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Add a bfloat16 option for the GPTQ and local-Hessian Hessian GEMMs - #3019
Adds hessian_input_dtype to the GPTQ and local_hessian algorithm configs: "float32" (the default, today's behavior) or "bfloat16".
update_hessian copies every batch of activations to float32 and accumulates XᵀX with a float32 GEMM, which runs on CUDA cores. With "bfloat16", a tensor-core GEMM reads the activations in bfloat16 and writes float32 (out_dtype=torch.float32). For bfloat16 activations, the products are exact in float32, so it differs from the float32 GEMM only in how it rounds the sums. It also needs no float32 copy of each batch, which is twice the size of the bfloat16 batch.
Against a float64 reference, the bfloat16 option's GPTQ Hessian is off by up to 2.8e-5 of the mean diagonal at 32K tokens per batch (1.3e-5 at 4K), versus 4.7e-6 for the float32 GEMM. A bfloat16 output would be off by 9.2e-3. GPTQ then adds 1% of the mean diagonal as damping, so the difference does not reach the result, which matches the KL below. The Hessian is stored in float32 either way, so the option saves only the transient float32 copy, not Hessian memory.
Where CUDA GEMMs don't take out_dtype (CPU inputs, or an older torch), "bfloat16" falls back to float32 with a one-time warning instead of being ignored. That check is cached per device.
It applies to every GPTQ Hessian: fused MoE experts and linear layers alike.
local_hessian builds 16x16 per-block Hessians the same way, so it gets the same option: a batched GEMM (bmm) that reads bfloat16 and writes float32. On an RTX PRO 6000 at 32K tokens it is 6.3x faster for 4,096 features (2.47 -> 0.40 ms per update) and 7.7x for 2,048, and it no longer makes the 512 / 256 MiB float32 copy. Its error is up to 1.4e-4 of the block diagonal, versus 1.9e-5 for float32. That Hessian only weights the error of each candidate scale in the search, and it is never inverted.
The field lives in a small mixin both configs share. One helper, bfloat16_hessian_gemm, decides the GEMM for both and warns when it is unavailable.
imatrix keeps its float32 statistic: it is a per-column sum of squares, not a GEMM, so tensor cores do not apply.
GEMM alone on GB300. Accumulating about 360 batches of 1 to 2,000 tokens each into one Hessian, steady state:
Hessian width
float32 GEMM
bfloat16 in, float32 out
2,560 (Qwen3.8-Flash-Next experts)
96 ms
11 ms (8.7x)
4,096 (GLM-5.3-Flash experts)
244 ms
15 ms (16x)
Real models on 4x GB300 (oci-jhb), float32 vs bfloat16. Layerwise GPTQ on the routed experts at IQ2_XXS, 1,024 x 512 calibration tokens, KL to BF16 over wikitext-2 (100 x 512 tokens, second half scored). Measured on top of #2945 and #3002, with flash-linear-attention installed, before this PR made the option opt-in:
GPTQ, all layers
Layerwise calibration
Whole job
KL to BF16 (paired delta, 95%)
GLM-5.3-Flash
730 s -> 553 s (-24%)
16:30 -> 13:09 (-20%)
40:41 -> 36:04 (-11%)
0.6306 -> 0.6293 (-0.0013 ± 0.0080, p 0.75)
Qwen3.8-Flash-Next
624 s -> 581 s (-7%)
15:26 -> 14:33 (-6%)
37:27 -> 35:46 (-5%)
0.2480 -> 0.2494 (+0.0015 ± 0.0052, p 0.58)
The Qwen run with the bfloat16 GEMM rebuilt the GGML CUDA extension for its new source tree, which took 142 s. The table subtracts that one-time build, which is unrelated to this change. KL moves within run-to-run noise on both models.
GPU test test_bf16_hessian_input_gives_the_float32_hessian: input_dtype=torch.bfloat16 gives the float64 reference Hessian to within 1e-4 (the diagonal is about 2), with the Hessian on the inputs' GPU and on the CPU. Where the fast GEMM exists, an update allocates less than a float32 copy of its batch. Without the bfloat16 path the update allocates 16 MiB, the float32 copy, and the test fails.
GPU test test_gptq_hessian_input_dtype_reaches_the_hessian: through mtq.quantize with a GPTQ config, hessian_input_dtype: bfloat16 lowers the measured Hessian-forward peak by the float32 copy of the batch. It fails if the option does not reach update_hessian.
New GPU tests in tests/gpu/torch/quantization/test_local_hessian_gpu.py. test_bf16_local_hessian_input_gives_the_float32_hessian checks the per-block Hessian against float64, and that no float32 copy is made. test_local_hessian_input_dtype_reaches_the_hessian runs mtq.quantize with local_hessian, hessian_input_dtype: bfloat16 and debug: true, and gets a Hessian that differs from the float32 one only by rounding. Each fails without its piece.
tests/gpu/torch/quantization/{test_gptq,test_layerwise_calibrate}.py: 36 passed on 2x RTX PRO 6000. test_gptq.py, test_local_hessian_gpu.py and test_nvfp4_fp8_sweep_kernel.py: 69 passed. The first version, with the bfloat16 GEMM always on, also passed test_gptq.py on 4x GB300 (torch 2.13, transformers 5.16).
tests/unit/torch/quantization/{test_gptq,test_ggml_gptq,test_local_hessian,test_config_validation}.py and tests/unit/recipe: 666 passed.
New CPU tests test_bf16_hessian_input_on_cpu_gives_the_float32_result_and_warns_once, one each in test_gptq.py and test_local_hessian.py. On CPU, where GEMMs take no out_dtype, hessian_input_dtype: bfloat16 gives the float32 result exactly and warns once over three batches. Without the once-per-device cache they see 3 and 9 warnings and fail.
torch 2.8.0+cu128, the oldest torch this package supports, on 2x RTX PRO 6000 with transformers 5.18. mm, addmm and bmm all have out_dtype overloads there, so every Hessian GEMM takes the fast path. tests/gpu/torch/quantization/{test_gptq,test_local_hessian_gpu}.py: 24 passed, including the four hessian_input_dtype tests, which skip without the fast path. tests/unit/torch/quantization/{test_gptq,test_local_hessian}.py: 19 passed, on torch 2.8 and 2.12 alike. torch 2.6 has no such overloads, so there "bfloat16" falls back to float32 with the warning.
Before your PR is "Ready for review"
Is this change backward compatible?: ✅ (new option; the default keeps the float32 GEMM)
If you copied code from any other sources or added a new PIP dependency, did you follow guidance in CONTRIBUTING.md: N/A
GPTQ and local-Hessian calibration now support an optional bfloat16 input mode for Hessian calculations, while retaining float32 accumulation. This can reduce calibration memory use on supported CUDA hardware.
The default remains float32. If the hardware does not support the required operations, calibration falls back to float32 and displays a warning.
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Walkthrough
GPTQ and local-Hessian calibration now accept a hessian_input_dtype setting. BF16 inputs use float32-output Hessian GEMMs when supported. Unsupported requests fall back to float32. Tests cover fallback behavior, Hessian accuracy, and memory use.
Changes: Configurable Hessian input dtype
Layer / File(s)
Summary
Configure and route the Hessian input dtype modelopt/torch/quantization/config.py, modelopt/torch/quantization/model_calib.py, modelopt/torch/quantization/utils/calib_utils.py
Adds hessian_input_dtype, defaulting to float32, to GPTQ and local-Hessian configuration. Both calibration paths pass the selected dtype to Hessian accumulation.
Select the Hessian GEMM path modelopt/torch/quantization/model_calib.py, modelopt/torch/quantization/utils/calib_utils.py
Uses BF16 inputs with float32 Hessian output when the CUDA device supports the required GEMMs. Unsupported BF16 requests warn once per device and use float32 instead.
Validate and document BF16 accumulation tests/gpu/torch/quantization/test_gptq.py, tests/gpu/torch/quantization/test_local_hessian_gpu.py, tests/unit/torch/quantization/test_gptq.py, tests/unit/torch/quantization/test_local_hessian.py, CHANGELOG.rst
Adds CPU and GPU tests for fallback behavior, Hessian accuracy, and memory use. The changelog documents the configuration option.
sequenceDiagram
participant Config
participant GPTQ
participant LocalHessianCalibrate
participant HessianAccumulator
participant update_hessian
Config->>GPTQ: Provide hessian_input_dtype
Config->>LocalHessianCalibrate: Provide hessian_input_dtype
GPTQ->>update_hessian: Pass selected input dtype
LocalHessianCalibrate->>HessianAccumulator: Pass selected input dtype
HessianAccumulator->>update_hessian: Accumulate Hessian inputs
update_hessian->>update_hessian: Probe GEMM support and select BF16 or float32
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Possibly related PRs
NVIDIA/Model-Optimizer#2864: Reworks the update_hessian data layout and same-device update path, which the BF16 branch extends.
Suggested reviewers:fridah-nv, kevalmorabia97
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Review comments at @modelopt/torch/quantization/utils/calib_utils.py:
- Around line 137-139: Update update_hessian to call _has_float32_out_gemm with
input_flat.device and input_flat.dtype; change the probe to test that device and
dtype, and cache results by both values so support is determined independently
for each device/dtype pair.
Review comments at @tests/gpu/torch/quantization/test_gptq.py:
- Around line 99-100: In the `device == "cuda"` test, apply the strict `growth`
allocation bound only when `_has_float32_out_gemm()` reports fast-path support.
Keep the Hessian accuracy assertions active for both the fast GEMM and fallback
paths.
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…GEMM
update_hessian cast every input batch to float32 and ran a float32 GEMM,
which runs on CUDA cores. BF16 and FP16 products are exact in float32, so
a tensor-core GEMM that takes the inputs directly and writes float32
differs only in how it rounds the sums: about 1e-5 of the Hessian's
diagonal, against 1e-6 for the float32 GEMM and 1e-2 for a BF16 output.
On GB300 it is 9-16x faster for 2560- and 4096-wide expert Hessians and
needs no float32 copy of the inputs. A torch without float32-output
GEMMs, CPU inputs and float32 inputs keep the float32 path.
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Signed-off-by: Chenjie Luo <chenjiel@nvidia.com>
GPTQ's algorithm config gains hessian_input_dtype ("float32" or
"bfloat16", default "float32"). The default keeps the float32 copy and
float32 GEMM; "bfloat16" feeds the activations to the GEMM in bfloat16
and accumulates in float32, so recipes choose speed over the exact
float32 sums. Where CUDA GEMMs do not take out_dtype, "bfloat16" falls
back to float32 with a warning instead of being ignored. The out_dtype
check is now cached per device rather than for the current GPU only.
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Signed-off-by: Chenjie Luo <chenjiel@nvidia.com>
local_hessian's per-block Hessians (16x16 blocks of X^T X) took the same
float32 copy and float32 GEMM as GPTQ's. With hessian_input_dtype:
bfloat16 they use a batched tensor-core GEMM that reads bfloat16 and
accumulates in float32: 6-8x faster at 32K tokens x 2-4K features on an
RTX PRO 6000, with no 256-512 MiB float32 copy, and up to about 1.5e-4
of the block diagonal from the float64 sums (float32: 2e-5). The field
moves to a mixin both configs share, and one helper decides the GEMM and
warns when it is unavailable. The GPTQ error figure is corrected to up to
about 3e-5 at 32K-token batches.
imatrix keeps its float32 statistic: it is a per-column sum of squares,
not a GEMM, so tensor cores do not apply.
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Signed-off-by: Chenjie Luo <chenjiel@nvidia.com>
cjluo-nv
changed the title
Accumulate GPTQ Hessians from BF16/FP16 inputs with a float32-output GEMM
Add a bfloat16 option for the GPTQ and local-Hessian Hessian GEMMs
Oct 27, 2026
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Bot review (gpt-6.1-sol) — DM the bot to share feedback.
Nudge: the fast path looks sound, but the advertised compatibility fallback needs coverage and validation on the oldest supported Torch.
Needs action:
Extend the existing CPU GPTQ/local-Hessian tests with hessian_input_dtype="bfloat16"; verify float32-equivalent results and a single fallback warning across repeated batches.
Run the new GPU tests on Torch 2.8 and record results in the PR body, including whether each GEMM uses the fast path or fallback.
No action needed:
The new test file matches LICENSE_HEADER; default float32 behavior and GGML helper inheritance are preserved.
On CPU, hessian_input_dtype: bfloat16 falls back to the float32 Hessian.
New CPU tests for GPTQ and local Hessian check that it then gives the
same result as float32 and warns exactly once over several batches.
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Signed-off-by: Chenjie Luo <chenjiel@nvidia.com>
CPU fallback coverage: new test_bf16_hessian_input_on_cpu_gives_the_float32_result_and_warns_once in both tests/unit/torch/quantization/test_gptq.py and test_local_hessian.py. On CPU, hessian_input_dtype: bfloat16 gives exactly the float32 result and warns once over three batches. Without the once-per-device cache they see 3 and 9 warnings and fail.
torch 2.8: on 2.8.0+cu128 (2x RTX PRO 6000, transformers 5.18), mm, addmm and bmm all have out_dtype overloads, so every Hessian GEMM takes the fast path. tests/gpu/torch/quantization/{test_gptq,test_local_hessian_gpu}.py: 24 passed, including the four hessian_input_dtype tests, which skip without the fast path. The unit tests above pass on 2.8 and 2.12. Recorded in the PR description.
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Nudge: prior technical concerns are resolved, but embedded AI-agent directives in review comments require human inspection before merge.
Needs action:
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No action needed:
✔️ Resolved since the last review: per-device capability probing, fallback-safe memory assertions, repeated-batch CPU fallback coverage, and Torch 2.8 validation reported in the PR body.
The CPU tests compare float32-equivalent results and enforce one fallback warning. GPU accuracy checks remain active on both paths; memory bounds apply only to supported fast paths.
The new test file matches LICENSE_HEADER; existing assertions were not weakened.
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LGTM. Do you know the breakdown of the whole jobs? seem like the improvment from GEMM translates to 10% e2e time reduction, wondering what are other pieces in the pipeline.
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What does this PR do?
Type of change: new feature (performance)
Adds
hessian_input_dtypeto the GPTQ andlocal_hessianalgorithm configs:"float32"(the default, today's behavior) or"bfloat16".update_hessiancopies every batch of activations to float32 and accumulatesXᵀXwith a float32 GEMM, which runs on CUDA cores. With"bfloat16", a tensor-core GEMM reads the activations in bfloat16 and writes float32 (out_dtype=torch.float32). For bfloat16 activations, the products are exact in float32, so it differs from the float32 GEMM only in how it rounds the sums. It also needs no float32 copy of each batch, which is twice the size of the bfloat16 batch.Against a float64 reference, the bfloat16 option's GPTQ Hessian is off by up to 2.8e-5 of the mean diagonal at 32K tokens per batch (1.3e-5 at 4K), versus 4.7e-6 for the float32 GEMM. A bfloat16 output would be off by 9.2e-3. GPTQ then adds 1% of the mean diagonal as damping, so the difference does not reach the result, which matches the KL below. The Hessian is stored in float32 either way, so the option saves only the transient float32 copy, not Hessian memory.
out_dtype(CPU inputs, or an older torch),"bfloat16"falls back to float32 with a one-time warning instead of being ignored. That check is cached per device.local_hessianbuilds 16x16 per-block Hessians the same way, so it gets the same option: a batched GEMM (bmm) that reads bfloat16 and writes float32. On an RTX PRO 6000 at 32K tokens it is 6.3x faster for 4,096 features (2.47 -> 0.40 ms per update) and 7.7x for 2,048, and it no longer makes the 512 / 256 MiB float32 copy. Its error is up to 1.4e-4 of the block diagonal, versus 1.9e-5 for float32. That Hessian only weights the error of each candidate scale in the search, and it is never inverted.bfloat16_hessian_gemm, decides the GEMM for both and warns when it is unavailable.Usage
In a recipe or config:
Testing
GEMM alone on GB300. Accumulating about 360 batches of 1 to 2,000 tokens each into one Hessian, steady state:
Real models on 4x GB300 (oci-jhb), float32 vs bfloat16. Layerwise GPTQ on the routed experts at IQ2_XXS, 1,024 x 512 calibration tokens, KL to BF16 over wikitext-2 (100 x 512 tokens, second half scored). Measured on top of #2945 and #3002, with flash-linear-attention installed, before this PR made the option opt-in:
The Qwen run with the bfloat16 GEMM rebuilt the GGML CUDA extension for its new source tree, which took 142 s. The table subtracts that one-time build, which is unrelated to this change. KL moves within run-to-run noise on both models.
test_bf16_hessian_input_gives_the_float32_hessian:input_dtype=torch.bfloat16gives the float64 reference Hessian to within 1e-4 (the diagonal is about 2), with the Hessian on the inputs' GPU and on the CPU. Where the fast GEMM exists, an update allocates less than a float32 copy of its batch. Without the bfloat16 path the update allocates 16 MiB, the float32 copy, and the test fails.test_gptq_hessian_input_dtype_reaches_the_hessian: throughmtq.quantizewith a GPTQ config,hessian_input_dtype: bfloat16lowers the measured Hessian-forward peak by the float32 copy of the batch. It fails if the option does not reachupdate_hessian.tests/gpu/torch/quantization/test_local_hessian_gpu.py.test_bf16_local_hessian_input_gives_the_float32_hessianchecks the per-block Hessian against float64, and that no float32 copy is made.test_local_hessian_input_dtype_reaches_the_hessianrunsmtq.quantizewithlocal_hessian,hessian_input_dtype: bfloat16anddebug: true, and gets a Hessian that differs from the float32 one only by rounding. Each fails without its piece.tests/gpu/torch/quantization/{test_gptq,test_layerwise_calibrate}.py: 36 passed on 2x RTX PRO 6000.test_gptq.py,test_local_hessian_gpu.pyandtest_nvfp4_fp8_sweep_kernel.py: 69 passed. The first version, with the bfloat16 GEMM always on, also passedtest_gptq.pyon 4x GB300 (torch 2.13, transformers 5.16).tests/unit/torch/quantization/{test_gptq,test_ggml_gptq,test_local_hessian,test_config_validation}.pyandtests/unit/recipe: 666 passed.test_bf16_hessian_input_on_cpu_gives_the_float32_result_and_warns_once, one each intest_gptq.pyandtest_local_hessian.py. On CPU, where GEMMs take noout_dtype,hessian_input_dtype: bfloat16gives the float32 result exactly and warns once over three batches. Without the once-per-device cache they see 3 and 9 warnings and fail.mm,addmmandbmmall haveout_dtypeoverloads there, so every Hessian GEMM takes the fast path.tests/gpu/torch/quantization/{test_gptq,test_local_hessian_gpu}.py: 24 passed, including the fourhessian_input_dtypetests, which skip without the fast path.tests/unit/torch/quantization/{test_gptq,test_local_hessian}.py: 19 passed, on torch 2.8 and 2.12 alike. torch 2.6 has no such overloads, so there"bfloat16"falls back to float32 with the warning.Before your PR is "Ready for review"
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Summary by CodeRabbit
bfloat16input mode for Hessian calculations, while retaining float32 accumulation. This can reduce calibration memory use on supported CUDA hardware.float32. If the hardware does not support the required operations, calibration falls back to float32 and displays a warning.