Math Bridge: int8 Weight Round Trip

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Math BridgeEdge & FogStruggle-friendly runway

Why does 0.236 become code 60?

Follow one weight through scale selection, rounding, reconstruction, and an honest validation boundary.

Edge Eddie, the guideEdge Eddie guides
The one targetAudit one symmetric int8 round trip exactly.
The chapter caseRange [−0.50,0.50], weight 0.236, codes −127…127.
What it buys youA calculable local error without overclaiming model quality.

A field team faces an unresolved physical question: Why does 0.236 become code 60? They must answer it before changing maximum absolute calibrated weight on the real device. Predict the direction first.

See the relationship before changing it

The figure reads from left to right. The blue card is maximum absolute calibrated weight. The middle card applies this page's relationship. The green card is rms floor. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

The retained audit below checks several chapter fixtures. This added model holds every other chapter fixture fixed, so the numeric fixture does not switch without explanation.

Maximum absolute calibrated weight changes rms floor An input card leads through the page relationship to the rms floor result. SET INPUT ONE CONTROL APPLY RULE predict calculate check units READ RESULT
Walk the arrows. The range is shared across many values, so protecting a large outlier spends resolution on every ordinary weight. Calibration chooses that trade; validation decides whether it is acceptable.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline for maximum absolute calibrated weight is 0.5.

  2. 2

    Name the relationship. s=max|w|/127; code=round(w/s); ŵ=codes; error=|ŵ-w|

  3. 3

    Substitute the chapter fixture. Set maximum absolute calibrated weight to 0.5. The page ledger gives rms floor as 0.001.

  4. 4

    Read the result. Keep the stated output unit beside the value. Use it only inside the technical boundary on this page.

Predict, then change maximum absolute calibrated weight

Try Predict the direction of rms floor. Move one control, calculate, then check your prediction.

0.5
Chapter baseline
RMS floor

Observe The range is shared across many values, so protecting a large outlier spends resolution on every ordinary weight. Calibration chooses that trade; validation decides whether it is acceptable. Reset the control to 0.5 and compare rms floor.

Explain Only maximum absolute calibrated weight moves here. The other chapter fixtures remain fixed.

Check yourself

What should you do before trusting a moved-control result?
Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only maximum absolute calibrated weight moves. Field effects named in the page's technical boundary stay fixed.

Honesty note. This teaching model changes only maximum absolute calibrated weight. It replays the chapter fixture; it is not a field prediction.

1. Draw the int8 ruler

A symmetric int8 quantiser maps zero to zero and the chosen maximum magnitude to code 127. The scale is the gap between adjacent ruler marks. Each weight moves to its nearest available mark unless it lies outside the calibrated range.

Edge Eddie: Compression begins with a range decision, not with the round function.

2. Name each move

1

Set the scales = max|w|/127.

2

Normalize the weightraw code = w/s.

3

Round onceInteger code = round(raw code).

4

Reconstructŵ = integer code × s.

5

Bound ideal error|ŵ − w| ≤ s/2; σ = s/√12 across uniform positions.

3. Work 0.236 exactly

s = 0.50/127 = 0.0039370; 0.236/s = 59.944 → 60

Reconstruction gives 60s = 0.236220. The absolute error is 0.000220, below the half-step bound 0.001969. The ideal per-weight RMS floor is 0.0011365 and the ideal eight-bit ceiling is 49.9 dB.

4. Try one controlled change

s=max|w|/127; code=round(w/s); ŵ=codes; error=|ŵ−w|

TryMove only the calibrated maximum magnitude. The example weight, code count, and eight-bit ideal ceiling stay fixed.

Scale
RMS floor
Raw code
Rounded code
Reconstructed weight
Absolute error
Half-step bound
Ideal ceiling

ObserveAt max |w| = 0.50, code 60 reconstructs 0.236220 with 0.000220 error. A wider range makes the scale and error bound wider, although the chosen code may change in steps.

ExplainThe range is shared across many values, so protecting a large outlier spends resolution on every ordinary weight. Calibration chooses that trade; validation decides whether it is acceptable.

Technical boundaries.

This is one symmetric per-tensor weight quantiser with no clipping.

Granularity
Per-channel scales may preserve narrow channels better
Activations
They need their own calibration, zero point, clipping, and error analysis
Network
Layer interactions can amplify or cancel local weight errors

Use representative calibration data and compare the complete target artifact against the baseline task gates.

5. Read the half-step bound correctly

It applies to an in-range value rounded to the nearest uniform code. A clipped value can miss by much more. The RMS expression describes many positions under an ideal uniform-error assumption, not this single weight's exact error.

6. Carry a trustworthy optimization record

Record range selection, granularity, calibration set, clipped fraction, representative layer errors, full-model metrics, thresholds, latency, memory, runtime support, artifact hash, and rollback rule.

7. Check yourself

Why divide 0.50 by 127 rather than 255?
Answer: In this symmetric signed scheme, positive magnitudes run from code 0 to 127.
Why is the reconstructed value not exactly 0.236?
Answer: Only integer multiples of the selected scale are representable.
Does the 0.000220 error approve the optimized model?
Answer: No. It covers one weight; the full calibrated artifact and task behavior must pass.
Honesty boundary.

The page reproduces one chapter weight and exposes what that example cannot prove.

0.50
Chapter range maximum
60
Nearest code for 0.236
0.000220
One local reconstruction error

Go deeper in the chapter, then calibrate and validate the entire deployed model.

Return to Edge AI Model Optimization with the maths unpacked →