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Weight the IQ1 encoders by the square root of GPTQ's Hessian diagonal - #2723

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@cjluo-nv cjluo-nv commented Oct 9, 2026 •

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What does this PR do?

Type of change: new feature

#2686 let the IQ2 encoders weight their codebook search by a per-input-column importance, which GPTQ fills with the square root of its Hessian diagonal. This PR does the same for IQ1_S and IQ1_M.

Weighted encoders. quantize_iq1_s and quantize_iq1_m take the same optional importance w as the IQ2 encoders. Each 8-value group is approximated by s·(q + δ), with q from the ternary grid and δ = ±1/8. The search now minimises Σ w·(x − s·(q + δ))² instead of the plain squared error.

  • The weighting covers each group's grid entry, its shift δ, and the local scale it shares with neighbouring groups (4 groups in IQ1_S, 2 in IQ1_M).
  • The super-block scale predictors stay unweighted, as in IQ2.
  • The CUDA kernel gets the weighting through the same kWeighted template flag as IQ2, so the unweighted kernel compiles as before.
  • With uniform importance, the payload is identical to the unweighted one.
  • Both format records now declare weighted=True, so GPTQ's importance_weighted option reaches them.

The built-in general/ptq/iq1_s and iq1_m recipes now set importance_weighted: true, as the IQ2 recipes do in #2686.

Usage

The built-in IQ1 recipes turn it on:

python examples/hf_ptq/hf_ptq.py --pyt_ckpt_path <model> --recipe general/ptq/iq1_s --export_path <dir>

Calling the encoder directly, for example with an imatrix from elsewhere:

from modelopt.torch.quantization.ggml.iq1_s import quantize_iq1_s

packed, shape = quantize_iq1_s(weight, importance=imatrix)  # imatrix: [in_features], finite, >= 0

Testing

Qwen3.8-27B, MLP-only IQ1 with GPTQ, using the default general/ptq/iq1_* recipes. The setup is the same as #2686:

  • Calibration: hf_ptq.py defaults (cnn_nemotron_v2_mix, 1024 × 512).
  • Scoring: KL divergence from BF16 on wikitext-2 test, 100 × 512-token chunks, scored as llama.cpp's llama-perplexity --kl-divergence does.
  • All runs use this branch, before its rebase onto the merged Weight the IQ2 encoders by the square root of GPTQ's Hessian diagonal #2686. The only difference between them is the importance passed to the search.

Mean KL divergence for each format and each choice of importance:

Format Unweighted diag(H) sqrt(diag(H)) (this PR) sqrt − unweighted, paired (chunks where sqrt is lower)
IQ1_S 0.926 0.941 0.847 −0.079 ± 0.007 (95/100)
IQ1_M 0.560 0.587 0.544 −0.016 ± 0.004 (66/100)
Format Perplexity (BF16: 6.746): unweighted / diag(H) / sqrt Same top token: unweighted / diag(H) / sqrt
IQ1_S 15.44 / 15.65 / 14.20 60.7 / 59.2 / 61.1 %
IQ1_M 10.81 / 11.06 / 10.62 69.5 / 67.8 / 69.4 %
  • IQ1 follows the same pattern as all three IQ2 formats.
  • The gain is largest on IQ1_S: 8.5% lower KL divergence and 1.2 lower perplexity.
  • Same-top-token agreement improves on IQ1_S and is unchanged within noise on IQ1_M (−0.13 ± 0.23 points).
  • Paired differences compare both arms on the same tokens. The standard error is over the 100 chunks.
  • Every unweighted arm ran with uniform importance. That gives byte-identical codes: the tests check it, and so did a run on Qwen3.8-27B's layer-10 MLP weights (0 of 348,160 blocks differ for either format).

GPTQ's per-layer relative error (the Relative MSE error it logs), weighted ÷ unweighted, geometric mean over 64 layers:

Format Importance gate_proj up_proj down_proj
IQ1_S diag(H) 0.98 (42/64 layers lower) 1.00 (24/64) 0.93 (41/64)
IQ1_S sqrt(diag(H)) 0.96 (63/64) 0.99 (60/64) 0.91 (62/64)
IQ1_M diag(H) 0.99 (41/64) 1.01 (23/64) 0.92 (42/64)
IQ1_M sqrt(diag(H)) 0.96 (61/64) 0.98 (59/64) 0.90 (63/64)

Unit tests: 137 passed in test_iq_formats.py and test_ggml_gptq.py, with and without a GPU visible, plus the recipe tests. The weighted tests are driven by the format registry, so they now run for IQ1_S and IQ1_M too:

  • uniform importance reproduces the unweighted payload exactly;
  • importance lowers the importance-weighted error below 0.75 × that of the unweighted search;
  • invalid importance is rejected.

The GPTQ test now covers IQ1_S as a weighted format and uses Q8_0 as the unweighted one.

GPU tests: 96 passed.

  • The weighted CUDA packers match the PyTorch weighted encoders, with at most 1 block in 1,000 differing.
  • With uniform importance, the CUDA packers reproduce the unweighted payload.
  • They reject an importance that doesn't tile the blocks.

pre-commit passes.

Before your PR is "Ready for review"

Make sure you read and follow Contributor guidelines and your commits are signed (git commit -s -S).

Make sure you read and follow the Security Best Practices (e.g. avoiding hardcoded trust_remote_code=True, torch.load(..., weights_only=False), pickle, etc.).

  • Is this change backward compatible?: ✅ The API is compatible, since importance is optional. The codes GPTQ picks for the built-in IQ1 recipes change, which is the point of this PR.
  • If you copied code from any other sources or added a new PIP dependency, did you follow guidance in CONTRIBUTING.md: N/A
  • Did you write any new necessary tests?: ✅
  • Did you update Changelog?: ✅ This extends Weight the IQ2 encoders by the square root of GPTQ's Hessian diagonal #2686's entry to the IQ1 formats and recipes.
  • Did you get Claude approval on this PR?: ❌ Not yet.

Additional Information

Follows #2665 (block-GPTQ for the GGML formats) and #2686 (weighted IQ2 encoders).

🤖 Generated with Claude Code

Summary by CodeRabbit

  • New Features
    • IQ1_S and IQ1_M quantization now support optional per-column importance weights, helping prioritize values that matter most during codebook search.
    • GPTQ calibration presets for IQ1_S and IQ1_M now enable importance-weighted quantization by default.
    • Importance-weighted calibration is supported across the built-in IQ1 and IQ2 recipes.

IQ1_S and IQ1_M now take the same optional per-input-column importance
as the IQ2 formats and search for the codes minimising
sum w (x - s (q + delta))^2: the grid entry, the shift and the local
scale each group shares are all chosen by the weighted error. The CUDA
kernel gets it through a kWeighted template flag, so the unweighted
kernel compiles as before, and uniform importance reproduces the
unweighted payload exactly. The super-block scale predictors are
unchanged.

Both records declare a weighted search, so GPTQ's importance_weighted
option now reaches them, and the built-in iq1_s and iq1_m recipes set
it. On Qwen3.8-27B (MLP only, GPTQ, wikitext-2 KL divergence from BF16)
the square root of the Hessian diagonal lowers IQ1_S from 0.926 to
0.847 and IQ1_M from 0.560 to 0.544.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Signed-off-by: Chenjie Luo <chenjiel@nvidia.com>
@cjluo-nv
cjluo-nv requested review from a team as code owners October 9, 2026 16:42
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cjluo-nv requested review from Fridah-nv and h-guo18 October 9, 2026 16:42
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📝 Walkthrough

Walkthrough

IQ1_S and IQ1_M quantization now support optional per-input-column importance weights in Python and CUDA encoding. Their GPTQ presets enable importance weighting, and tests cover weighted IQ1_S and unweighted Q8_0.

Changes

IQ1 Importance Weighting

Layer / File(s) Summary
Weighted IQ1 search
modelopt/torch/kernels/quantization/ggml/common.cuh, modelopt/torch/kernels/quantization/ggml/iq1_family.cuh, modelopt/torch/quantization/ggml/iq1_s.py, modelopt/torch/quantization/ggml/iq1_m.py
The Python and CUDA search paths use importance-weighted statistics and error terms when weights are provided. Without weights, the existing unweighted search remains available.
Importance API and encoding paths
modelopt/torch/quantization/ggml/iq1_s.py, modelopt/torch/quantization/ggml/iq1_m.py, modelopt/torch/kernels/quantization/ggml/iq1_family.cuh, modelopt/torch/kernels/quantization/ggml/iq1_s.cu, modelopt/torch/kernels/quantization/ggml/iq1_m.cu, modelopt/torch/kernels/quantization/ggml/ggml.cpp
The IQ1 quantizers accept optional importance, prepare block weights, and pass them through fallback or CUDA encoding. CUDA packers validate supplied weights and dispatch weighted encoding.
GPTQ presets and validation
modelopt_recipes/configs/ptq/presets/model/iq1_*.yaml, modelopt/torch/quantization/config.py, modelopt/torch/quantization/extensions.py, CHANGELOG.rst, tests/gpu/torch/quantization/test_iq_formats_cuda.py, tests/unit/torch/quantization/test_ggml_gptq.py
The IQ1 GPTQ presets enable importance weighting. Documentation describes the supported formats and packer arguments. Tests cover importance validation and weighted IQ1_S GPTQ behavior.

Priority: ➖ Normal

Estimated code review effort: 3 (Moderate) | ~25 minutes

Change: Feature

Sequence Diagram(s)

sequenceDiagram
  participant GPTQ
  participant Quantizer as quantize_iq1_s
  participant Packer as iq1_s_pack_cuda
  participant Encoder as iq1_encode_blocks
  GPTQ->>Quantizer: Pass importance values
  Quantizer->>Packer: Pass block importance
  Packer->>Packer: Validate importance
  Packer->>Encoder: Pass importance for weighted dispatch
  Encoder->>Encoder: Run weighted codebook search
Loading

Suggested reviewers: hychiang-git


Merge Risk: 🔵 Low · up to daf1b

Standard GPTQ and quantizer usage validates importance values. Only direct calls to the CUDA packers can pass invalid weights, so this is a small follow-up rather than a merge blocker.

🚥 Pre-merge checks | ✅ 5 | ❌ 1

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✅ Passed checks (5 passed)
Check name Status Explanation
Description Check Passed Check skipped - CodeRabbit’s high-level summary is enabled.
Title check Passed The title clearly and concisely describes the main change: applying the square root of GPTQ's Hessian diagonal as importance weighting for the IQ1 encoders.
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Out of Scope Changes check Passed Check skipped because no linked issues were found for this pull request.
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Inline comments:
Review comments at @modelopt/torch/kernels/quantization/ggml/iq1_m.cu:
- Around line 110-111: Update the importance validation used by the IQ1_M packer
in `iq1_m.cu` and the IQ1_S packer in `iq1_s.cu` so the shared validator rejects
non-finite and negative importance values before encoding; retain the existing
metadata checks.

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📒 Files selected for processing (14)
  • CHANGELOG.rst
  • modelopt/torch/kernels/quantization/ggml/common.cuh
  • modelopt/torch/kernels/quantization/ggml/ggml.cpp
  • modelopt/torch/kernels/quantization/ggml/iq1_family.cuh
  • modelopt/torch/kernels/quantization/ggml/iq1_m.cu
  • modelopt/torch/kernels/quantization/ggml/iq1_s.cu
  • modelopt/torch/quantization/config.py
  • modelopt/torch/quantization/extensions.py
  • modelopt/torch/quantization/ggml/iq1_m.py
  • modelopt/torch/quantization/ggml/iq1_s.py
  • modelopt_recipes/configs/ptq/presets/model/iq1_m.yaml
  • modelopt_recipes/configs/ptq/presets/model/iq1_s.yaml
  • tests/gpu/torch/quantization/test_iq_formats_cuda.py
  • tests/unit/torch/quantization/test_ggml_gptq.py

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Comment on lines +110 to +111
if (importance.has_value())
check_importance("IQ1_M", input, *importance);

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🎯 Functional Correctness | 🟡 Minor | ⚡ Quick win

Validate importance values for both direct CUDA packers. check_importance checks metadata but accepts negative and non-finite values. A direct caller can bypass Python validation and receive codes selected from invalid weighted error scores.

  • modelopt/torch/kernels/quantization/ggml/iq1_m.cu#L110-L111: require finite, non-negative importance before encoding.
  • modelopt/torch/kernels/quantization/ggml/iq1_s.cu#L100-L101: apply the same requirement through the shared validator.
📍 Affects 2 files
  • modelopt/torch/kernels/quantization/ggml/iq1_m.cu#L110-L111 (this comment)
  • modelopt/torch/kernels/quantization/ggml/iq1_s.cu#L100-L101
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Review comment at @modelopt/torch/kernels/quantization/ggml/iq1_m.cu around
lines 110 - 111:
Update the importance validation used by the IQ1_M packer in `iq1_m.cu` and the
IQ1_S packer in `iq1_s.cu` so the shared validator rejects non-finite and
negative importance values before encoding; retain the existing metadata checks.

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Preview removed because the pull request was closed.
2026-10-09 17:49 UTC

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Bot review (bedrock-claude-opus-5-5) — DM the bot to share feedback.

LGTM: the change is correct and the tests are driven by the format registry, but a human has to sign off because existing tests were edited (the edits are justified).

Needs action:

  • Confirm the edits to existing tests. In test_ggml_gptq.py, iq1_s is now expected to be weighted, and q8_0 replaces it as the unweighted case, because iq1_s now sets weighted=True. The CUDA rejection test drops the scales argument for IQ1_S because its packer predicts scales internally.

No action needed:

  • Design is settled. This isn't a new system: it extends #2686's existing approach. It reuses importance_blocks/chunk_importance, the kWeighted template flag, check_importance and the GGMLFormat.weighted registry field.
  • Shapes check out. chunk_importance returns [blocks, 32, 8], which matches what _search_shifted_grid expects. weight_sum is kept with keepdim, so it broadcasts correctly against [blocks, 32, 128]. On the CUDA side, weight_sum defaults to 8, so the unweighted kernel behaves as before.
  • Uniform importance gives a byte-identical payload in practice. The grid values are ternary, so the weighted matmul norms and sums come out exact. The tests check this on both CPU and CUDA.
  • The IQ1_S find_scale scale predictor stays unweighted, as the PR body says and as IQ2 does.
  • Core logic is well under the size budget, and there are no licensing changes.

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Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 78.14%. Comparing base (bc9f439) to head (daf1b68).
⚠️ Report is 3 commits behind head on main.

Additional details and impacted files
@@            Coverage Diff             @@
##             main    #2723      +/-   ##
==========================================
+ Coverage   71.71%   78.14%   +6.42%     
==========================================
  Files         642      642              
  Lines       71345    71410      +65     
==========================================
+ Hits        51168    55804    +4636     
+ Misses      20177    15606    -4571     
Flag Coverage Δ
examples-diffusers 20.25% <9.09%> (-0.01%) ⬇️
examples-gpt-oss 13.48% <9.09%> (+0.01%) ⬆️
examples-hf_ptq 23.44% <27.27%> (+0.03%) ⬆️
examples-llm_distill 13.56% <9.09%> (+0.03%) ⬆️
examples-llm_eval 17.32% <9.09%> (+<0.01%) ⬆️
examples-llm_qat 17.56% <9.09%> (+0.02%) ⬆️
examples-llm_sparsity 15.85% <9.09%> (+<0.01%) ⬆️
examples-megatron_bridge 26.46% <9.09%> (-0.16%) ⬇️
examples-specdec_bench 13.25% <9.09%> (+0.01%) ⬆️
examples-speculative_decoding 17.60% <9.09%> (-0.06%) ⬇️
examples-torch_onnx 21.60% <9.09%> (-0.01%) ⬇️
examples-torch_trt 15.25% <9.09%> (+<0.01%) ⬆️
examples-vllm_serve 13.92% <9.09%> (+0.01%) ⬆️
gpu 58.85% <100.00%> (+25.31%) ⬆️
regression 15.10% <9.09%> (+<0.01%) ⬆️
unit 59.88% <90.90%> (+0.01%) ⬆️

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@cjluo-nv
cjluo-nv enabled auto-merge (squash) October 9, 2026 17:41
@cjluo-nv
cjluo-nv merged commit fe13c5c into main Oct 9, 2026
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@cjluo-nv
cjluo-nv deleted the chenjiel/iq1-weighted-encoders branch October 9, 2026 17:49
cjluo-nv added a commit that referenced this pull request Oct 12, 2026
#2723 gave IQ1_S and IQ1_M a weighted search, so their recipes now
follow GPTQ with a single imatrix pass for the fused MoE experts, as the
IQ2 recipes do and as the preset test requires.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Signed-off-by: Chenjie Luo <chenjiel@nvidia.com>
cjluo-nv added a commit that referenced this pull request Oct 13, 2026
#2723 gave IQ1_S and IQ1_M a weighted search, so their recipes now
follow GPTQ with a single imatrix pass for the fused MoE experts, as the
IQ2 recipes do and as the preset test requires.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Signed-off-by: Chenjie Luo <chenjiel@nvidia.com>
cjluo-nv added a commit that referenced this pull request Oct 15, 2026
… experts (#2735)

### What does this PR do?

Type of change: new feature

Adds **imatrix calibration** (`algorithm: {method: imatrix}`) for the
GGML formats, and uses it in the built-in IQ1 and IQ2 recipes for
**fused MoE experts**, which GPTQ does not reach.

**What imatrix does.** It encodes each weight once. The codebook search
is weighted by the square root of the inputs' per-column second moment
`E[x_j²]`, which is llama.cpp's importance-matrix statistic.
- **Collection:** after `max_calibrate`, one forward with weight
fake-quant disabled collects the statistic for every weight whose
quantizer backend registered an imatrix encoder.
- **Encoding:** the GGML encoder encodes each weight with its statistic,
writes the decoded weight back, and pins the payload, so later forwards
and export use exactly those codes.
- **Coverage:** dense quantized linears and HF fused-MoE experts
(`_QuantFusedExperts`). Each expert gets its own statistic, over the
tokens routed to it.
- **Idle experts:** a weight no calibration token reaches gets the plain
search.
- **Single pass by default:** one forward collects every statistic, as
llama.cpp does. `layerwise: {enable: true}` instead collects each
layer's statistics after the earlier layers are quantized.
- **Checked up front:** a weight the encoder can't take, such as an IQ
weight whose input width isn't a multiple of 256, is refused before any
forward runs, including max calibration's for enabled activation
quantizers, and before any weight or amax changes, naming its module.
- **Bounded memory:** the input hook squares 1,024 rows at a time. For
one 4,096-token batch into a 17,408-wide projection, the calibration
forward's peak is 204 MiB above resident, against 689 MiB when squaring
the whole input at once.
- **Single rank:** the statistics aren't summed across data-parallel
ranks yet, so imatrix warns when run on several ranks, as
`local_hessian` does.

**How it composes with GPTQ.** A weight that already holds a pinned
payload is left alone. So `[{method: gptq}, {method: imatrix}]` runs
GPTQ on the dense linears and imatrix on the experts GPTQ skips.
- **The built-in `general/ptq/iq1_s`, `iq1_m`, `iq2_xxs`, `iq2_xs` and
`iq2_s` recipes now use this list.** GPTQ stays layerwise, and imatrix
runs in a single pass after it, so its statistics already see GPTQ's
codes in the dense linears.
- **New experts-only recipes for every IQ format:**
`general/ptq/iq1_s_experts_only`, `iq1_m_experts_only`,
`iq2_xxs_experts_only`, `iq2_xs_experts_only` and `iq2_s_experts_only`
put the format on the MoE routed experts only (the scope of
`nvfp4_experts_only`), calibrated with imatrix alone. Shared experts,
dense layers and attention stay in BF16.
- On a dense model, the imatrix pass finds nothing left to encode, so
the codes are unchanged.
- IQ1_S and IQ1_M have a weighted search since #2723, so their recipes
get the step too. The preset test requires it for every weighted format.
The MoE measurements below are IQ2_XXS.

**Why the square root.** It's the same exponent GPTQ uses (#2686).
Without error compensation, the raw `E[x²]` is the exact diagonal of the
output error. But it is heavy-tailed, and noisy for an expert that sees
about 3% of the calibration tokens. The square root measured better on
the dense MLP and on the routed experts (tables below). The one
exception was quantizing the shared expert alone (a dense MLP that sees
every token), where raw was slightly better: 0.081 vs 0.087 KL
divergence, against 0.137 for the plain encode.

**Plumbing.**
- **Registry:** imatrix plugs in through `register_imatrix_encoder`, a
backend registry next to `register_gptq_helper`.
- **Shared input hooks:** the hooks local-Hessian calibration used for
dense linears and fused experts are now shared as
`_register_weight_input_hooks`. Their marker is renamed to
`_WeightInputHook`, so Nemotron-H's MTP head also runs its forward
during imatrix.
- **Shared floor:** GPTQ's floor on the Hessian diagonal is shared as
`floored_second_moments`.
- **hf_ptq:** `--moe_calib_experts_ratio` now applies to every algorithm
in a list.

### Usage

The built-in IQ1 and IQ2 recipes use it with no change:

```bash
python examples/hf_ptq/hf_ptq.py --pyt_ckpt_path <moe model> --recipe general/ptq/iq2_xxs --export_path <dir>
```

As a standalone method (one encode per weight, no Hessian), or after
GPTQ in a custom recipe:

```yaml
algorithm:
  - method: gptq
    block_size: 256
    perc_damp: 0.3
    importance_weighted: true
    layerwise: {enable: true}
  - method: imatrix          # encodes the fused MoE experts GPTQ leaves, in a single pass
```

### Testing

Unless noted, runs use `hf_ptq.py` defaults for calibration
(`cnn_nemotron_v2_mix`, 1024 × 512). They are scored by KL divergence
from BF16 on wikitext-2 test, 100 × 512-token chunks, scored as
llama.cpp's `llama-perplexity --kl-divergence` does; the scoring code is
#2662, run locally. Paired differences compare two arms on the same
tokens, with the standard error over the 100 chunks. The exponent was
set through an eval-only switch; the final recipes match the tested
ones.

**Qwen3.5-35B-A3B (256 experts, top-8), `iq2_xxs_experts_only`: IQ2_XXS
on the routed experts only, shared expert BF16**

| Calibration | Mean KL divergence | Perplexity (BF16: 6.398) | Same top
token |
|---|---|---|---|
| plain encode (`max`) | 0.1847 | 7.515 | 82.15 % |
| **imatrix (this PR's recipe)** | **0.1801** | **7.485** | 82.29 % |

imatrix vs plain: −0.0046 ± 0.0011 KL divergence (z = −4.2), lower in
68/100 chunks. This is the scope GPTQ cannot reach at all, so it
isolates what imatrix adds.

**Single pass vs layerwise (Qwen3.5-35B-A3B, IQ2_XXS)**

| Scope | Plain / GPTQ only | imatrix, single pass (the recipes) |
imatrix, layerwise |
|---|---|---|---|
| experts only | 0.1847 | 0.1801 | 0.1778 |
| MLP + experts, after GPTQ | 0.2193 | 0.2135 | 0.2122 |

Layerwise minus single pass is −0.0023 ± 0.0006 (z = −3.8) experts-only
and −0.0013 ± 0.0006 (z = −2.1) after GPTQ. On the two larger models
below, the two tie. The recipes use the single pass: the layerwise gain
is small here and absent on the larger models, and the single pass keeps
no cache of each layer's inputs (layerwise ran out of memory at 1024
samples on Qwen3.8-Flash-Next). For a model partly offloaded to CPU,
layerwise is the faster choice, because each layer moves to the GPU once
instead of on every batch.

**Larger MoE models, experts only (IQ2_XXS)**

Run on 8×H100 nodes, with the same KL-divergence setup, on the BF16
checkpoints of Qwen3.8-Flash-Next (180B, 512 experts) and GLM-5.3-Flash
(321B, 288 experts).
- **Calibration** uses 256 samples instead of 1024, to fit the layerwise
arms in memory and within the cluster's 4-hour job limit. On
Qwen3.8-Flash-Next, the single pass at 1024 samples gives 0.2857, the
same as at 256 within noise (+0.0008 ± 0.0012).
- **Qwen3.8-Flash-Next:** the experts' `down_proj` has 640 inputs, not a
multiple of 256, so only `gate_up_proj` is quantized and `down_proj`
stays BF16 in every arm.

| Model | Plain encode | imatrix, single pass (the recipes) | imatrix,
layerwise |
|---|---|---|---|
| Qwen3.8-Flash-Next (BF16 perplexity 3.28) | 0.2958 (perplexity 3.61) |
**0.2865** (3.60), −0.0093 ± 0.0026, lower in 64/100 | 0.2864 (3.59),
−0.0094 ± 0.0026, lower in 65/100 |
| GLM-5.3-Flash (BF16 perplexity 3.23) | 0.7415 (6.15) | **0.7265**
(6.10), −0.0150 ± 0.0039, lower in 61/100 | 0.7269 (6.10), −0.0146 ±
0.0037, lower in 71/100 |

Mean KL divergence, with paired differences against the plain encode.
- imatrix beats the plain encode on both models.
- Layerwise and the single pass tie: −0.0001 ± 0.0014 on
Qwen3.8-Flash-Next and +0.0004 ± 0.0027 on GLM-5.3-Flash.

**Qwen3.5-35B-A3B (256 experts, top-8), IQ2_XXS on the MLP: routed
experts and shared expert**

| Calibration | Mean KL divergence | Perplexity (BF16: 6.398) | Same top
token |
|---|---|---|---|
| plain encode (`max`) | 0.3115 | 8.50 | 77.9 % |
| imatrix only, raw `E[x²]` | 0.2522 | 7.99 | 79.6 % |
| imatrix only, square root | 0.2467 | 7.92 | 80.0 % |
| GPTQ only (experts get the plain encode; the recipe before this PR) |
0.2193 | 7.75 | 80.7 % |
| GPTQ, then imatrix on the experts, raw | 0.2255 | 7.81 | 80.3 % |
| GPTQ, then imatrix on the experts, square root, layerwise | 0.2122 |
7.71 | 81.0 % |
| **GPTQ, then imatrix on the experts, square root, single pass (this
PR)** | **0.2135** | **7.71** | **81.0 %** |

The imatrix rows other than the last ran layerwise.
- **vs GPTQ only:** −0.0058 ± 0.0014 KL divergence (z = −4.2), lower in
73/100 chunks.
- **Square root vs raw, both layerwise:** −0.0133 ± 0.0012, lower in
89/100.
- **Raw weighting on the experts is worse than no weighting** (+0.0062 ±
0.0016 vs GPTQ only), which is why the square root is the fixed choice.

**Qwen3.8-27B (dense), MLP only, imatrix alone vs GPTQ**

| Calibration | IQ2_XXS | IQ1_S |
|---|---|---|
| plain encode | 0.450 | 1.469 |
| imatrix, raw | 0.362 | 1.219 |
| imatrix, square root | 0.347 | 1.137 |
| GPTQ, unweighted | 0.307 | 0.926 |
| GPTQ, square root | 0.287 | 0.847 |

- **imatrix alone closes 53–63% of the gap from the plain encode to
GPTQ**, with no Hessian or inverse.
- **The square root beats raw:** −0.015 for IQ2_XXS and −0.082 for
IQ1_S, the latter lower in 90/100 chunks.
- **The imatrix rows ran layerwise; the IQ1_S rows use #2723's weighted
IQ1 encoders.**

**Unit tests** (`tests/unit/torch/quantization/test_ggml_imatrix.py`,
CPU):
- imatrix hands the IQ2 search the floored square root of each linear's
input `E[x²]`, and pins the codes; the forward then uses them;
- its output error beats the plain encode;
- `[gptq, imatrix]` keeps GPTQ's payload byte for byte;
- on a tiny Llama, layerwise imatrix gives layer 1 statistics that see
layer 0's quantized MLP, while layer 0's match the single pass;
- a module calibration never reaches gets the plain search;
- a width the encoder can't take is refused before any forward runs,
with and without an enabled activation quantizer, leaving every weight
and amax unchanged;
- running on several ranks warns that the statistics aren't synced;
- on a fused-experts MoE block with a shared expert, quantized with the
`iq2_xxs_experts_only` recipe: each expert's `gate_up_proj` and
`down_proj` get the statistic of the tokens routed to that expert, an
idle expert gets the plain search but still pinned codes, and the shared
expert stays in BF16.

Other tests updated or added:
- `test_presets.py` now expects GPTQ followed by imatrix for every
weighted format, and checks that each experts-only recipe quantizes only
the routed experts, with imatrix.
- `modelopt_recipes/ptq.md` lists the new recipes and the IQ recipes'
new algorithm.
- `test_example_utils.py` covers `--moe_calib_experts_ratio` on
algorithm lists.
- Related suites, in the TensorRT-LLM 1.3.0rc22 container: 1,611 unit
tests (36 files plus `test_example_utils.py`) and 164 GPU tests pass.
These cover local-Hessian (shared hooks), Nemotron-H MTP, fused experts,
GGML GPTQ and backend, config validation, and recipes.
- Folding: after #2710, imatrix-pinned BF16 weights, dense and
fused-expert slices, still hold exactly the pinned codes after
`mtq.fold_weight` and the vLLM fake-quant export's fold.
- Not run: multi-GPU, data-parallel or FSDP2 calibration. The
CPU-offload path ran end to end on GLM-5.3-Flash.

`pre-commit` passes.

### Before your PR is "*Ready for review*"

Make sure you read and follow [Contributor
guidelines](https://github.com/NVIDIA/Model-Optimizer/blob/main/CONTRIBUTING.md)
and your commits are signed (`git commit -s -S`).

Make sure you read and follow the [Security Best
Practices](https://github.com/NVIDIA/Model-Optimizer/blob/main/SECURITY.md#security-coding-practices-for-contributors)
(e.g. avoiding hardcoded `trust_remote_code=True`, `torch.load(...,
weights_only=False)`, `pickle`, etc.).

- Is this change backward compatible?: ✅ A new method, nothing removed.
The built-in IQ1 and IQ2 recipes now encode fused MoE experts with
imatrix; dense models get the same codes as before.
- If you copied code from any other sources or added a new PIP
dependency, did you follow guidance in `CONTRIBUTING.md`: N/A
- Did you write any new necessary tests?: ✅
- Did you update
[Changelog](https://github.com/NVIDIA/Model-Optimizer/blob/main/CHANGELOG.rst)?:
✅
- Did you get Claude approval on this PR?: ❌ Not yet.

### Additional Information

Follows #2665 (GPTQ for GGML), #2686 (weighted IQ2 search) and #2723
(weighted IQ1 search).

🤖 Generated with [Claude Code](https://claude.com/claude-code)


<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit

- **New Features**
- Added imatrix calibration for GGML-compatible quantization, using
input statistics to guide quantization and separate statistics for fused
MoE experts.
  - Added expert-only IQ1 and IQ2 recipes for routed MoE experts.
- **Improvements**
- Updated existing IQ recipes to apply imatrix quantization to fused MoE
experts not processed by GPTQ.
- Imatrix encoding preserves weights already quantized by an earlier
method.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->

---------

Signed-off-by: Chenjie Luo <chenjiel@nvidia.com>
Co-authored-by: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
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