Certifying Compressed Language Models: An Audit and a Statistical Toolkit
Organizations: Georgia Institute of Technology
Abstract
A fraction of a point of benchmark accuracy is the usual evidence that a compressed model is equivalent to its original. That quantity is least informative when two models are most alike: a net delta is what survives cancellation between opposing per-item changes, and cancellation is most complete in the regime equivalence claims occupy. Across an atlas of 1,707 paired model-by-task cells mined from public per-item evaluation dumps (1.3B-405B), churn runs roughly five times the net accuracy delta, and cells scoring identically to their baseline still disagree on individual items. In a preregistered audit of 17 equivalence claims from three registered frames (method papers, model cards, vendor documentation), 16 are eligible. None states a prospective numerical equivalence margin, and none releases task-matched per-item outputs, though 3 release outputs for other tasks only; 5 report too little to assess numerically, so a reader cannot check them at any sample size. We audit evidential sufficiency, not truth: no claim is called false. We supply the missing instrument: paired equivalence testing at a declared margin, with certification tables giving the items an evaluation needs, computed from disagreement observed under compression, not from independent-binomial variance. A controlled experiment pairs GPTQ and AWQ on byte-identical calibration samples across five seeds. Under the frozen eight-cell decision rule H3 is supported: changing the calibration draw was sufficient to reverse the observed method ordering in 5 of 8 confirmatory cells. The reporting standard we propose is five lines: declare a margin, run the paired test, report churn beside net delta, cite the sample size you met, release per-item outputs. It applies to any comparison between two models alike enough to be worth comparing. All per-item outputs, protocols and code are released.
Figures & tables
| Benchmark | Atlas cells | Discordance p25/med/p75 | Required p25/ med /p75 | Naive | Advantage |
|---|---|---|---|---|---|
| musr | 24 | 0.015 / 0.034 / 0.044 | 232 / 519 / 681 | 7,617 | |
| gpqa | 24 | 0.035 / 0.048 / 0.067 | 545 / 749 / 1,035 | 7,233 | |
| bbh | 192 | 0.024 / 0.044 / 0.060 | 371 / 681 / 928 | 6,492 | |
| mmlu_pro | 5 | 0.048 / 0.053 / 0.059 | 739 / 827 / 913 | 7,695 | |
| hellaswag | 23 | 0.031 / 0.045 / 0.099 | 477 / 695 / 1,538 | 4,905 | |
| arc_challenge | 17 | 0.072 / 0.079 / 0.099 | 1,112 / 1,218 / 1,536 | 7,363 |
| S1 | S2 | |
|---|---|---|
| Cells | 1,398 | 309 |
| Median accuracy-state churn | 0.137452 | 0.048000 |
| Median net accuracy delta | 0.026316 | 0.009242 |
| TOST-equivalent at 2 pp | 68 (4.9%) | 53 (17.2%) |
| Exact McNemar | 371 (26.5%) | 19 (6.1%) |
| Prospective numerical decision margin | Retrospective numerical description of a result | Qualitative language only, no number | |
| Numerically assessable | 0 | 5 | 7 |
| Not numerically assessable | 0 | 1 | 3 |
| Total | 0 | 6 | 10 |
| Classification across the atlas-IQR interval | Claims |
|---|---|
| Above the planning threshold throughout | 10 |
| Changes classification within the interval | 1 |
| Below the planning threshold throughout | 0 |
| Total assessable | 11 |
| Model | Task | Flip | Range/gap | |||
| Qwen2.5-1.5B | MMLU | 0.012292 | 0.040521 | 0.018445 | TRUE | TRUE |
| Qwen2.5-1.5B | GSM8K | 0.096800 | 0.014000 | 0.033000 | FALSE | FALSE |
| Llama-3.2-3B | MMLU | 0.030922 | 0.063809 | 0.029341 | FALSE | TRUE |
| Llama-3.2-3B | GSM8K | 0.017800 | 0.011000 | 0.034000 | TRUE | TRUE |
| Qwen2.5-7B | MMLU | 0.006267 | 0.015667 | 0.012391 | FALSE | TRUE |
| Qwen2.5-7B | GSM8K | 0.005800 | 0.048000 | 0.035000 | TRUE | TRUE |
| Atlas (observational) | Controlled | |
|---|---|---|
| Ratio of medians | 5.40 | 12.1 |
| Median of per-cell ratios | 3.85 | 12.7 |
| Cells entering the per-cell median | 1,562 of 1,707 | 8 of 8 |
Appendix figures & tables14 assets
Supplementary material from the paper’s appendix.
Appendix
| Date | Artifact | Commit | What it fixed in advance |
|---|---|---|---|
| 2026-07-11 | PREREGISTRATION.md | — | Grid, metrics, TOST margin (2 pp), H3 decision rule |
| 2026-07-15 | Three registrations | b74fd58 | Audit, atlas-mining, and mini-grid protocols |
| 2026-07-15 | Audit Amendment 1 | d6e02dd | Blind-extraction independence mechanism |
| 2026-07-15 | Pair manifest | f06348f | The 59 atlas pairs, before any flip statistic |
| 2026-07-15 | Claim table | 715a7ce | The 17 audited claims, before any verdict |
| 2026-07-20 | WikiText-2 amendment | — | “Document” definition, Decision Point A |
| Claim | Frame | Source |
|---|---|---|
| R01 | F1 | GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers (Frantar, Ashkboos, Hoefler, Alistarh) |
| R02 | F1 | LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale (Dettmers, Lewis, Belkada, Zettlemoyer) |
| R03 | F1 | SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models (Xiao, Lin, Seznec, Wu, Demouth, Han) |
| R04 | F1 | AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration (Lin, Tang, Tang, Yang, Chen, Wang, Xiao, Dang, Gan, Han) |
| R05 | F1 | SqueezeLLM: Dense-and-Sparse Quantization (Kim, Hooper, Gholami, Dong, Li, Shen, Mahoney, Keutzer) |
| R06 | F1 | A Simple and Effective Pruning Approach for Large Language Models [Wanda] (Sun, Liu, Bair, Kolter) |
| Claim | Family | Bits | Benchmark | |
|---|---|---|---|---|
| R01 | gptq | 4 | piqa | 1,838 |
| R02 | w8a8_int8 | 8 | (mixed/unmatched) | — |
| R03 | w8a8_int8 | 8 | (mixed/unmatched) | 18,300 |
| R04 | awq | 4 | gsm8k | 1,319 |
| R05 | squeezellm | 4 | mmlu | 14,042 |
| R06 | pruning | — | (mixed/unmatched) | 18,904 |
| Claim | MDD (paired) | MDD (indep.) | @Q1 | @median | @Q3 | ||
|---|---|---|---|---|---|---|---|
| R01 | 1,838 | 2.36 | 3.62 | 1,364 | 2,010 | 4,328 | 0.1189 |
| R02 | — | — | — | 619 | 866 | 1,237 | — |
| R03 | 18,300 | 0.49 | 1.38 | 619 | 866 | 1,237 | — |
| R04 | 1,319 | 2.09 | 3.77 | 1,137 | 1,137 | 1,137 | — |
| R05 | 14,042 | 0.90 | 1.63 | 1,525 | 2,255 | 3,865 | 0.9085 |
| R06 | 18,904 | 0.70 | 1.36 | 932 | 1,841 | 6,046 | — |
| Locus of the claim | Form it takes in the card | Cards |
|---|---|---|
| Prose assertion | states recovery percentages outright | 3 |
| Prose juxtaposition | states two scores, characterises neither | 2 |
| Table cell only | no comparative sentence anywhere | 1 |
| MDD | MDD / 2 pp | |||
| Claim | paired | indep. binomial | paired | indep. binomial |
| R01 | 2.36 pp | 3.62 pp | ||
| R05 | 0.90 pp | 1.63 pp | ||
| R07 | 0.87 pp | 1.63 pp | ||
| R06 | 0.70 pp | 1.36 pp | ||
| R17 | 0.61 pp | 1.09 pp | ||
| Benchmark | Atlas cells | Discordance p25/med/p75 | Required p25/ med /p75 | Naive | Advantage |
|---|---|---|---|---|---|
| musr | 24 | 0.015 / 0.034 / 0.044 | 928 / 2,076 / 2,721 | 30,468 | |
| gpqa | 24 | 0.035 / 0.048 / 0.067 | 2,180 / 2,993 / 4,138 | 28,931 | |
| bbh | 192 | 0.024 / 0.044 / 0.060 | 1,484 / 2,721 / 3,710 | 25,967 | |
| mmlu_pro | 5 | 0.048 / 0.053 / 0.059 | 2,955 / 3,305 / 3,649 | 30,778 | |
| hellaswag | 23 | 0.031 / 0.045 / 0.099 | 1,905 / 2,777 / 6,151 | 19,618 | |
| arc_challenge | 17 | 0.072 / 0.079 / 0.099 | 4,447 / 4,870 / 6,141 | 29,451 |
| Benchmark | Atlas cells | Discordance p25/med/p75 | Required p25/ med /p75 | Naive | Advantage |
|---|---|---|---|---|---|
| musr | 24 | 0.015 / 0.034 / 0.044 | 104 / 231 / 303 | 3,386 | |
| gpqa | 24 | 0.035 / 0.048 / 0.067 | 243 / 333 / 460 | 3,215 | |
| bbh | 192 | 0.024 / 0.044 / 0.060 | 165 / 303 / 413 | 2,886 | |
| mmlu_pro | 5 | 0.048 / 0.053 / 0.059 | 329 / 368 / 406 | 3,420 | |
| hellaswag | 23 | 0.031 / 0.045 / 0.099 | 212 / 309 / 684 | 2,180 | |
| arc_challenge | 17 | 0.072 / 0.079 / 0.099 | 495 / 542 / 683 | 3,273 |
| Field | Value |
|---|---|
| pair_index / source | 35 / S1 |
| Task | harness_hendrycksTest_high_school_geography_5 (MMLU) |
| Base model | project-baize/baize-v2-7b |
| Quantized model | TheBloke/Project-Baize-v2-7B-GPTQ (GPTQ) |
| 198 | |
| Baseline accuracy | 0.429293 |
| Cell | Winner flip | Range/gap holds | ||
| Qwen2.5-1.5B / MMLU | TRUE | 0.012292 | 0.040521 | TRUE |
| Qwen2.5-1.5B / GSM8K | FALSE | 0.096800 | 0.033000 | FALSE |
| Llama-3.2-3B / MMLU | FALSE | 0.030922 | 0.063809 | TRUE |
| Llama-3.2-3B / GSM8K | TRUE | 0.017800 | 0.034000 | TRUE |
| Winner flip in 2 of 4 cells (threshold : met) | ||||
| Range/gap holds in 3 of 4 cells (threshold : met) | ||||
| Model | Task | |||||
|---|---|---|---|---|---|---|
| Qwen2.5-1.5B | MMLU | |||||
| Qwen2.5-1.5B | GSM8K | |||||
| Llama-3.2-3B | MMLU | |||||
| Llama-3.2-3B | GSM8K | |||||
| Qwen2.5-7B | MMLU | |||||
| Qwen2.5-7B | GSM8K |
| Seed-level SD | Item-level SE | ||||
|---|---|---|---|---|---|
| Model | Task | GPTQ | AWQ | GPTQ | AWQ |
| Qwen2.5-1.5B | MMLU | 0.019130 | 0.006897 | 0.004215 | 0.004212 |
| Qwen2.5-1.5B | GSM8K | 0.006340 | 0.015116 | 0.015796 | 0.015658 |
| Llama-3.2-3B | MMLU | 0.024925 | 0.011157 | 0.004214 | 0.004216 |
| Llama-3.2-3B | GSM8K | 0.004615 | 0.012300 | 0.015154 | 0.015308 |
| Qwen2.5-7B | MMLU | 0.006224 | 0.004537 | 0.003983 | 0.004002 |
| Task | in paired SE | in paired SE |
|---|---|---|
| MMLU ( ) | 5.53 – 17.45 | 2.21 – 8.45 |
| GSM8K ( ) | 1.92 – 3.61 | 0.44 – 5.65 |
| Cond | Configuration vs. reference | Acc | Net | c i / i c | ||
| GSM8K , , reference accuracy , | ||||||
| A | exemplars as separate turns | 0.515 | 0.240 | 30 / 18 | 0.836 | |
| B | strict-match rescore | 0.120 | 0.455 | 91 / 0 | 1.585 | |
| C | chat template off, 3-shot | 0.475 | 0.320 | 42 / 22 | 1.115 | |
| D | stock defaults (chat off, 5-shot) | 0.495 | 0.300 | 38 / 22 | 1.045 | |
| MMLU , , reference accuracy , | ||||||
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