From a04885dfaac7d9e61965acc694add83101232c31 Mon Sep 17 00:00:00 2001 From: realAsma Date: Wed, 9 Sep 2026 21:29:17 +0000 Subject: [PATCH 01/11] docs: add Local Hessian NVFP4 scaling blog Signed-off-by: realAsma --- docs/source/announcements/local-hessian.rst | 455 ++++++++++++++++++++ docs/source/index.rst | 7 + 2 files changed, 462 insertions(+) create mode 100644 docs/source/announcements/local-hessian.rst diff --git a/docs/source/announcements/local-hessian.rst b/docs/source/announcements/local-hessian.rst new file mode 100644 index 00000000000..2a54438776f --- /dev/null +++ b/docs/source/announcements/local-hessian.rst @@ -0,0 +1,455 @@ +:orphan: + +Local Hessian: Better NVFP4 Weight Scales from Layer Inputs +############################################################ + +:Author: Model Optimizer Team +:Date: September 9, 2026 +:Tags: local-hessian, quantization, nvfp4, calibration, modelopt + +NVFP4 represents each group of 16 weights with FP4 values and an FP8 block +scale [1]_. Choosing that scale is consequential: a large scale preserves a +block's outlier but spaces the representable values farther apart, while a +smaller scale resolves typical values better but clips the outlier. Max scaling +always chooses the first tradeoff. Weight mean squared error (MSE) improves it +by measuring the weights, but still treats every weight error as equally +important. + +**Local Hessian**, also called **FP4 minimum-output-squared-error (MOSE) +scaling**, chooses the scale that best preserves what a linear layer computes. +It uses calibration inputs to score each candidate scale by its contribution to +layer-output error. The method does not update the full-precision weights: the +NVFP4 format, kernels, export path, and deployment runtime do not change. + +The algorithm, without the algebra +********************************** + +For each linear layer, Local Hessian does the following: + +#. Run representative calibration data through the model and collect the input + statistics for every 16-value input-channel block. +#. For each weight block and output channel, try the 126 positive, finite FP8 + E4M3 block-scale candidates supported by NVFP4. +#. Quantize and dequantize the block with each candidate. +#. Estimate how much that block's weight error changes the layer output on the + calibration inputs. +#. Keep the candidate with the smallest estimated output error. + +Searching every block scale jointly would be combinatorial. Local Hessian makes +the practical approximation that each block can be optimized independently. +This turns the search into many small problems that can run in parallel. The +full derivation, including what the approximation drops, is in the `appendix`_. + +Why layer inputs change the answer +================================== + +Consider two weight errors of the same size. If one multiplies an input feature +that is often large, it can perturb the layer output much more than the other. +Weight MSE assigns them the same cost; Local Hessian does not. For an input +block :math:`X_k` and weight error :math:`\Delta w`, it scores + +.. math:: + + \mathcal{J}_k(s) = \Delta w(s)^{\top} H_k \Delta w(s), + \qquad + H_k = \frac{1}{N}X_k^{\top}X_k. + +The :math:`16\times16` matrix :math:`H_k` captures both the energy of each +input coordinate and correlations within the block. The scale :math:`s` affects +the score through :math:`\Delta w(s)=\mathcal{Q}_s(w)-w`. This is the same +quadratic form as the isolated block's output-reconstruction error. It is +sometimes called a local Hessian because :math:`X_k^{\top}X_k` is proportional +to the Hessian of squared reconstruction loss for that linear layer. + +Using Local Hessian in Model Optimizer +************************************** + +Use the Local Hessian NVFP4 configuration and provide a forward loop over +representative inputs: + +.. code-block:: python + + import modelopt.torch.quantization as mtq + + model = mtq.quantize( + model, + mtq.NVFP4_W4A4_WEIGHT_LOCAL_HESSIAN_CFG, + forward_loop, + ) + +The default Local Hessian block size is 16, matching NVFP4, and the calibration +forward loop is required. The implementation first max-calibrates the model, +collects per-block input second moments with weight fake quantization disabled, +and then runs a fused scale sweep where supported. Unsupported weight layouts +retain max-calibrated scales or fall back to weight MSE, with a warning where +applicable. At present, the per-block input statistics are not synchronized +across distributed ranks, so use the algorithm as a single-rank calibration +method. + +Result 1: Scale selection matters on Qwen3.5-9B +************************************************ + +Table 1 isolates weight-scale selection on Qwen3.5-9B under NVFP4 W4A4: FP4 +weights and FP4 activations. MMLU, HellaSwag, and WinoGrande are zero-shot; +GSM8K is five-shot with strict-match accuracy; WikiText reports word +perplexity. Accuracy values are percentage points. "Average drop" is the mean +of :math:`\max(\text{BF16 score}-\text{quantized score}, 0)` over the four +accuracy tasks, so lower is better. GPTQ here uses max-based scales [2]_. + +All three tables in this article report Model Optimizer team measurements. +Their supporting checkpoints, run logs, evaluator outputs, and workbooks are +team-owned artifacts; a public artifact bundle is not currently available. +Derived summary values use the workbooks' full-precision scores; task scores in +the tables are rounded for display. + +**Table 1. Qwen3.5-9B, NVFP4 W4A4 scale-setting comparison. Bold marks the +best quantized result in each column.** + +.. list-table:: + :header-rows: 1 + + * - Method + - MMLU + - HellaSwag + - WinoGrande + - GSM8K + - Average drop + - WikiText PPL + * - BF16 reference + - 78.69 + - 78.04 + - 73.40 + - 87.64 + - 0.00 + - 9.20 + * - Max scale + - 75.81 + - 76.33 + - 70.64 + - 74.60 + - 5.10 + - 10.08 + * - Weight MSE scale + - 76.49 + - 76.61 + - **72.45** + - 76.72 + - 3.87 + - 9.98 + * - Four-over-six scale + - 75.32 + - **76.62** + - 70.40 + - 76.42 + - 4.75 + - 10.02 + * - Local Hessian scale + - **76.81** + - 76.50 + - 71.19 + - **80.89** + - **3.10** + - **9.90** + * - GPTQ with max scale + - 75.77 + - 76.51 + - 70.17 + - 75.97 + - 4.84 + - 10.02 + +Among the four scale-only methods, Local Hessian reduces average accuracy drop +from 5.10 to 3.10 percentage points relative to max scaling and has the lowest +perplexity. It also produces a smaller average drop and lower perplexity than +the recorded GPTQ baseline, without applying a full-precision weight update. +The result is not a claim that one method wins every cell: for example, weight +MSE is higher on HellaSwag and WinoGrande. + +The retained team workbook identifies this model only as Qwen3.5-9B; it does +not record a model repository or checkpoint revision. It defines the reported +metrics as zero-shot MMLU accuracy, zero-shot HellaSwag normalized accuracy, +zero-shot WinoGrande accuracy, five-shot GSM8K strict-match accuracy, and +WikiText word perplexity. The same workbook contains one value per +configuration, but does not retain the calibration dataset or size, benchmark +dataset revisions, evaluator and version, hardware, repeat count, or +uncertainty. Tables 1 and 2 therefore support comparisons among these recorded +configurations, not claims of statistical significance or exact reproduction. + +Result 2: Local Hessian composes with GPTQ +****************************************** + +Local Hessian changes scales; GPTQ uses approximate second-order information to +update quantized weights and compensate error [2]_. Because they act on +different parts of the quantization problem, they can be combined. Table 2 uses +the same Qwen3.5-9B W4A4 tasks and metric definitions as Table 1. + +**Table 2. Qwen3.5-9B, NVFP4 W4A4 GPTQ composition.** + +.. list-table:: + :header-rows: 1 + + * - Method + - MMLU + - HellaSwag + - WinoGrande + - GSM8K + - Average drop + - WikiText PPL + * - GPTQ with max scale + - 75.77 + - 76.51 + - 70.17 + - 75.97 + - 4.84 + - 10.02 + * - GPTQ + weight MSE scale + - 75.94 + - **76.59** + - **71.51** + - **82.18** + - **2.89** + - 9.95 + * - GPTQ + Local Hessian scale + - **76.98** + - **76.59** + - 70.96 + - 81.50 + - 2.94 + - **9.91** + +Replacing max scales with Local Hessian scales in the GPTQ pipeline improves +all four recorded task accuracies, lowers average drop from 4.84 to 2.94 +percentage points, and lowers perplexity from 10.02 to 9.91. GPTQ plus weight +MSE has a slightly smaller average drop in this experiment; GPTQ plus Local +Hessian has the best MMLU and perplexity. This is exactly why scale selection +should remain a composable choice rather than being tied to one weight-update +algorithm. + +The Qwen3.8-27B delivery candidate +********************************** + +We then used Local Hessian while building a Qwen3.8-27B W4A4 delivery +candidate. The controlled ablation uses the same mixed-precision assignment for +both checkpoints: the dense model's MLP projections and language-model head use +either NVFP4 W4A4 or FP8, while all attention projections use FP8. Across the +layers common to both checkpoints, only the NVFP4 weight-scale rule changes +from max to Local Hessian. The max checkpoint omits the multi-token prediction +module, which accounts for the raw checkpoint-size difference; the retained +workbook normalizes both configurations to 6.31 effective bits for the +ablation. Every evaluation uses an FP8 E4M3 key-value cache. The BF16 baseline +and candidates derive from ``Qwen/Qwen3.8-27B`` revision +``1d4bf0f2ff6012fd82039f2fa52739d0dd7c60c0``. The retained records do not +specify the calibration dataset, sample count, sequence length, or batch size. + +**Table 3. Qwen3.8-27B candidate scores. Values after ± are reported standard +errors.** + +.. list-table:: + :header-rows: 1 + + * - Scale rule + - GPQA Diamond + - Terminal-Bench 2.1 + - AA-LCR + - MMMU-Pro + - SciCode + - IFBench + * - BF16 + - 88.92 ± 0.36 + - 75.56 + - 72.63 ± 0.64 + - 75.14 + - 47.93 + - 80.07 ± 0.29 + * - Max + - 87.94 ± 0.22 + - 70.79 + - **78.56 ± 0.72** + - 74.39 + - 47.04 + - 75.89 + * - Local Hessian + - **88.01 ± 0.32** + - **74.02** + - 73.38 ± 0.57 + - **74.86** + - **48.41 ± 0.43** + - **78.93 ± 0.59** + +The team's retained evaluation workbook defines the aggregate metric as a +signed mean degradation against BF16: +:math:`\operatorname{mean}(\min(\text{candidate}-\text{BF16},0))` over the +available scores other than SciCode. Local Hessian moves it from -2.14 to -0.78 +percentage points, recovering 1.36 points of mean degradation. Five of its six +scores are no more than 1.5 points below BF16, compared with four of six for +max scaling. The one regression relative to the max checkpoint is AA-LCR, +where max is also above the BF16 reference. + +The evaluation records define GPQA Diamond as pass@1 symbolic-correct accuracy +over 198 questions, averaged across 16 responses per question; AA-LCR as +pass@1 judge-correct accuracy over 100 questions, also averaged across 16 +responses; MMMU-Pro as pass@1 symbolic-correct accuracy over 1,730 entries; +SciCode as pass@1 subtask accuracy over 80 problems and 338 subtasks; IFBench +as pass@1 prompt-loose accuracy over 300 prompts, averaged across five +responses; and Terminal-Bench 2.1 as evaluator-final pass@1 over 89 tasks with +eight trials per task. MMMU-Pro uses one response per entry. SciCode uses one +evaluation run for BF16 and max and the mean of eight completed reruns for +Local Hessian; incomplete reruns are excluded. + +For GPQA Diamond, AA-LCR, and IFBench, reported standard errors are the +evaluators' across-response standard errors, expressed in percentage points. +The Local Hessian SciCode standard error is the sample standard deviation of +the eight run-level scores divided by :math:`\sqrt{8}`. Blank standard-error +cells mean no uncertainty estimate was supplied; they are not zeros. These +repeats measure sampling within one checkpoint configuration, not independent +quantization or checkpoint builds. + +The same workbook reports mean completion-token change relative to BF16, +excluding Terminal-Bench because the max-scale run has no comparable token +mean. That value is +46.1% for max scaling and +0.6% for Local Hessian. + +These results are checkpoint- and evaluation-specific. Within this controlled +scale ablation, Local Hessian materially tightened the candidate's quality +profile; the results do not imply that it will dominate max scaling on every +task or model. + +No new deployment contract +************************** + +Local Hessian is an offline calibration rule. After calibration, each block +still contains ordinary NVFP4 values and an ordinary FP8 E4M3 scale. Inference +does not evaluate a Hessian, replay calibration data, or use a new operator. +An exported Local Hessian checkpoint therefore needs no Local-Hessian-specific +runtime support. + +This separation is useful beyond GPTQ. A pipeline can change the scale rule +without changing its quantization format, mixed-precision assignment, export +schema, or serving stack. Scale search is also an active research area: +ScaleSearch searches nearby representable block scales using weight error +[3]_, ScaleSweep includes MSE and diagonally activation-weighted objectives +[4]_, and SOAR jointly optimizes global and block scales under reconstruction +error [5]_. Local Hessian's specific choice is the full :math:`16\times16` +within-block input second-moment matrix and an independent search for every +block and output channel. + +Next steps +********** + +Mixture-of-experts (MoE) models are the next important test. Routed experts see +different tokens, so their input statistics can differ sharply, and some +experts may see too few calibration samples. We plan to measure how calibration +coverage, routing balance, and scale sharing affect Local Hessian across MoE +architectures. Synchronizing the per-block statistics for distributed +calibration is another necessary step. + +We also want broader evidence across model families and evaluations, including +repeat-based uncertainty, and systematic tests of combinations with GPTQ and +other algorithms. Activation-quantization-aware MOSE, which adds an explicit +activation-error coupling term, is a separate extension; the method and results +in this article are Local Hessian without that coupling. + +Closing perspective +******************* + +Building day-zero quantized checkpoints repeatedly teaches the same lesson: the +best algorithm can change with the model and sometimes with the evaluation. +Local Hessian is not a universal replacement for every calibration method. It +is a strong, deployment-compatible addition to the Model Optimizer toolbox. + +That toolbox matters more than any single winner. Model Optimizer makes it +practical to combine algorithms, evaluate the resulting checkpoints, and +iterate while keeping the deployment target fixed. Better FP4 scale selection +is one more useful lever in that loop. + +.. _appendix: + +Appendix: Deriving the Local Hessian objective +********************************************** + +Start with one output channel and one input row. Let :math:`w_0\in\mathbb{R}^d` +be the original weight vector, :math:`w_q=w_0+\Delta w` its quantized value, +and :math:`x\in\mathbb{R}^{1\times d}` the layer input. The original and +quantized scalar outputs are + +.. math:: + + y_0=xw_0, + \qquad + y_q=xw_q. + +Their squared difference is exactly + +.. math:: + + \lVert y_q-y_0\rVert_2^2 + = \lVert x\Delta w\rVert_2^2 + = \Delta w^{\top}x^{\top}x\Delta w. + +For :math:`N` calibration tokens, stack their inputs in +:math:`X\in\mathbb{R}^{N\times d}`. The average reconstruction loss becomes + +.. math:: + + \frac{1}{N}\lVert X\Delta w\rVert_2^2 + = \Delta w^{\top}\left(\frac{1}{N}X^{\top}X\right)\Delta w. + +NVFP4 partitions the input dimension into blocks of :math:`b=16`. For block +:math:`k`, define :math:`X_k\in\mathbb{R}^{N\times b}` and + +.. math:: + + H_k=\frac{1}{N}X_k^{\top}X_k. + +For output channel :math:`j`, a candidate scale :math:`s` produces + +.. math:: + + \Delta w_{j,k}(s)=\mathcal{Q}_s(w_{0,j,k})-w_{0,j,k}. + +Local Hessian selects + +.. math:: + + s_{j,k}^{\star} + = \underset{s\in\mathcal{S}_{\mathrm{FP8}}}{\arg\min}\; + \Delta w_{j,k}(s)^{\top}H_k\Delta w_{j,k}(s). + +The implementation anchors the tensor scale at +:math:`s_{\mathrm{tensor}}=\operatorname{amax}(W_0)/6` and evaluates the 126 +valid positive, finite FP8 E4M3 block-scale multipliers. The normalization by +:math:`N` does not affect the selected scale because it multiplies every +candidate score by the same positive constant. + +For an entire layer, the exact error contains cross terms between different +input blocks: + +.. math:: + + \left\lVert\sum_k X_k\Delta w_{j,k}\right\rVert_2^2. + +Optimizing all block scales jointly would have a combinatorial search space. +Local Hessian drops the cross-block terms and minimizes each diagonal block's +contribution independently. It retains all correlations *within* each +16-coordinate block, unlike a diagonal importance-weighting approximation. +This is the approximation that makes the searches independent and parallel. + +.. _local-hessian-references: + +References +********** + +.. [1] E. Alvarez, O. Almog, E. Chung, S. Layton, D. Stosic, R. Krashinsky, + and K. Aubrey. `Introducing NVFP4 for Efficient and Accurate Low-Precision + Inference `_. + NVIDIA Technical Blog, 2025. +.. [2] E. Frantar, S. Ashkboos, T. Hoefler, and D. Alistarh. `GPTQ: Accurate + Post-Training Quantization for Generative Pre-trained Transformers + `_. ICLR, 2023. +.. [3] T. Gupta et al. `Search Your Block Floating Point Scales! + `_. MLSys, 2026. +.. [4] L. Lin and X. Wan. `ScaleSweep: Accurate NVFP4 Post-Training + Quantization of LLMs via Block Scale Initialization + `_. arXiv:2606.07618, 2026. +.. [5] C. Bao, X. Yan, Z. Li, G. Qin, G. Yu, and Y. Zhang. `SOAR: Scale + Optimization for Accurate Reconstruction in NVFP4 Quantization + `_. arXiv:2605.12245, 2026. diff --git a/docs/source/index.rst b/docs/source/index.rst index e2a871b5fe0..c0eed94970e 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -13,6 +13,7 @@ Release notes, technical updates, examples, and deployment stories from the Mode + @@ -24,6 +25,12 @@ Release notes, technical updates, examples, and deployment stories from the Mode
+
+
September 9, 2026 · Model Optimizer Team
+

Local Hessian: Better NVFP4 Weight Scales from Layer Inputs

+

Local Hessian uses calibration inputs to choose NVFP4 block scales that minimize estimated layer-output error without changing the deployment format.

+
local-hessianquantizationnvfp4calibrationmodelopt
+
August 24, 2026 · Model Optimizer Team

AutoQuantize: A Fast Automatic Mixed-Precision Assignment

From 44ffaffdd1b8446cd27772cd3962f22a5d472e26 Mon Sep 17 00:00:00 2001 From: realAsma Date: Wed, 9 Sep 2026 22:05:02 +0000 Subject: [PATCH 02/11] docs: streamline Local Hessian metric definitions Signed-off-by: realAsma --- docs/source/announcements/local-hessian.rst | 23 ++++++++++----------- 1 file changed, 11 insertions(+), 12 deletions(-) diff --git a/docs/source/announcements/local-hessian.rst b/docs/source/announcements/local-hessian.rst index 2a54438776f..8ccf86d900d 100644 --- a/docs/source/announcements/local-hessian.rst +++ b/docs/source/announcements/local-hessian.rst @@ -90,10 +90,11 @@ Result 1: Scale selection matters on Qwen3.5-9B ************************************************ Table 1 isolates weight-scale selection on Qwen3.5-9B under NVFP4 W4A4: FP4 -weights and FP4 activations. MMLU, HellaSwag, and WinoGrande are zero-shot; -GSM8K is five-shot with strict-match accuracy; WikiText reports word -perplexity. Accuracy values are percentage points. "Average drop" is the mean -of :math:`\max(\text{BF16 score}-\text{quantized score}, 0)` over the four +weights and FP4 activations. The retained team workbook defines MMLU as +zero-shot accuracy, HellaSwag as zero-shot normalized accuracy, WinoGrande as +zero-shot accuracy, GSM8K as five-shot strict-match accuracy, and WikiText as +word perplexity. Accuracy values are percentage points. "Average drop" is the +mean of :math:`\max(\text{BF16 score}-\text{quantized score}, 0)` over the four accuracy tasks, so lower is better. GPTQ here uses max-based scales [2]_. All three tables in this article report Model Optimizer team measurements. @@ -166,14 +167,12 @@ The result is not a claim that one method wins every cell: for example, weight MSE is higher on HellaSwag and WinoGrande. The retained team workbook identifies this model only as Qwen3.5-9B; it does -not record a model repository or checkpoint revision. It defines the reported -metrics as zero-shot MMLU accuracy, zero-shot HellaSwag normalized accuracy, -zero-shot WinoGrande accuracy, five-shot GSM8K strict-match accuracy, and -WikiText word perplexity. The same workbook contains one value per -configuration, but does not retain the calibration dataset or size, benchmark -dataset revisions, evaluator and version, hardware, repeat count, or -uncertainty. Tables 1 and 2 therefore support comparisons among these recorded -configurations, not claims of statistical significance or exact reproduction. +not record a model repository or checkpoint revision. The same workbook +contains one value per configuration, but does not retain the calibration +dataset or size, benchmark dataset revisions, evaluator and version, hardware, +repeat count, or uncertainty. Tables 1 and 2 therefore support comparisons +among these recorded configurations, not claims of statistical significance or +exact reproduction. Result 2: Local Hessian composes with GPTQ ****************************************** From 1dc6fc6b2cad50c2b6a226a15cef3d7a94b43f54 Mon Sep 17 00:00:00 2001 From: realAsma Date: Fri, 11 Sep 2026 22:19:26 +0000 Subject: [PATCH 03/11] docs: add accuracy figure and tighten Local Hessian blog Add a grouped bar chart of the Qwen3.8-27B W4A4 candidate scores as Figure 1, and rework the surrounding prose: - Rewrite the derivation with labeled, numbered equations and notation consistent with the appendix. - Add "How to Quantize with Local-Hessian NVFP4" with the config example and the end-to-end hf_ptq command. - Replace the deployment-contract section with a shorter one on zero deployment overhead, and condense Results and Next steps. - Fix the Four-over-six citation to point at Cook et al. (arXiv:2512.02010) and drop the now-unused references. - Style equation numbers inline and shrink the table note. 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We used this algorithm to create a low loss checkpoint +`nvidia/Qwen3.8-27B-NVFP4 `_ which can leverage NVFP4 tensor cores for performant inference on Blackwell GPUs. +Here is a comparison of accuracy results we observed for 'Local Hessian' algorithm compared to the default max algorithm: + +.. image:: assets/qwen3-27b-w4a4-scale-rule-accuracy.png + :alt: Qwen3.8-27B scores by NVFP4 weight-scale rule, BF16 baseline in gray + :width: 100% + +**Figure 1. Qwen3.8-27B NVFP4 accuracy comparison between the default NVFP4 algorithm (max) and 'Local-Hessian'.** + +Background: NVFP4 Scale Selection +********************************* + NVFP4 represents each group of 16 weights with FP4 values and an FP8 block -scale [1]_. Choosing that scale is consequential: a large scale preserves a -block's outlier but spaces the representable values farther apart, while a -smaller scale resolves typical values better but clips the outlier. Max scaling -always chooses the first tradeoff. Weight mean squared error (MSE) improves it -by measuring the weights, but still treats every weight error as equally -important. - -**Local Hessian**, also called **FP4 minimum-output-squared-error (MOSE) -scaling**, chooses the scale that best preserves what a linear layer computes. -It uses calibration inputs to score each candidate scale by its contribution to -layer-output error. The method does not update the full-precision weights: the -NVFP4 format, kernels, export path, and deployment runtime do not change. - -The algorithm, without the algebra -********************************** - -For each linear layer, Local Hessian does the following: - -#. Run representative calibration data through the model and collect the input - statistics for every 16-value input-channel block. -#. For each weight block and output channel, try the 126 positive, finite FP8 - E4M3 block-scale candidates supported by NVFP4. -#. Quantize and dequantize the block with each candidate. -#. Estimate how much that block's weight error changes the layer output on the - calibration inputs. -#. Keep the candidate with the smallest estimated output error. - -Searching every block scale jointly would be combinatorial. Local Hessian makes -the practical approximation that each block can be optimized independently. -This turns the search into many small problems that can run in parallel. The -full derivation, including what the approximation drops, is in the `appendix`_. - -Why layer inputs change the answer -================================== - -Consider two weight errors of the same size. If one multiplies an input feature -that is often large, it can perturb the layer output much more than the other. -Weight MSE assigns them the same cost; Local Hessian does not. For an input -block :math:`X_k` and weight error :math:`\Delta w`, it scores +scale [1]_. This block scale is used to scale the per-block values so to NVFP4 E2M1 range (-6.0, 6.0). +The default way is to set the block scale based on the per-block maximum value (max scaling) [1]_. + +As shown, originally in 'Four-Over-Six' paper [3]_, this block scale can be selected based on other +critieria like per-block error. While 'Four-Over-Six' selects the per-block scale from 2 candidates while +`Model-Optimizer Mean Square Error (MSE) `_ algorithm sets this based on exhuastive sweep over all positive and non-zero FP8 +scales (126 values). + +Both of these approaches for scale selection only considers weight tensor level error which we find does not correlate +well with downstream accuracy evaluation results. + +How Local Hessian Works +*********************** + +NVFP4 **Local-Hessian** chooses the scale to minimize the output error of NVFP4 matrix multiplication operation. +Specifically, we use this idea to select the per-block scale for NVFP4 weights only, +which does not required any new deployment kernels or changes from the default NVFP4 deployment - we are just computing the +per-block scales in a different way from the existing max based per-block scale selection. + + +Here is how it works. Consider a linear layer .. math:: + :label: lh-linear - \mathcal{J}_k(s) = \Delta w(s)^{\top} H_k \Delta w(s), + Y = WX, + \qquad + W\in\mathbb{R}^{C_{\mathrm{out}}\times C_{\mathrm{in}}}, \qquad - H_k = \frac{1}{N}X_k^{\top}X_k. + X\in\mathbb{R}^{C_{\mathrm{in}}\times N}, -The :math:`16\times16` matrix :math:`H_k` captures both the energy of each -input coordinate and correlations within the block. The scale :math:`s` affects -the score through :math:`\Delta w(s)=\mathcal{Q}_s(w)-w`. This is the same -quadratic form as the isolated block's output-reconstruction error. It is -sometimes called a local Hessian because :math:`X_k^{\top}X_k` is proportional -to the Hessian of squared reconstruction loss for that linear layer. +for :math:`N` calibration tokens. We quantize the weights, -Using Local Hessian in Model Optimizer -************************************** +.. math:: + :label: lh-quant -Use the Local Hessian NVFP4 configuration and provide a forward loop over -representative inputs: + W_q=\mathcal{Q}(W,s)=W+\Delta(W,s), + \qquad + \mathcal{Q}(W,s)=\operatorname{Cast}(W/s)\cdot s, -.. code-block:: python +where :math:`s` is the quantization scale, :math:`\operatorname{Cast}` +rounds to the low-precision datatype such as NVFP4, and :math:`\Delta` +is the resulting quantization error. - import modelopt.torch.quantization as mtq +Let :math:`Y_q=W_qX` be the output after quantizing the weights. + +We consider one output channel at a time. Write its weights as the row +:math:`w` and its quantization error as :math:`\Delta(w,s)`. Its +output mean squared error is + +.. math:: + :label: lh-output-error - model = mtq.quantize( - model, - mtq.NVFP4_W4A4_WEIGHT_LOCAL_HESSIAN_CFG, - forward_loop, - ) - -The default Local Hessian block size is 16, matching NVFP4, and the calibration -forward loop is required. The implementation first max-calibrates the model, -collects per-block input second moments with weight fake quantization disabled, -and then runs a fused scale sweep where supported. Unsupported weight layouts -retain max-calibrated scales or fall back to weight MSE, with a warning where -applicable. At present, the per-block input statistics are not synchronized -across distributed ranks, so use the algorithm as a single-rank calibration -method. - -Result 1: Scale selection matters on Qwen3.5-9B -************************************************ - -Table 1 isolates weight-scale selection on Qwen3.5-9B under NVFP4 W4A4: FP4 -weights and FP4 activations. The retained team workbook defines MMLU as -zero-shot accuracy, HellaSwag as zero-shot normalized accuracy, WinoGrande as -zero-shot accuracy, GSM8K as five-shot strict-match accuracy, and WikiText as -word perplexity. Accuracy values are percentage points. "Average drop" is the -mean of :math:`\max(\text{BF16 score}-\text{quantized score}, 0)` over the four -accuracy tasks, so lower is better. GPTQ here uses max-based scales [2]_. - -All three tables in this article report Model Optimizer team measurements. -Their supporting checkpoints, run logs, evaluator outputs, and workbooks are -team-owned artifacts; a public artifact bundle is not currently available. -Derived summary values use the workbooks' full-precision scores; task scores in -the tables are rounded for display. - -**Table 1. Qwen3.5-9B, NVFP4 W4A4 scale-setting comparison. Bold marks the -best quantized result in each column.** + E(s) = \lVert wX-w_qX\rVert_2^2 + = \lVert \Delta(w,s)\,X\rVert_2^2 + = \Delta(w,s)\,(XX^{\top})\,\Delta(w,s)^{\top}. + +Here :math:`XX^{\top}\in\mathbb{R}^{C_{\mathrm{in}}\times C_{\mathrm{in}}}` +is the Hessian (second order derivative) of :math:`E(s)` with respect to +:math:`\Delta(w,s)`, and it carries the output error minimization +objective into the scale decision. + +For NVFP4, the weight scale :math:`s` for one output channel is a vector +of dimension :math:`C_{\mathrm{in}}/16`, one entry per block. With +:math:`M` candidate values per entry, minimizing :math:`E(s)` jointly +means searching :math:`M^{C_{\mathrm{in}}/16}` combinations -- not +tractable. + +Per-Block Output Error Objective +================================ + +We simplify the objective in :eq:`lh-output-error` with one key +observation: each block's scale can be chosen in isolation, against the +output error that block alone contributes. +For block :math:`k`, with scale :math:`s_k`, weight error +:math:`\Delta(w_k,s_k)`, and inputs +:math:`X_k\in\mathbb{R}^{16\times N}`, + +.. math:: + :label: lh-block-error + + E_k(s_k) = \Delta(w_k,s_k)\,(X_kX_k^{\top})\,\Delta(w_k,s_k)^{\top}, + +where :math:`X_kX_k^{\top}` is only :math:`16\times16`. That is the +local Hessian, and it turns the search into many small independent +problems instead of one large one. + +For each per-block scale, we sweep over all possible 126 FP8 values, just like we do for MSE algorithm. +See the `Model Optimizer Local-Hessian code +`_ +for more details. + +Results +*********** + +Scale Selection Accuracy +======================== + +In Table 1 we compares Local-Hessian Vs other scale selection algorithms dor weights on Qwen 3.5 9B. + +Local Hessian gives the overall best accuracy among the NVFP4 +weight-scale selection methods, cutting the average drop from 5.10 to 3.10 +points against the default max rule. We get that from nothing but a +smarter way of computing the weight scale -- which says something about +micro-block formats like NVFP4: **the scale carries a lot of +information, and it pays to set it diligently.** .. list-table:: :header-rows: 1 - * - Method + * - Weight scale selection method - MMLU - HellaSwag - WinoGrande - GSM8K - - Average drop - - WikiText PPL + - Average drop :table-header-note:`(lower is better)` + - WikiText PPL :table-header-note:`(lower is better)` * - BF16 reference - 78.69 - 78.04 @@ -130,7 +156,7 @@ best quantized result in each column.** - 74.60 - 5.10 - 10.08 - * - Weight MSE scale + * - MSE scale - 76.49 - 76.61 - **72.45** @@ -149,38 +175,29 @@ best quantized result in each column.** - 76.50 - 71.19 - **80.89** - - **3.10** - - **9.90** - * - GPTQ with max scale - - 75.77 - - 76.51 - - 70.17 - - 75.97 - - 4.84 - - 10.02 + - :local-hessian-result:`3.10` + - :local-hessian-result:`9.90` + +.. rst-class:: table-note + +All layers except the final output layer (``lm_head``) use NVFP4 +weight and activation quantization (W4A4). + + +Local-Hessian + GPTQ Accuracy +============================= + +Local Hessian changes scales; GPTQ [2]_ changes weight rounding to +minimize per-layer output error. The two are orthogonal, so they +compose: Local Hessian rounds to nearest (RTN) by default, and GPTQ can +replace that rounding step once the scales are set. In Table 2, we show +that Local-Hessian scales improve GPTQ as well. + +Two things stand out: -Among the four scale-only methods, Local Hessian reduces average accuracy drop -from 5.10 to 3.10 percentage points relative to max scaling and has the lowest -perplexity. It also produces a smaller average drop and lower perplexity than -the recorded GPTQ baseline, without applying a full-precision weight update. -The result is not a claim that one method wins every cell: for example, weight -MSE is higher on HellaSwag and WinoGrande. - -The retained team workbook identifies this model only as Qwen3.5-9B; it does -not record a model repository or checkpoint revision. The same workbook -contains one value per configuration, but does not retain the calibration -dataset or size, benchmark dataset revisions, evaluator and version, hardware, -repeat count, or uncertainty. Tables 1 and 2 therefore support comparisons -among these recorded configurations, not claims of statistical significance or -exact reproduction. - -Result 2: Local Hessian composes with GPTQ -****************************************** - -Local Hessian changes scales; GPTQ uses approximate second-order information to -update quantized weights and compensate error [2]_. Because they act on -different parts of the quantization problem, they can be combined. Table 2 uses -the same Qwen3.5-9B W4A4 tasks and metric definitions as Table 1. +#. Local-Hessian scale selection alone (3.10 average drop) beats GPTQ with + max scales (4.84), with no weight update at all. +#. Composing the two improves further still, from 3.10 to 2.94. **Table 2. Qwen3.5-9B, NVFP4 W4A4 GPTQ composition.** @@ -201,236 +218,94 @@ the same Qwen3.5-9B W4A4 tasks and metric definitions as Table 1. - 75.97 - 4.84 - 10.02 - * - GPTQ + weight MSE scale - - 75.94 - - **76.59** - - **71.51** - - **82.18** - - **2.89** - - 9.95 * - GPTQ + Local Hessian scale - **76.98** - **76.59** - 70.96 - 81.50 - - 2.94 - - **9.91** - -Replacing max scales with Local Hessian scales in the GPTQ pipeline improves -all four recorded task accuracies, lowers average drop from 4.84 to 2.94 -percentage points, and lowers perplexity from 10.02 to 9.91. GPTQ plus weight -MSE has a slightly smaller average drop in this experiment; GPTQ plus Local -Hessian has the best MMLU and perplexity. This is exactly why scale selection -should remain a composable choice rather than being tied to one weight-update -algorithm. - -The Qwen3.8-27B delivery candidate -********************************** - -We then used Local Hessian while building a Qwen3.8-27B W4A4 delivery -candidate. The controlled ablation uses the same mixed-precision assignment for -both checkpoints: the dense model's MLP projections and language-model head use -either NVFP4 W4A4 or FP8, while all attention projections use FP8. Across the -layers common to both checkpoints, only the NVFP4 weight-scale rule changes -from max to Local Hessian. The max checkpoint omits the multi-token prediction -module, which accounts for the raw checkpoint-size difference; the retained -workbook normalizes both configurations to 6.31 effective bits for the -ablation. Every evaluation uses an FP8 E4M3 key-value cache. The BF16 baseline -and candidates derive from ``Qwen/Qwen3.8-27B`` revision -``1d4bf0f2ff6012fd82039f2fa52739d0dd7c60c0``. The retained records do not -specify the calibration dataset, sample count, sequence length, or batch size. - -**Table 3. Qwen3.8-27B candidate scores. Values after ± are reported standard -errors.** + - :local-hessian-result:`2.94` + - :local-hessian-result:`9.91` -.. list-table:: - :header-rows: 1 +Just Better Scales, No Runtime Cost +*********************************** - * - Scale rule - - GPQA Diamond - - Terminal-Bench 2.1 - - AA-LCR - - MMMU-Pro - - SciCode - - IFBench - * - BF16 - - 88.92 ± 0.36 - - 75.56 - - 72.63 ± 0.64 - - 75.14 - - 47.93 - - 80.07 ± 0.29 - * - Max - - 87.94 ± 0.22 - - 70.79 - - **78.56 ± 0.72** - - 74.39 - - 47.04 - - 75.89 - * - Local Hessian - - **88.01 ± 0.32** - - **74.02** - - 73.38 ± 0.57 - - **74.86** - - **48.41 ± 0.43** - - **78.93 ± 0.59** - -The team's retained evaluation workbook defines the aggregate metric as a -signed mean degradation against BF16: -:math:`\operatorname{mean}(\min(\text{candidate}-\text{BF16},0))` over the -available scores other than SciCode. Local Hessian moves it from -2.14 to -0.78 -percentage points, recovering 1.36 points of mean degradation. Five of its six -scores are no more than 1.5 points below BF16, compared with four of six for -max scaling. The one regression relative to the max checkpoint is AA-LCR, -where max is also above the BF16 reference. - -The evaluation records define GPQA Diamond as pass@1 symbolic-correct accuracy -over 198 questions, averaged across 16 responses per question; AA-LCR as -pass@1 judge-correct accuracy over 100 questions, also averaged across 16 -responses; MMMU-Pro as pass@1 symbolic-correct accuracy over 1,730 entries; -SciCode as pass@1 subtask accuracy over 80 problems and 338 subtasks; IFBench -as pass@1 prompt-loose accuracy over 300 prompts, averaged across five -responses; and Terminal-Bench 2.1 as evaluator-final pass@1 over 89 tasks with -eight trials per task. MMMU-Pro uses one response per entry. SciCode uses one -evaluation run for BF16 and max and the mean of eight completed reruns for -Local Hessian; incomplete reruns are excluded. - -For GPQA Diamond, AA-LCR, and IFBench, reported standard errors are the -evaluators' across-response standard errors, expressed in percentage points. -The Local Hessian SciCode standard error is the sample standard deviation of -the eight run-level scores divided by :math:`\sqrt{8}`. Blank standard-error -cells mean no uncertainty estimate was supplied; they are not zeros. These -repeats measure sampling within one checkpoint configuration, not independent -quantization or checkpoint builds. - -The same workbook reports mean completion-token change relative to BF16, -excluding Terminal-Bench because the max-scale run has no comparable token -mean. That value is +46.1% for max scaling and +0.6% for Local Hessian. - -These results are checkpoint- and evaluation-specific. Within this controlled -scale ablation, Local Hessian materially tightened the candidate's quality -profile; the results do not imply that it will dominate max scaling on every -task or model. - -No new deployment contract -************************** - -Local Hessian is an offline calibration rule. After calibration, each block -still contains ordinary NVFP4 values and an ordinary FP8 E4M3 scale. Inference -does not evaluate a Hessian, replay calibration data, or use a new operator. -An exported Local Hessian checkpoint therefore needs no Local-Hessian-specific -runtime support. - -This separation is useful beyond GPTQ. A pipeline can change the scale rule -without changing its quantization format, mixed-precision assignment, export -schema, or serving stack. Scale search is also an active research area: -ScaleSearch searches nearby representable block scales using weight error -[3]_, ScaleSweep includes MSE and diagonally activation-weighted objectives -[4]_, and SOAR jointly optimizes global and block scales under reconstruction -error [5]_. Local Hessian's specific choice is the full :math:`16\times16` -within-block input second-moment matrix and an independent search for every -block and output channel. +Local Hessian and the other ModelOpt scale-selection algorithms for +NVFP4 weight scales are free. Weight scales are computed only once, at +checkpoint creation, and that same scale is reused on every +deployment. Selecting scales this way improves accuracy without +incurring any deployment throughput penalty. -Next steps -********** -Mixture-of-experts (MoE) models are the next important test. Routed experts see -different tokens, so their input statistics can differ sharply, and some -experts may see too few calibration samples. We plan to measure how calibration -coverage, routing balance, and scale sharing affect Local Hessian across MoE -architectures. Synchronizing the per-block statistics for distributed -calibration is another necessary step. - -We also want broader evidence across model families and evaluations, including -repeat-based uncertainty, and systematic tests of combinations with GPTQ and -other algorithms. Activation-quantization-aware MOSE, which adds an explicit -activation-error coupling term, is a separate extension; the method and results -in this article are Local Hessian without that coupling. - -Closing perspective +Using Local Hessian ******************* -Building day-zero quantized checkpoints repeatedly teaches the same lesson: the -best algorithm can change with the model and sometimes with the evaluation. -Local Hessian is not a universal replacement for every calibration method. It -is a strong, deployment-compatible addition to the Model Optimizer toolbox. - -That toolbox matters more than any single winner. Model Optimizer makes it -practical to combine algorithms, evaluate the resulting checkpoints, and -iterate while keeping the deployment target fixed. Better FP4 scale selection -is one more useful lever in that loop. - -.. _appendix: +See the `local_hessian_calibrate API +`_ +for the calibration entry point. -Appendix: Deriving the Local Hessian objective -********************************************** +To use it in your own configuration, set the ``algorithm`` field: -Start with one output channel and one input row. Let :math:`w_0\in\mathbb{R}^d` -be the original weight vector, :math:`w_q=w_0+\Delta w` its quantized value, -and :math:`x\in\mathbb{R}^{1\times d}` the layer input. The original and -quantized scalar outputs are - -.. math:: - - y_0=xw_0, - \qquad - y_q=xw_q. - -Their squared difference is exactly - -.. math:: - - \lVert y_q-y_0\rVert_2^2 - = \lVert x\Delta w\rVert_2^2 - = \Delta w^{\top}x^{\top}x\Delta w. - -For :math:`N` calibration tokens, stack their inputs in -:math:`X\in\mathbb{R}^{N\times d}`. The average reconstruction loss becomes +.. code-block:: python -.. math:: + import modelopt.torch.quantization as mtq - \frac{1}{N}\lVert X\Delta w\rVert_2^2 - = \Delta w^{\top}\left(\frac{1}{N}X^{\top}X\right)\Delta w. + config = { + "quant_cfg": [...], # quantizer configuration + "algorithm": {"method": "local_hessian", "fp8_scale_sweep": True}, + } -NVFP4 partitions the input dimension into blocks of :math:`b=16`. For block -:math:`k`, define :math:`X_k\in\mathbb{R}^{N\times b}` and + model = mtq.quantize(model, config, forward_loop) -.. math:: +See :ref:`quant-cfg` for how to write the ``quant_cfg`` field. - H_k=\frac{1}{N}X_k^{\top}X_k. +To reproduce the published Qwen3.8-27B checkpoint end to end: -For output channel :math:`j`, a candidate scale :math:`s` produces +.. code-block:: bash -.. math:: + python examples/hf_ptq/hf_ptq.py \ + --pyt_ckpt_path Qwen/Qwen3.8-27B \ + --recipe modelopt_recipes/models/Qwen/Qwen3.8-27B/ptq/nvfp4_local_hessian-fp8_attn-kv_fp8_cast.yaml \ + --dataset nemotron-post-training-v3 \ + --calib_size 512 \ + --calib_seq 2048 \ + --batch_size 1 \ + --export_path - \Delta w_{j,k}(s)=\mathcal{Q}_s(w_{0,j,k})-w_{0,j,k}. +Batch size 1 keeps padding tokens from polluting the output error +statistics used by Local Hessian and GPTQ. -Local Hessian selects -.. math:: +Next steps +********** - s_{j,k}^{\star} - = \underset{s\in\mathcal{S}_{\mathrm{FP8}}}{\arg\min}\; - \Delta w_{j,k}(s)^{\top}H_k\Delta w_{j,k}(s). +- **Adapt Local Hessian for sparse MoEs.** Many experts in a sparse MoE + see very little calibration data. Local-Hessian workflow needs to be adapted to that + low-data regime. -The implementation anchors the tensor scale at -:math:`s_{\mathrm{tensor}}=\operatorname{amax}(W_0)/6` and evaluates the 126 -valid positive, finite FP8 E4M3 block-scale multipliers. The normalization by -:math:`N` does not affect the selected scale because it multiplies every -candidate score by the same positive constant. +Bitter Lesson: Best Method - It Depends! +**************************************************************** -For an entire layer, the exact error contains cross terms between different -input blocks: +We, the Model Optimizer team, have quantized over 80 models, all available in +the `Inference Optimized Checkpoints (with Model Optimizer) +`_ +collection. -.. math:: +Building checkpoints for various models and evaluating them teaches this +bitter lesson: the best algorithm can change with the model, the +calibration dataset, and sometimes the evaluation. - \left\lVert\sum_k X_k\Delta w_{j,k}\right\rVert_2^2. +Local Hessian gives the best accuracy recovery overall in our internal +evaluations on small dense models. However, the winning +algorithm/combination might change depending on the model. On +Qwen3.5-9B, Local Hessian + GPTQ came out ahead; on Qwen3.8-27B, plain +RTN rounding beat GPTQ on top of the same scales. Scale selection is the +reliable part; what you pair it with is not. -Optimizing all block scales jointly would have a combinatorial search space. -Local Hessian drops the cross-block terms and minimizes each diagonal block's -contribution independently. It retains all correlations *within* each -16-coordinate block, unlike a diagonal importance-weighting approximation. -This is the approximation that makes the searches independent and parallel. +What matters more than any single algorithm is a place to build +quantized checkpoints, evaluate them (see our agentic skills for +frontier evaluation), and iterate quickly. Model Optimizer is that +one-stop shop for inference optimization, and Local Hessian is one more +useful lever in the loop. .. _local-hessian-references: @@ -444,11 +319,7 @@ References .. [2] E. Frantar, S. Ashkboos, T. Hoefler, and D. Alistarh. `GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers `_. ICLR, 2023. -.. [3] T. Gupta et al. `Search Your Block Floating Point Scales! - `_. MLSys, 2026. -.. [4] L. Lin and X. Wan. `ScaleSweep: Accurate NVFP4 Post-Training - Quantization of LLMs via Block Scale Initialization - `_. arXiv:2606.07618, 2026. -.. [5] C. Bao, X. Yan, Z. Li, G. Qin, G. Yu, and Y. Zhang. `SOAR: Scale - Optimization for Accurate Reconstruction in NVFP4 Quantization - `_. arXiv:2605.12245, 2026. +.. [3] J. Cook, J. Guo, G. Xiao, Y. Lin, K. Wyss, M. Nazemi, A. Mishra, + C. del Mundo, T. Blankevoort, and S. Han. `Four Over Six: More Accurate + NVFP4 Quantization with Adaptive Block Scaling + `_. arXiv:2512.02010, 2025. \ No newline at end of file From 098303fcc09d9e6698a4c1f74f279d77c38ce90a Mon Sep 17 00:00:00 2001 From: realAsma Date: Fri, 11 Sep 2026 22:41:41 +0000 Subject: [PATCH 04/11] docs: condense the Local Hessian derivation Cut the "How Local Hessian Works" section from 61 to 45 lines without losing either equation: - Fold the linear-layer and quantization definitions into prose; only the output-error and per-block objectives keep display math. - Drop the per-block subsection heading and the restated symbol declarations that the equations already show. - State what the Hessian does instead of that it carries the objective, and give its shape. - Index blocks with b, and render the output-error equation on two aligned lines. Signed-off-by: realAsma --- docs/source/announcements/local-hessian.rst | 100 +++++++------------- 1 file changed, 35 insertions(+), 65 deletions(-) diff --git a/docs/source/announcements/local-hessian.rst b/docs/source/announcements/local-hessian.rst index e1f898ea77d..04b0fdadbf5 100644 --- a/docs/source/announcements/local-hessian.rst +++ b/docs/source/announcements/local-hessian.rst @@ -39,83 +39,53 @@ well with downstream accuracy evaluation results. How Local Hessian Works *********************** -NVFP4 **Local-Hessian** chooses the scale to minimize the output error of NVFP4 matrix multiplication operation. -Specifically, we use this idea to select the per-block scale for NVFP4 weights only, -which does not required any new deployment kernels or changes from the default NVFP4 deployment - we are just computing the -per-block scales in a different way from the existing max based per-block scale selection. - - -Here is how it works. Consider a linear layer - -.. math:: - :label: lh-linear - - Y = WX, - \qquad - W\in\mathbb{R}^{C_{\mathrm{out}}\times C_{\mathrm{in}}}, - \qquad - X\in\mathbb{R}^{C_{\mathrm{in}}\times N}, - -for :math:`N` calibration tokens. We quantize the weights, - -.. math:: - :label: lh-quant - - W_q=\mathcal{Q}(W,s)=W+\Delta(W,s), - \qquad - \mathcal{Q}(W,s)=\operatorname{Cast}(W/s)\cdot s, - -where :math:`s` is the quantization scale, :math:`\operatorname{Cast}` -rounds to the low-precision datatype such as NVFP4, and :math:`\Delta` -is the resulting quantization error. - -Let :math:`Y_q=W_qX` be the output after quantizing the weights. - -We consider one output channel at a time. Write its weights as the row -:math:`w` and its quantization error as :math:`\Delta(w,s)`. Its -output mean squared error is +NVFP4 **Local-Hessian** chooses each per-block weight scale to minimize +the *output* error of the matrix multiplication rather than the weight +error. Nothing about the format changes -- we just compute the per-block +scales differently from max scaling. + +Consider a linear layer :math:`Y=WX` with weights +:math:`W\in\mathbb{R}^{C_{\mathrm{out}}\times C_{\mathrm{in}}}` and +calibration inputs +:math:`X\in\mathbb{R}^{C_{\mathrm{in}}\times N}`, where :math:`N` is the +number of calibration tokens. Quantizing divides by a scale and casts, +:math:`\mathcal{Q}(W,s)=\operatorname{Cast}(W/s)\cdot s`, leaving an +error :math:`\Delta(W,s)=\mathcal{Q}(W,s)-W`. Taking one output channel +at a time, with its weights in the row :math:`w`, the output mean +squared error is .. math:: :label: lh-output-error - E(s) = \lVert wX-w_qX\rVert_2^2 - = \lVert \Delta(w,s)\,X\rVert_2^2 - = \Delta(w,s)\,(XX^{\top})\,\Delta(w,s)^{\top}. + E(s) &= \lVert wX-w_qX\rVert_2^2 + = \lVert \Delta(w,s)\,X\rVert_2^2 \\ + &= \Delta(w,s)\,(XX^{\top})\,\Delta(w,s)^{\top}. -Here :math:`XX^{\top}\in\mathbb{R}^{C_{\mathrm{in}}\times C_{\mathrm{in}}}` -is the Hessian (second order derivative) of :math:`E(s)` with respect to -:math:`\Delta(w,s)`, and it carries the output error minimization -objective into the scale decision. +The input second-moment matrix +:math:`XX^{\top}\in\mathbb{R}^{C_{\mathrm{in}}\times C_{\mathrm{in}}}` is +the 'Hessian' of the output error, i.e, +:math:`\partial^2E(s)/\partial\Delta(w,s)^2`: it weights each +weight error by how much that input coordinate actually moves the +output. -For NVFP4, the weight scale :math:`s` for one output channel is a vector -of dimension :math:`C_{\mathrm{in}}/16`, one entry per block. With -:math:`M` candidate values per entry, minimizing :math:`E(s)` jointly -means searching :math:`M^{C_{\mathrm{in}}/16}` combinations -- not -tractable. - -Per-Block Output Error Objective -================================ - -We simplify the objective in :eq:`lh-output-error` with one key -observation: each block's scale can be chosen in isolation, against the -output error that block alone contributes. -For block :math:`k`, with scale :math:`s_k`, weight error -:math:`\Delta(w_k,s_k)`, and inputs -:math:`X_k\in\mathbb{R}^{16\times N}`, +For NVFP4, :math:`s` is not a scalar: each output channel has +:math:`C_{\mathrm{in}}/16` blocks, one scale each. With :math:`M` +candidates per block, minimizing :math:`E(s)` jointly means searching +:math:`M^{C_{\mathrm{in}}/16}` combinations -- this is not tractable. So we +choose each block's scale in isolation, against the output error that +block alone contributes. For block :math:`b`, .. math:: :label: lh-block-error - E_k(s_k) = \Delta(w_k,s_k)\,(X_kX_k^{\top})\,\Delta(w_k,s_k)^{\top}, - -where :math:`X_kX_k^{\top}` is only :math:`16\times16`. That is the -local Hessian, and it turns the search into many small independent -problems instead of one large one. + E_b(s_b) = \Delta(w_b,s_b)\,(X_bX_b^{\top})\,\Delta(w_b,s_b)^{\top}, -For each per-block scale, we sweep over all possible 126 FP8 values, just like we do for MSE algorithm. -See the `Model Optimizer Local-Hessian code +where the local Hessian :math:`X_bX_b^{\top}` is only +:math:`16\times16`. For each block we sweep all 126 candidate FP8 +scales, just as the MSE algorithm does. See the `Model Optimizer +Local-Hessian code `_ -for more details. +for details. Results *********** From a86c1b13ddcf2feec0cfca0eddcb87732938b208 Mon Sep 17 00:00:00 2001 From: realAsma Date: Fri, 11 Sep 2026 23:00:16 +0000 Subject: [PATCH 05/11] docs: add mean accuracy drop to Figure 1, reword the landing card Figure 1 now carries the aggregate the blog argues from: a boxed summary of mean(min(candidate - BF16, 0)) for each scale rule, placed above the plot at the right so it clears the bars. The script derives it from the plotted series rather than hardcoding, so it cannot drift from the bars if the benchmark set changes. The value is 2.31 / 0.77 over the five benchmarks shown, not the 2.14 / 0.78 in the team workbook, which averages a different set (includes AA-LCR, excludes SciCode). Matching the figure keeps it verifiable from the chart. Also rewords the announcements landing-page card to promise the method and the comparison, updating data-summary and the visible text together so tag filtering and display stay in sync. 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-
+
September 9, 2026 · Model Optimizer Team

Local Hessian: Better NVFP4 Weight Scales from Layer Inputs

-

Local Hessian uses calibration inputs to choose NVFP4 block scales that minimize estimated layer-output error without changing the deployment format.

+

How Local Hessian sets NVFP4 block scales from layer inputs, and how it measures up against max, MSE, Four-over-six and GPTQ.

local-hessianquantizationnvfp4calibrationmodelopt
From 9a9fca6e45fc5f7fb2e9d0706283f8893bd33530 Mon Sep 17 00:00:00 2001 From: realAsma Date: Sat, 12 Sep 2026 00:40:57 +0000 Subject: [PATCH 06/11] docs: add calibration notes, renumber refs, drop closing section - Enable layerwise calibration in the config example, with get_qdq_activations_from_prev_layer, and explain the sequence in a note: each layer is calibrated, its outputs collected with fake quantization, and those activations feed the next layer. - Move the batch-size-1 rationale into a second note, generalized to any calibration that depends on activation statistics. - Renumber references by first citation: Four-over-six is [2], GPTQ [3]. - Remove the closing "Bitter Lesson" section. Signed-off-by: realAsma --- docs/source/announcements/local-hessian.rst | 63 +++++++++------------ 1 file changed, 28 insertions(+), 35 deletions(-) diff --git a/docs/source/announcements/local-hessian.rst b/docs/source/announcements/local-hessian.rst index 04b0fdadbf5..b8888912583 100644 --- a/docs/source/announcements/local-hessian.rst +++ b/docs/source/announcements/local-hessian.rst @@ -28,7 +28,7 @@ NVFP4 represents each group of 16 weights with FP4 values and an FP8 block scale [1]_. This block scale is used to scale the per-block values so to NVFP4 E2M1 range (-6.0, 6.0). The default way is to set the block scale based on the per-block maximum value (max scaling) [1]_. -As shown, originally in 'Four-Over-Six' paper [3]_, this block scale can be selected based on other +As shown, originally in 'Four-Over-Six' paper [2]_, this block scale can be selected based on other critieria like per-block error. While 'Four-Over-Six' selects the per-block scale from 2 candidates while `Model-Optimizer Mean Square Error (MSE) `_ algorithm sets this based on exhuastive sweep over all positive and non-zero FP8 scales (126 values). @@ -157,7 +157,7 @@ weight and activation quantization (W4A4). Local-Hessian + GPTQ Accuracy ============================= -Local Hessian changes scales; GPTQ [2]_ changes weight rounding to +Local Hessian changes scales; GPTQ [3]_ changes weight rounding to minimize per-layer output error. The two are orthogonal, so they compose: Local Hessian rounds to nearest (RTN) by default, and GPTQ can replace that rounding step once the scales are set. In Table 2, we show @@ -221,7 +221,14 @@ To use it in your own configuration, set the ``algorithm`` field: config = { "quant_cfg": [...], # quantizer configuration - "algorithm": {"method": "local_hessian", "fp8_scale_sweep": True}, + "algorithm": { + "method": "local_hessian", + "fp8_scale_sweep": True, + "layerwise": { + "enable": True, + "get_qdq_activations_from_prev_layer": True, + }, + }, } model = mtq.quantize(model, config, forward_loop) @@ -241,8 +248,19 @@ To reproduce the published Qwen3.8-27B checkpoint end to end: --batch_size 1 \ --export_path -Batch size 1 keeps padding tokens from polluting the output error -statistics used by Local Hessian and GPTQ. +.. note:: + + We use layerwise calibration: layers are calibrated one at a time. + The first layer is quantized and calibrated, its outputs are then + collected with fake quantization applied, and those activations feed + the next layer. Each layer therefore calibrates on the input + distribution it will actually see at deployment. + +.. note:: + + We set batch size 1 for calibration that depends on activation + statistics -- Local Hessian, GPTQ and similar -- so that padding + tokens do not contaminate those statistics. Next steps @@ -252,31 +270,6 @@ Next steps see very little calibration data. Local-Hessian workflow needs to be adapted to that low-data regime. -Bitter Lesson: Best Method - It Depends! -**************************************************************** - -We, the Model Optimizer team, have quantized over 80 models, all available in -the `Inference Optimized Checkpoints (with Model Optimizer) -`_ -collection. - -Building checkpoints for various models and evaluating them teaches this -bitter lesson: the best algorithm can change with the model, the -calibration dataset, and sometimes the evaluation. - -Local Hessian gives the best accuracy recovery overall in our internal -evaluations on small dense models. However, the winning -algorithm/combination might change depending on the model. On -Qwen3.5-9B, Local Hessian + GPTQ came out ahead; on Qwen3.8-27B, plain -RTN rounding beat GPTQ on top of the same scales. Scale selection is the -reliable part; what you pair it with is not. - -What matters more than any single algorithm is a place to build -quantized checkpoints, evaluate them (see our agentic skills for -frontier evaluation), and iterate quickly. Model Optimizer is that -one-stop shop for inference optimization, and Local Hessian is one more -useful lever in the loop. - .. _local-hessian-references: References @@ -286,10 +279,10 @@ References and K. Aubrey. `Introducing NVFP4 for Efficient and Accurate Low-Precision Inference `_. NVIDIA Technical Blog, 2025. -.. [2] E. Frantar, S. Ashkboos, T. Hoefler, and D. Alistarh. `GPTQ: Accurate - Post-Training Quantization for Generative Pre-trained Transformers - `_. ICLR, 2023. -.. [3] J. Cook, J. Guo, G. Xiao, Y. Lin, K. Wyss, M. Nazemi, A. Mishra, +.. [2] J. Cook, J. Guo, G. Xiao, Y. Lin, K. Wyss, M. Nazemi, A. Mishra, C. del Mundo, T. Blankevoort, and S. Han. `Four Over Six: More Accurate NVFP4 Quantization with Adaptive Block Scaling - `_. arXiv:2512.02010, 2025. \ No newline at end of file + `_. arXiv:2512.02010, 2025. +.. [3] E. Frantar, S. Ashkboos, T. Hoefler, and D. Alistarh. `GPTQ: Accurate + Post-Training Quantization for Generative Pre-trained Transformers + `_. ICLR, 2023. From 66468082406799f1bf0f060b8dd2bce3b3523f75 Mon Sep 17 00:00:00 2001 From: realAsma Date: Sat, 12 Sep 2026 02:45:26 +0000 Subject: [PATCH 07/11] docs: add a title to the Local Hessian accuracy figure Figure 1 now carries "Qwen 3.8 27B NVFP4 Quantized Accuracy" so the image is self-describing when reused outside the blog. 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Co-Authored-By: Claude Opus 5 (1M context) Signed-off-by: realAsma --- docs/source/_static/announcements.css | 24 ++- .../qwen3-27b-scaled-weight-distribution.png | Bin 0 -> 64880 bytes .../qwen3-27b-w4a4-scale-rule-accuracy.png | Bin 96425 -> 96118 bytes docs/source/announcements/local-hessian.rst | 143 ++++++++++++------ docs/source/index.rst | 8 +- 5 files changed, 122 insertions(+), 53 deletions(-) create mode 100644 docs/source/announcements/assets/qwen3-27b-scaled-weight-distribution.png diff --git a/docs/source/_static/announcements.css b/docs/source/_static/announcements.css index 0d3aa46859c..331588a58e7 100644 --- a/docs/source/_static/announcements.css +++ b/docs/source/_static/announcements.css @@ -158,6 +158,20 @@ div.math span.eqno { transform: translateY(-50%); } +/* Display equations: shibuya gives `.yue .math-wrapper` a 2rem margin top and + bottom, and MathJax adds its own margin on the container inside it. The + wrapper sets `overflow-x: auto`, so none of it collapses with the + neighbouring paragraph margins and the gap around every equation ends up + oversized. Drop the MathJax margin and set the spacing on the wrapper. */ +.yue .math-wrapper { + margin-top: 1rem; + margin-bottom: 1rem; +} + +.yue .math-wrapper mjx-container[display="true"] { + margin: 0; +} + .yue strong.local-hessian-result { color: #76b900; font-size: 1.15em; @@ -173,7 +187,15 @@ div.math span.eqno { font-size: 0.75rem; line-height: 1.4; color: var(--sy-c-light); - margin-top: -2.25rem; +} + +/* A `.table-note` right after a table is that table's caption, so pull it up + against the table. Shibuya gives `.table-wrapper` a 2rem bottom margin; this + margin collapses with the note's own, so the negative value here nets out to + a small gap. The `.yue .table-wrapper +` prefix is needed to outrank the + theme's paragraph spacing, and keeps figure captions on default spacing. */ +.yue .table-wrapper + p.table-note { + margin-top: -1.75rem; } .table-note strong, diff --git a/docs/source/announcements/assets/qwen3-27b-scaled-weight-distribution.png b/docs/source/announcements/assets/qwen3-27b-scaled-weight-distribution.png new file mode 100644 index 0000000000000000000000000000000000000000..78305f4ab57c1aab1cef0fe15819fa9b5847ba80 GIT binary patch literal 64880 zcmcG$1yq&o);78Tr5gnVrKKe$q!9$9B@{s#>F!3Q8x%!ENu1x9VH@6pk0wAFb<{2d*1eSPuf*4BX&r@@S&A+4j66T{)J&+%*Q936SQea@#= zSA*x~OoAsy6PybzE-%iz@LL!ZHe)}W=n4P6I6vLDQPdz=k)qDq=x#g_5+fn%XF%Si z7jr}fo)J!#jNJ_8#k^B2)G>`9SP3) zM!kOh`jv{<@ioL&E2W*_T(YmPZ;U*6K&D#g*w`}@Q&T#zi<|E_^@_v>>7#EanIU@4>DHLbqqCuvVhO#5r~-Q5MXORYoe>+3BiJ7RZsclQfj zR{Ck6 zZgM3!%d4ogy=8l{cjyuT)+0D4=F;#xQz2sH&b@m#f(fWwKRu|M`4LO6RldcvHd;ol zQ)>OPt}dllG>TgMu|n^N*>q!I7k-*{rR)02j*WG=&1fktoEv_7U~kWLus#~BnfG{h 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-Improving NVFP4 Accuracy with Local Hessian Weight Scales +Improving NVFP4 Accuracy with Local-Hessian Weight Scales ######################################################### :Author: Model Optimizer Team @@ -13,7 +13,7 @@ Improving NVFP4 Accuracy with Local Hessian Weight Scales In this blog, we share about Model Optimizer 'Local-Hessian', an algorithm for NVFP4 per-block scale selection to minimize the output error. We used this algorithm to create a low loss checkpoint `nvidia/Qwen3.8-27B-NVFP4 `_ which can leverage NVFP4 tensor cores for performant inference on Blackwell GPUs. -Here is a comparison of accuracy results we observed for 'Local Hessian' algorithm compared to the default max algorithm: +Here is a comparison of accuracy results we observed for 'Local-Hessian' algorithm compared to the default max algorithm: .. image:: assets/qwen3-27b-w4a4-scale-rule-accuracy.png :alt: Qwen3.8-27B scores by NVFP4 weight-scale rule, BF16 baseline in gray @@ -21,8 +21,8 @@ Here is a comparison of accuracy results we observed for 'Local Hessian' algorit **Figure 1. Qwen3.8-27B NVFP4 accuracy comparison between the default NVFP4 algorithm (max) and 'Local-Hessian'.** -Background: NVFP4 Scale Selection -********************************* +Scale Selection For NVFP4 +************************** NVFP4 represents each group of 16 weights with FP4 values and an FP8 block scale [1]_. This block scale is used to scale the per-block values so to NVFP4 E2M1 range (-6.0, 6.0). @@ -36,7 +36,7 @@ scales (126 values). Both of these approaches for scale selection only considers weight tensor level error which we find does not correlate well with downstream accuracy evaluation results. -How Local Hessian Works +How Local-Hessian Works *********************** NVFP4 **Local-Hessian** chooses each per-block weight scale to minimize @@ -48,25 +48,40 @@ Consider a linear layer :math:`Y=WX` with weights :math:`W\in\mathbb{R}^{C_{\mathrm{out}}\times C_{\mathrm{in}}}` and calibration inputs :math:`X\in\mathbb{R}^{C_{\mathrm{in}}\times N}`, where :math:`N` is the -number of calibration tokens. Quantizing divides by a scale and casts, -:math:`\mathcal{Q}(W,s)=\operatorname{Cast}(W/s)\cdot s`, leaving an -error :math:`\Delta(W,s)=\mathcal{Q}(W,s)-W`. Taking one output channel -at a time, with its weights in the row :math:`w`, the output mean -squared error is +number of calibration tokens. Quantizing divides the weights by a scale +and casts, where the cast rounds each value onto the grid of the +low-precision format: + +.. math:: + :label: lh-quant + + \mathcal{Q}(W,s)=\operatorname{Cast}(W/s)\cdot s. + +This leaves a quantization error + +.. math:: + :label: lh-quant-error + + \Delta(W,s)=\mathcal{Q}(W,s)-W. + +What we actually care about is the error this puts on the layer output, +measured over the calibration set: .. math:: :label: lh-output-error - E(s) &= \lVert wX-w_qX\rVert_2^2 - = \lVert \Delta(w,s)\,X\rVert_2^2 \\ - &= \Delta(w,s)\,(XX^{\top})\,\Delta(w,s)^{\top}. + E(s) &= \lVert WX-\mathcal{Q}(W,s)\,X\rVert_F^2 + = \lVert \Delta(W,s)\,X\rVert_F^2 \\ + &= \operatorname{tr}\!\left(\Delta(W,s)\,(XX^{\top})\, + \Delta(W,s)^{\top}\right). The input second-moment matrix :math:`XX^{\top}\in\mathbb{R}^{C_{\mathrm{in}}\times C_{\mathrm{in}}}` is -the 'Hessian' of the output error, i.e, -:math:`\partial^2E(s)/\partial\Delta(w,s)^2`: it weights each +half the Hessian of the output error, +:math:`\partial^2E(s)/\partial\Delta(W,s)^2=2XX^{\top}`: it weights each weight error by how much that input coordinate actually moves the -output. +output. The trace sums one such quadratic form per output channel, so +the output channels are independent and can be handled separately. For NVFP4, :math:`s` is not a scalar: each output channel has :math:`C_{\mathrm{in}}/16` blocks, one scale each. With :math:`M` @@ -78,24 +93,28 @@ block alone contributes. For block :math:`b`, .. math:: :label: lh-block-error - E_b(s_b) = \Delta(w_b,s_b)\,(X_bX_b^{\top})\,\Delta(w_b,s_b)^{\top}, + E_b(s_b) = \Delta(W_b,s_b)\,(X_bX_b^{\top})\,\Delta(W_b,s_b)^{\top}, -where the local Hessian :math:`X_bX_b^{\top}` is only -:math:`16\times16`. For each block we sweep all 126 candidate FP8 -scales, just as the MSE algorithm does. See the `Model Optimizer -Local-Hessian code +where :math:`W_b\in\mathbb{R}^{1\times16}` is one NVFP4 block of weights, +:math:`s_b` is that block's scale, and +:math:`X_b\in\mathbb{R}^{16\times N}` holds the rows of :math:`X` the +block multiplies, so the local Hessian :math:`X_bX_b^{\top}` is only +:math:`16\times16`. We sweep all 126 candidate FP8 scales per block, just +as the MSE algorithm does; because blocks are independent, a `Triton kernel +`_ +does the whole layer at once. See the `Model Optimizer Local-Hessian code `_ for details. -Results -*********** +Local-Hessian Results +********************** -Scale Selection Accuracy -======================== +Accuracy Comparison +==================== In Table 1 we compares Local-Hessian Vs other scale selection algorithms dor weights on Qwen 3.5 9B. -Local Hessian gives the overall best accuracy among the NVFP4 +Local-Hessian gives the overall best accuracy among the NVFP4 weight-scale selection methods, cutting the average drop from 5.10 to 3.10 points against the default max rule. We get that from nothing but a smarter way of computing the weight scale -- which says something about @@ -140,7 +159,7 @@ information, and it pays to set it diligently.** - 76.42 - 4.75 - 10.02 - * - Local Hessian scale + * - Local-Hessian scale - **76.81** - 76.50 - 71.19 @@ -150,26 +169,25 @@ information, and it pays to set it diligently.** .. rst-class:: table-note -All layers except the final output layer (``lm_head``) use NVFP4 -weight and activation quantization (W4A4). +**Table 1: Scale selection algorithm comparison.** All layers except the final +output layer (``lm_head``) use NVFP4 weight and activation quantization (W4A4). -Local-Hessian + GPTQ Accuracy -============================= +Local-Hessian With GPTQ +================================= -Local Hessian changes scales; GPTQ [3]_ changes weight rounding to +Local-Hessian changes scales; GPTQ [3]_ changes weight rounding to minimize per-layer output error. The two are orthogonal, so they -compose: Local Hessian rounds to nearest (RTN) by default, and GPTQ can +compose: Local-Hessian rounds to nearest (RTN) by default, and GPTQ can replace that rounding step once the scales are set. In Table 2, we show that Local-Hessian scales improve GPTQ as well. Two things stand out: #. Local-Hessian scale selection alone (3.10 average drop) beats GPTQ with - max scales (4.84), with no weight update at all. -#. Composing the two improves further still, from 3.10 to 2.94. - -**Table 2. Qwen3.5-9B, NVFP4 W4A4 GPTQ composition.** + max scales (4.84). +#. Combining Local-Hessian scales with GPTQ improves the average drop further, + from 3.10 to 2.94. .. list-table:: :header-rows: 1 @@ -181,14 +199,14 @@ Two things stand out: - GSM8K - Average drop - WikiText PPL - * - GPTQ with max scale + * - Max scale + GPTQ - 75.77 - 76.51 - 70.17 - 75.97 - 4.84 - 10.02 - * - GPTQ + Local Hessian scale + * - Local-Hessian scale + GPTQ - **76.98** - **76.59** - 70.96 @@ -196,17 +214,48 @@ Two things stand out: - :local-hessian-result:`2.94` - :local-hessian-result:`9.91` +.. rst-class:: table-note + +**Table 2: GPTQ composition on Qwen3.5-9B, NVFP4 W4A4.** + +.. note:: + + Composition is not always a win: on Qwen3.8-27B, Local-Hessian + GPTQ scored + below Local-Hessian alone, so the published checkpoint uses Local-Hessian + only. This shows the best algorithm could vary depending on the model. + +Scale Selection Reshapes Distribution +************************************* + +Figure 2 plots the scaled weights :math:`W/s` -- the values handed to the +E2M1 cast. Max scaling piles the mass up near 6.0, the largest E2M1 value, +while MSE and Local-Hessian both cluster it on the representable grid +values. Grid alignment is not the whole story, though: among the scales +that do align, Local-Hessian picks the ones that hold up better on +evaluation. + + +.. image:: assets/qwen3-27b-scaled-weight-distribution.png + :alt: Scaled weight distribution for max, MSE and Local-Hessian scales against the NVFP4 E2M1 grid + :width: 100% + +.. rst-class:: table-note + +**Figure 2. Scaled weight distribution across algorithms.** Blue +dashed lines are the NVFP4 E2M1 representable values. Distribution is for the +first gate-projection layer of Qwen3.8-27B. + Just Better Scales, No Runtime Cost *********************************** -Local Hessian and the other ModelOpt scale-selection algorithms for +Local-Hessian and the other ModelOpt scale-selection algorithms for NVFP4 weight scales are free. Weight scales are computed only once, at checkpoint creation, and that same scale is reused on every deployment. Selecting scales this way improves accuracy without incurring any deployment throughput penalty. -Using Local Hessian +Using Local-Hessian ******************* See the `local_hessian_calibrate API @@ -250,23 +299,21 @@ To reproduce the published Qwen3.8-27B checkpoint end to end: .. note:: - We use layerwise calibration: layers are calibrated one at a time. - The first layer is quantized and calibrated, its outputs are then - collected with fake quantization applied, and those activations feed - the next layer. Each layer therefore calibrates on the input - distribution it will actually see at deployment. + Calibration is layerwise: each layer is calibrated on the fake-quantized + outputs of the one before it, so later layers get an activation + distribution that accounts for the quantization of the earlier layers. .. note:: We set batch size 1 for calibration that depends on activation - statistics -- Local Hessian, GPTQ and similar -- so that padding + statistics -- Local-Hessian, GPTQ and similar -- so that padding tokens do not contaminate those statistics. Next steps ********** -- **Adapt Local Hessian for sparse MoEs.** Many experts in a sparse MoE +- **Adapt Local-Hessian for sparse MoEs.** Many experts in a sparse MoE see very little calibration data. Local-Hessian workflow needs to be adapted to that low-data regime. diff --git a/docs/source/index.rst b/docs/source/index.rst index f7c03a8241f..d5f79f80113 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -13,7 +13,7 @@ Release notes, technical updates, examples, and deployment stories from the Mode - + @@ -25,10 +25,10 @@ Release notes, technical updates, examples, and deployment stories from the Mode

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  • -
    +
    From c63ebb8461d098a051819aa287b824d6dfdd5337 Mon Sep 17 00:00:00 2001 From: realAsma Date: Mon, 14 Sep 2026 20:56:12 +0000 Subject: [PATCH 10/11] docs: say E2M1 grid explicitly in the distribution section Co-Authored-By: Claude Opus 5 (1M context) Signed-off-by: realAsma --- docs/source/announcements/local-hessian.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/source/announcements/local-hessian.rst b/docs/source/announcements/local-hessian.rst index b26027840ee..84d4a20ec1a 100644 --- a/docs/source/announcements/local-hessian.rst +++ b/docs/source/announcements/local-hessian.rst @@ -229,7 +229,7 @@ Scale Selection Reshapes Distribution Figure 2 plots the scaled weights :math:`W/s` -- the values handed to the E2M1 cast. Max scaling piles the mass up near 6.0, the largest E2M1 value, -while MSE and Local-Hessian both cluster it on the representable grid +while MSE and Local-Hessian both cluster it on the representable E2M1 grid values. Grid alignment is not the whole story, though: among the scales that do align, Local-Hessian picks the ones that hold up better on evaluation. From 98e268fd3d6168bd829ba841a53e0ee26c2ca85d Mon Sep 17 00:00:00 2001 From: realAsma Date: Mon, 14 Sep 2026 21:03:38 +0000 Subject: [PATCH 11/11] docs: reword the Local-Hessian announcement card summary Co-Authored-By: Claude Opus 5 (1M context) Signed-off-by: realAsma --- docs/source/index.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/source/index.rst b/docs/source/index.rst index d5f79f80113..4df288fb823 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -28,7 +28,7 @@ Release notes, technical updates, examples, and deployment stories from the Mode
    September 9, 2026 · Model Optimizer Team

    Local-Hessian: Better NVFP4 Weight Scales from Layer Inputs

    -

    How Local-Hessian sets NVFP4 block scales from layer inputs, and how it measures up against max, MSE, Four-over-six and GPTQ.

    +

    How Local-Hessian sets NVFP4 block scales to minimize output error, and how it measures up against max, MSE, Four-over-six and GPTQ.

    local-hessianquantizationnvfp4calibrationmodelopt