We show that a quantized model that keeps its classification accuracy still changes $14$ to $46\%$ of its top-1 retrieval results, and that aggregate ranking metrics reveal only part of this damage. We tie this failure to the gap between the two highest scores and use that gap to decide when a quantized answer can be trusted and where additional precision should be spent.

We show that the top-1 result is guaranteed to survive quantization only when this gap exceeds twice the largest rounding error. In classification, scores are the logits, and the loss function pushes the correct class away from other classes, encouraging this gap.

In retrieval, scores are query-document scores, and nothing separates the top-1 item from the second. This gap can be measured without labels.

Before deployment, it predicts which models will break under quantization, and at deployment time it tells, per input, whether the quantized answer still matches the full-precision answer. Most classification inputs have a gap wide enough to trust the quantized answer, but few retrieval queries do.

That gap motivates a different fix in each task. In retrieval, spending extra bit-width on the layers whose quantization moves the gap most recovers up to three-quarters of an extra bit's benefit for half its cost.

In classification, routing the few low-gap inputs to full precision recovers most of the lost accuracy at a fraction of the cost.