Topic
6 notes · all notes
concept note
A '2-bit' model almost never stores two bits per weight. Group scales, zero points, and vector-quantization codebooks all add overhead, and papers count that overhead differently, so the bit column in a benchmark table is itself a result. I worked out the arithmetic behind the numbers this site quotes (2.0, 2.12, 2.25, 2.27) and where they stop being comparable.
concept note
Weight quantization is most of this site; the harder half of deployment is activations, where a few feature channels run tens of times larger than the rest and wreck any shared grid. Three methods define the lineage: LLM.int8 keeps the outliers in fp16, SmoothQuant migrates them into the weights, QuaRot rotates them away. I audited all three repos and verified the mechanism of each in NumPy.
concept note
A uniform quantizer has one knob, the step size. LSQ's contribution was to learn it by gradient descent on the task loss, with a step-size gradient that is sensitive to how close each value sits to a rounding boundary, plus a scale factor that keeps its updates balanced against the weights'. SEQ is ParetoQ's low-bit descendant: the same learned step size, a better-shaped grid. I read the LSQ paper and its LaTeX, audited the quantizer code that four other notes here depend on, and verified the gradient and both grids.
Markus Nagel et al., 2021 — arXiv (Qualcomm AI Research)
Nagel et al.'s 2021 white paper is still the best single on-ramp into quantization, and it's the first stop in this site's reading chain. I read it against AIMET, the toolkit its authors built to ship its recipes, verified its core algorithms numerically, and marked what the LLM era kept, what it broke, and the one footnote that predicted the whole outlier crisis.
Jerry Chee et al., 2023 — NeurIPS 2023
QuIP is where LLM quantization got its theory: a proof that GPTQ was secretly optimal within its class, a definition of what makes matrices hard to quantize, and the two-sided random rotation that fixes it. Every rotation-based method since descends from this paper. I audited the Cornell repo, reproduced the central theorem numerically to exact equality, and traced which pieces the successors kept.
concept note
Quantization and pruning papers lean on 'the Hessian' constantly, and they don't all mean the same matrix. Notes on what it is, why the layer-wise version is exactly computable, and the three different jobs it does across the literature. With small numerical experiments, one of which I got wrong on the first try.