Quantization from the Ground Up (opens in new tab)

"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.

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 nitpick -- in the "asymmetric quantification" code, shouldn't "zero" be called "midpoint" or similar? Or is "zero" an accepted mathematics term in this domain?

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'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.

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.

Really good visualizations overall.