! The KL divergence comparisons between original and different quantisation levels is on-point. I'm not sure people realize how powerful quantisation methods are and what they've done for democratising local AI. And there are some great players out there like Unsloth and Pruna.
Thank you! I was really surprised how robust models are to losing information. It seems wrong that they can be compressed so much and still function at all, never mind function quite closely to the original size.
Think we're only going to keep seeing more progress in this area on the research side, too.
Quantization is important for me because it's the only way out I can see for a future of programming that doesn't involve going through a giant bigco who can run, as the article says, a machine with 2TB of memory. And not just memory, but my understanding is that for the model to be performant, it has to be VRAM to boot.
This comes as the latest concern of mine in a long line around "how software gets written" remaining free-as-in-freedom. I've always been really uneasy about how reliant many programming languages were on Jetbrains editors, only vaguely comforted by their "open-core" offering, which naturally only existed for languages with strong OSS competition for IDEs (so... java and python, really). "Intellisense" seemed very expensive to implement and was hugely helpful in writing programs without stopping every 4 seconds to look up whether removing whitespace at the end of a line is trim, strip, or something else in this language. I was naturally pleased to see language servers take off, even if it was much to my chagrin that it came from Microsoft, who clearly was out of open standards to EEE and decided to speed up the process by making some new ones.
Now LLMs are the next big worry of mine. It seems pretty bad for free and open software if the "2-person project, funded indirectly by the welfare state of a nordic or eastern-european nation" model that drives ridiculously important core libre/OSS libraries now is even less able to compete with trillion dollar corporations.
Open-weight, quantized, but still __good__ models seem like the only way out. I remain somewhat hopeful just from how far local models have come - they're significantly more usable than they were a year ago, and we've got more tools like LM Studio etc making running them easy. But there's still a good way to go.
I'll be sad if a "programming laptop" ends up going from "literally anything that can run debian" to "yeah you need an RTX 7090, 128GB of VRAM, and the 2kW wearable power supply backpack addon at a minimum".
I've been watching the drizzle of LLM papers come through, and I think we're going to hit a 1T param MoE on consumer hardware before this year is out. It'll still be behind the bigco models, but it'll be a force multiplier. Ideally, we'd get these models to run on a CPU. MS BitNet is one way to do this. You can already run ternary LLMs on consumer CPUs with a decent tps.
Can we still classify 5090s as consumer hardware given how expensive they are? They're £3k at the moment, and it looks like it's only going to get worse unless the AI bubble pops.
I was thinking more in terms of 24GB of VRAM total. I started sketching the architecture for such a model this afternoon, nothing novel, just combining existing advancements in the field. It looks achievable.
You can still continue to master actual software engineering while others spend their time turning their minds into a palimpsest of tricks and lessons of how to convince one model after another after another after another into giving reasonable output. That you'd still have to vet yourself anyway.
While I think a lot of the AI hype is just hype - everyone saying most of these things have _hitherto untold riches_ levels of financial incentives to say them - I think it's also undeniable that LLMs speed up many aspects of coding.
I also think that AI might be the beginning of the end of copyright. While before, everyone with money clearly had tremendous incentive to keep copyright strong, now all of a sudden trillions of dollars are basically predicated on the idea that LLMs aren't violating copyright. Copyleft has been a major tool in the FOSS toolbox. If that's weakening, I don't ALSO want free software to be locked out of agentic programming too.
It's the corrupting nature of capitalism really laid bare. A net loss for so many of their constituents that politicians all over the world are falling over themselves to pave the way for foreign companies to exploit their constituents IP.
A true tragedy of the commons unfolding before us.
I get why, and I get why it's the only realistic choice, but it really is showing the weaknesses of modern politics.
The 2 bit is probably slower because it clashes with some register sizes and how data is read in blocks. No additional benefit because the architecture doesn't read 2 bits but probably min 4 bits and then it clashes with utilization.
Most (all?) of this holds for quantizing convnets too, if you're looking for an easy exercise you can play around with quantizing resnet50 or something and plotting layer activations
Definitely could be, but in the time I spent talking to the 4-bit models in comparison to the 16-bit original it seemed surprisingly capable still. I do recommend benchmarking quantized models at the specific tasks you care about.
something I have been wondering about is doing regressive layer specific quantization based on large test sets. ie reduce very specifically layers that don't improve general quality.
This is a very well established idea. It's called dynamic quantization. Vary the quantization bit-width (or skip quantization altogether) on a layer by layer basis, using a calibration dataset.
EvoPress is the first time that comes to my mind, when I think of dynamic quantization.
I was a little confused by this part:
"This is what's happening to the parameters of models when they're quantized down to sizes that are possible to run on your laptop. Instead of floats, small integers are what get stored and loaded into memory. When the time comes to use the quantized values, to generate an answer to a question for example, the values are dequantized on the fly. You might think this sounds slower, but we'll see later on that this actually ends up being faster as well as smaller."
I thought that most GPUs supported floating point math in these quantized formats, like they can natively do math on an float4 number (that's maybe packed, 2 float4s into a single byte, or more probably 16 float4s in an 8 byte array or maybe something even bigger)
Am I getting this wrong - is it instead the GPU pulls in the quantized numbers and then converts them back into 32-bit or 64-bit float to actually run through the ALUs on the GPU? (and the memory bandwidth savings make up for the extra work to convert them back into 32 bit numbers once you get them onto the GPU?)
Or is it some weird hybrid, like there is native support for float8 and Bfloat16, but if you want to use float2 you have to convert it to float4 or something the hardware can work with.
I am confused what actually happens in the vectorized ADD and MULT instructions in the GPU with these quantized numbers.
The hardware situation is way better than you think, and quantization is a huge part of why.
Take Qwen 3.5 27B, which is a solid coding model. At FP16 it needs 54GB of VRAM. Nobody's running that on consumer hardware. At Q4_K_M quantization, it needs 16GB. A used RTX 3090 has 24GB and goes for about $900. That model runs locally with room for context.
For 14B coding models at Q4, you're looking at about 10GB. A used RTX 3060 12GB handles that for under $270.
The gap between "needs a datacenter" and "runs on my desk" is almost entirely quantization. A 27B model at Q4 loses surprisingly little quality for most coding tasks. It's not free, but it's not an RTX 7090 either. A used 3090 is probably the most recommended card in the local LLM community right now, and for good reason.
The float comparison slider is great.
One thing from practical experience - the quality gap between model sizes shows up in a way benchmarks don't capture. I have a system where a smaller model generates plans and a larger model can override them. On any single output they look comparable. The difference shows up 3-4 steps later — small model makes a decision that sounds reasonable but compounds into a bad plan. Perplexity won't catch that, KL divergence won't either. They both measure one prediction at a time.
My word... samwho is doing some of the best technical explainers on the internet right now.
Leading to my question: Ok keeping a zero and a minus-zero does make sense for some limits calculations... But when all you have is 4 bits, is this not quite wasteful? Would using the bits for eg. a 2.5 not improve the model?
Oh well that's a rabbit hole: NVIDIA Blackwell has this, also GGUFs sidestep this with Qi_j / Qi_K... Great article, spikes curiosity!
Heartily second that! It was cool to see a combination of DOM, SVG, and canvas visualization all in use for this post.
I read the entire thing top-to-bottom, as a visual learner this is superb.
One nitpick -- in the "asymmetric quantification" code, shouldn't "zero" be called "midpoint" or similar? Or is "zero" an accepted mathematics term in this domain?
“Zero point” is how I saw it referred to in the literature, so that’s what I went with. I personally prefer to think of it as an offset, but I try to stick with terms folks are likely to see in the wild.
Fair enough, thanks!
You’re welcome! Thanks so much for the kind words.
Sam's previous posts are well worth digging up too. This one is outstanding, but they're all good. I really enjoyed this and learned a lot.
I'm a bit envious of his job. Learning to teach others, and building out such cool interactive, visual documents to do it? He makes it look easier than it is, of course. A lot of effort and imagination went into this, and I'm sure it wasn't a walk in the park. Still, it seems so gratifying.
This is beautifully written and visualised, well done! The KL divergence comparisons between original and different quantisation levels is on-point. I'm not sure people realize how powerful quantisation methods are and what they've done for democratising local AI. And there are some great players out there like Unsloth and Pruna.
Thank you! I was really surprised how robust models are to losing information. It seems wrong that they can be compressed so much and still function at all, never mind function quite closely to the original size.
Think we're only going to keep seeing more progress in this area on the research side, too.
You can even train in 4 & 8 bits with newer microscaled formats! From https://arxiv.org/pdf/2310.10537 to gpt-oss being trained (partially) natively in MXFP4 - https://huggingface.co/blog/RakshitAralimatti/learn-ai-with-...
To Nemotron 3 Super, which had 25T of nvfp4 native pretraining! https://docs.nvidia.com/nemotron/0.1.0/nemotron/super3/pretr...
Quantization is important for me because it's the only way out I can see for a future of programming that doesn't involve going through a giant bigco who can run, as the article says, a machine with 2TB of memory. And not just memory, but my understanding is that for the model to be performant, it has to be VRAM to boot.
This comes as the latest concern of mine in a long line around "how software gets written" remaining free-as-in-freedom. I've always been really uneasy about how reliant many programming languages were on Jetbrains editors, only vaguely comforted by their "open-core" offering, which naturally only existed for languages with strong OSS competition for IDEs (so... java and python, really). "Intellisense" seemed very expensive to implement and was hugely helpful in writing programs without stopping every 4 seconds to look up whether removing whitespace at the end of a line is trim, strip, or something else in this language. I was naturally pleased to see language servers take off, even if it was much to my chagrin that it came from Microsoft, who clearly was out of open standards to EEE and decided to speed up the process by making some new ones.
Now LLMs are the next big worry of mine. It seems pretty bad for free and open software if the "2-person project, funded indirectly by the welfare state of a nordic or eastern-european nation" model that drives ridiculously important core libre/OSS libraries now is even less able to compete with trillion dollar corporations.
Open-weight, quantized, but still __good__ models seem like the only way out. I remain somewhat hopeful just from how far local models have come - they're significantly more usable than they were a year ago, and we've got more tools like LM Studio etc making running them easy. But there's still a good way to go.
I'll be sad if a "programming laptop" ends up going from "literally anything that can run debian" to "yeah you need an RTX 7090, 128GB of VRAM, and the 2kW wearable power supply backpack addon at a minimum".
I've been watching the drizzle of LLM papers come through, and I think we're going to hit a 1T param MoE on consumer hardware before this year is out. It'll still be behind the bigco models, but it'll be a force multiplier. Ideally, we'd get these models to run on a CPU. MS BitNet is one way to do this. You can already run ternary LLMs on consumer CPUs with a decent tps.
Though what is consumer hardware right now?
Can we still classify 5090s as consumer hardware given how expensive they are? They're £3k at the moment, and it looks like it's only going to get worse unless the AI bubble pops.
I was thinking more in terms of 24GB of VRAM total. I started sketching the architecture for such a model this afternoon, nothing novel, just combining existing advancements in the field. It looks achievable.
You can still continue to master actual software engineering while others spend their time turning their minds into a palimpsest of tricks and lessons of how to convince one model after another after another after another into giving reasonable output. That you'd still have to vet yourself anyway.
While I think a lot of the AI hype is just hype - everyone saying most of these things have _hitherto untold riches_ levels of financial incentives to say them - I think it's also undeniable that LLMs speed up many aspects of coding.
I also think that AI might be the beginning of the end of copyright. While before, everyone with money clearly had tremendous incentive to keep copyright strong, now all of a sudden trillions of dollars are basically predicated on the idea that LLMs aren't violating copyright. Copyleft has been a major tool in the FOSS toolbox. If that's weakening, I don't ALSO want free software to be locked out of agentic programming too.
Only for the AI companies. Not for you or I.
It's the corrupting nature of capitalism really laid bare. A net loss for so many of their constituents that politicians all over the world are falling over themselves to pave the way for foreign companies to exploit their constituents IP.
A true tragedy of the commons unfolding before us.
I get why, and I get why it's the only realistic choice, but it really is showing the weaknesses of modern politics.
The 2 bit is probably slower because it clashes with some register sizes and how data is read in blocks. No additional benefit because the architecture doesn't read 2 bits but probably min 4 bits and then it clashes with utilization.
Really good visualizations overall.
Most (all?) of this holds for quantizing convnets too, if you're looking for an easy exercise you can play around with quantizing resnet50 or something and plotting layer activations
5-10% accuracy is like the difference between a usable model, and unusable model.
Definitely could be, but in the time I spent talking to the 4-bit models in comparison to the 16-bit original it seemed surprisingly capable still. I do recommend benchmarking quantized models at the specific tasks you care about.
Yes I was wondering why they mentioned those numbers without mentioning their practical significance.
Man what a brilliant technical essay.. hat's off to the writer for clarity and visualizations.
Thank you!
something I have been wondering about is doing regressive layer specific quantization based on large test sets. ie reduce very specifically layers that don't improve general quality.
This is a very well established idea. It's called dynamic quantization. Vary the quantization bit-width (or skip quantization altogether) on a layer by layer basis, using a calibration dataset.
EvoPress is the first time that comes to my mind, when I think of dynamic quantization.
https://arxiv.org/abs/2410.14649
This is a thing! For example, https://arxiv.org/abs/2511.06516
that's brilliant, I wonder why we haven't seen much use of it to do very heavy quantization
since when ngrok is doing ai
https://ngrok.ai/
Oh, _that_ quantization.