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Multigrid

Quantisation Quality Demo: Run the Quantiser

A real absmax integer quantiser on a bits slider, with exact reconstruction error, the group-size trade, and an outlier control that shows how one weight ruins its neighbours.

Original vs reconstructed — first 64 values
Weights at 4-bit, group size 64
3.96 GiB

Against 14.90 GiB at 16-bit float, a 3.76× reduction — for an RMS reconstruction error of 0.0206 and a signal-to-noise ratio of 11.4 dB.

Values quantised
256
Groups (one scale each)
4
Integer bits per weight
4
Scale overhead per weight
0.250 bits
Effective bits per weight
4.250
RMS reconstruction error
0.0206
Largest single error
0.0629
Signal-to-noise ratio
11.4 dB
Size for 8B parameters
3.96 GiB
…at 16-bit float
14.90 GiB
What this assumes: this is symmetric absmax integer quantisation with per-group scales, which is the core of most weight-only schemes and is not all of any of them — real formats add zero-points, mixed precision for sensitive layers, and outlier channels held at higher precision, and every one of those improves on what you see here. The sample, unless you paste your own, is a seeded normal draw, because trained weights are roughly normal per channel; your model’s distribution is not this one. The 16-bit comparison is a float baseline, not this quantiser at 16 bits. Sizes are weights only: KV cache and activations are separate, and are usually what actually decides whether a model fits.

What “4-bit” is actually doing

Quantisation is discussed almost entirely in labels — Q4, INT8, FP8 — and the labels hide the two decisions that determine whether the result is usable. The first is how many distinct values a weight can take: 4-bit signed absmax gives you fifteen, spaced evenly from the largest magnitude in its group down to its negative. The second is how big that group is, because every weight in a group shares one scale factor, and the scale is set by the largest value present.

The outlier slider is there because that second decision is where quantisation actually fails. Drag it up and one weight in the first group grows; the scale grows with it; and every other weight in that group is now being represented on a ruler far too coarse for it, snapping to zero or to a step several times its own size. This is the mechanism behind every “the quantised version got noticeably worse” report, and it is why outlier-aware formats and small group sizes exist. Shrink the group and watch the damage localise.

The memory column is the reason anyone accepts any of this, and it has an honest catch that the effective-bits row makes visible: a group size of 8 stores a 16-bit scale for every 8 weights, which is 2 extra bits per weight — a 4-bit model that is really 6-bit. That trade is the whole design space.

What no amount of arithmetic here can tell you is quality. Reconstruction error is not accuracy loss: models are surprisingly tolerant of noise in most layers and surprisingly intolerant in a few. Measuring that needs the model and an eval on your own task, and any page claiming to show you four quant levels of the same model without running one is showing you an illustration.

The reasoning behind this

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Quantisation Quality Demo: Run the Quantiser · Multigrid