Quantization Error Is Spectrally Flat: A Single Random Probe Is a Calibrated, Data-Free Sensitivity Estimator, with Application to Budget-Targeted Mixed-Precision Quantization

תקציר מקורי באנגליתarXiv:2609.33923v2 Announce Type: replace-cross Abstract: A single random Gaussian probe gives an unbiased estimate of the squared Frobenius norm of a layer's quantization error. The estimator is well-behaved because round-to-nearest error is spectrally flat. Across 1,683 tensors from a 35B MoE and a 9B dense model, effective dimensionality is 0.93 to 0.96 times the i.i.d. noise value of the same shape, and on the MoE the median is unchanged from 2-bit to 8-bit. The probe coefficient of variation is predictable from tensor shape. One probe measures per-tensor sensitivity to within 4 to 7%; twenty probes reach 1.3 to 1.4%.RAM applies the propagated form of this estimator to budget-targeted mixed-precision quantization with no calibration data. Gaussian probes carrying the network's own inpu