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quants: MSE scale search to minimize NVFP4 reconstruction error #23692

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quants: MSE scale search to minimize NVFP4 reconstruction error #23692

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ggml-quants: MSE scale search to minimize FP4 SRE
sanmai May 26, 2026
676fc6a
Merge branch 'master' into feat/MSE-scale-search-FP4-rel
sanmai May 26, 2026
d24bb54
Merge branch 'master' into feat/MSE-scale-search-FP4-rel
sanmai May 26, 2026
b2b5e36
Merge branch 'master' into feat/MSE-scale-search-FP4-rel
sanmai Aug 18, 2026
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54 changes: 45 additions & 9 deletions ggml/src/ggml-quants.c
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Original file line number Diff line number Diff line change
Expand Up @@ -381,6 +381,50 @@ void quantize_row_mxfp4_ref(const float * GGML_RESTRICT x, block_mxfp4 * GGML_RE
}
}

// Find the optimal UE4M3 micro-scale for a sub-block: starting from E2M1 max,
// iterate over the adjacent codes to minimize the squared reconstruction error.
static inline uint8_t best_scale_nvfp4(const float * GGML_RESTRICT xb, int n) {
static const int try_offsets[3] = { 0, -1, 1 };

// largest absolute input value
float amax = 0.0f;
for (int j = 0; j < n; j++) {
if (amax < fabsf(xb[j])) {
amax = fabsf(xb[j]);
}
}

// UE4M3 scale: amax / 6.0 maps the max E2M1 value (6.0) to amax
const int first_code = (int) ggml_fp32_to_ue4m3(amax / 6.0f);

// best sum of squared errors
float best_sse = FLT_MAX;
int best_code = 0;
for (int t = 0; t < 3; t++) {
const int code = first_code + try_offsets[t];

// skip underflow/overflow scale codes
if (code < 0 || code > 0x7E) {
continue;
}
const float d = ggml_ue4m3_to_fp32((uint8_t) code);

float sse = 0.0f;
for (int j = 0; j < n; j++) {
// find the best code, reconstruct, collect the squared error
const int l = best_index_mxfp4(xb[j], d);
const float diff = xb[j] - d*kvalues_mxfp4[l];
sse += diff*diff;
}
if (sse < best_sse) {
best_sse = sse;
best_code = code;
}
}

return (uint8_t) best_code;
}

@sanmai sanmai Aug 18, 2026

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CUDA counterpart:

llama.cpp/ggml/src/ggml-cuda/quantize.cu

Lines 233 to 279 in 7acdbb1

static constexpr int test_offsets[5] = { 0, -1, 1, -2, 2 };
const int first_fp8_code = (int) ggml_cuda_fp32_to_ue4m3(amax_sub / 6.0f);
uint8_t fp8_code = (uint8_t) first_fp8_code;
float subblock_scale = ggml_cuda_ue4m3_to_fp32(fp8_code);
float inv_scale_err = subblock_scale > 0.0f ? 0.5f / subblock_scale : 0.0f;
#if CUDART_VERSION >= 12080
float best_err = nvfp4_native_scale_error(vals, inv_col_scale, inv_scale_err, subblock_scale);
#else
float best_err = 0.0f;
#pragma unroll
for (int k = 0; k < QK_NVFP4_SUB; ++k) {
const float v = vals[k] * inv_col_scale;
const uint8_t q = ggml_cuda_float_to_fp4_e2m1(v, inv_scale_err);
const float err_diff = fabsf(v) - fabsf(kvalues_fp4[q & 0x7]) * subblock_scale;
best_err = fmaf(err_diff, err_diff, best_err);
}
#endif // CUDART_VERSION >= 12080
#pragma unroll
for (int i = 1; i < 5; ++i) {
const int test_code = first_fp8_code + test_offsets[i];
if (test_code < 0 || test_code > 0x7e) {
continue;
}
const float test_scale = ggml_cuda_ue4m3_to_fp32((uint8_t) test_code);
const float test_inv_scale = test_scale > 0.0f ? 0.5f / test_scale : 0.0f;
#if CUDART_VERSION >= 12080
const float cur_err = nvfp4_native_scale_error(vals, inv_col_scale, test_inv_scale, test_scale);
#else
float cur_err = 0.0f;
#pragma unroll
for (int k = 0; k < QK_NVFP4_SUB; ++k) {
const float v = vals[k] * inv_col_scale;
const uint8_t q = ggml_cuda_float_to_fp4_e2m1(v, test_inv_scale);
const float err_diff = fabsf(v) - fabsf(kvalues_fp4[q & 0x7]) * test_scale;
cur_err = fmaf(err_diff, err_diff, cur_err);
}
#endif // CUDART_VERSION >= 12080
if (cur_err < best_err) {
best_err = cur_err;
fp8_code = (uint8_t) test_code;
subblock_scale = test_scale;
}
}

@sanmai sanmai Aug 18, 2026 •
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As updated in #25730 and added in #21896


void quantize_row_nvfp4_ref(const float * GGML_RESTRICT x, block_nvfp4 * GGML_RESTRICT y, int64_t k) {
static const int qk = QK_NVFP4;
static const int qk_sub = QK_NVFP4_SUB;
Expand All @@ -394,15 +438,7 @@ void quantize_row_nvfp4_ref(const float * GGML_RESTRICT x, block_nvfp4 * GGML_RE
for (int s = 0; s < n_sub; s++) {
const float * xb = x + i*qk + s*qk_sub;

float amax = 0.0f;
for (int j = 0; j < qk_sub; j++) {
if (amax < fabsf(xb[j])) {
amax = fabsf(xb[j]);
}
}

// UE4M3 scale: amax / 6.0 maps the max E2M1 value (6.0) to amax
const uint8_t ue = ggml_fp32_to_ue4m3(amax / 6.0f);
const uint8_t ue = best_scale_nvfp4(xb, qk_sub);
y[i].d[s] = ue;
const float d = ggml_ue4m3_to_fp32(ue);

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