PAPER.md

Quantization Regime and Governed Routing: A 2×2 Study of QAT Q4_0 versus PTQ Q4_K_M for Gemma 4 12B (dense) and 26B MoE under a Fixed Governance Stack

Dates: runs 2026-08-10, repeats and controls 2026-08-10/11 (Asia/Tokyo) · Hardware: single NVIDIA RTX 5070 Ti (16 GB) · Backend: Ollama 0.30.6 Series: companion/sequel to the Gemma 4 MTP Quality–Throughput Study (repo gemma4-mtp-quality-study, DOI 10.5281/zenodo.21860461) Status: exploratory engineering study on a frozen local harness; single-run per cell; not preregistered; not an independent benchmark standard

---

Abstract

We measure what quantization regime — quantization-aware-trained Q4_0 (QAT) versus post-training-quantized Q4_K_M (PTQ) — is worth on governed routing tasks: answer-entitlement decisions (verify / date-bound / re-anchor / abstain) made under a fixed governance stack, rather than answer-content benchmarks. We run a 2×2 design (regime × released model pair) over Gemma 4 12B (dense, 11.9B — a clean same-base pair) and a 26B-class MoE pair (25.8B PTQ vs 25.2B QAT released artifacts — a quasi-contrast that may embed a base revision), each on a 100-task Smoke-100 and a 500-task Core-500 candidate suite, all cells same-day on one consumer GPU with the governance stack bit-identical and temperature 0. Aggregate route correctness spans 0.738–0.760 on Core-500; we ran no equivalence test, and one cross-model contrast (12B-PTQ vs 26B-PTQ) is nominally significant (exact McNemar p=0.035). The paired within-model regime effects are individually marginal and oppositely signed: QAT −0.012 on the dense 12B (p=0.070) and +0.018 on the MoE pair (p=0.078). The regime × pair interaction — this study's headline, an exploratory single-run finding — is +0.030 with a stem-clustered bootstrap 95% CI of [+0.010, +0.052] (primary; Core-500 is 100 stems × 5 paraphrases, so tasks are not independent) and [+0.008, +0.052] under naive task-iid resampling. The interaction concentrates almost entirely in the volatile-current family, where the two pairs' scores cross (0.5314/0.4971 vs 0.4971/0.5314). Attribution: with the released artifacts, regime is confounded on the MoE side with a possible base revision and with a CPU-offload compute path, so we claim conditionality on the released artifact pair, not on architecture per se. Meanwhile regime choice massively perturbs the text of temperature-0 outputs: only 23–32 % of same-task responses are byte-identical across regimes (median first divergence at 46–73 characters), against same-configuration Smoke-100 repeat baselines of 100/100 in all four cells (including the CPU-offloaded PTQ MoE cell, repeated across run windows) and a 100/100 byte-identity control for the one regime-correlated configuration difference (num_ctx). Safety-critical failure rates are 0.000 in seven of eight runs; the eighth (26B-PTQ Core-500) logged a single over-verification event (0.008 on stable controls). We conclude that on this stack the QAT premium is not a scalar — it differs in sign across the two released pairs at ≈3 percentage points, too small to survive aggregate averaging but visible in a paired crossed design — and that quantization regime should be treated as a behavioral change (different outputs), not merely a quality change (different scores).

---

1. Background and motivation

The predecessor study (Gemma 4 MTP Quality–Throughput Study, 2026-08-09, same GPU) measured multi-token-prediction speed/quality trade-offs with both models already in QAT Q4_0 form, leaving the value of QAT itself unmeasured. Separately, the same day as this study, the local MMV-Medium governance release (MMV-M-RC3.3) underwent a model-binding update from the PTQ gemma4:12b to the QAT gemma4:26b-a4b-it-qat on head-to-head evidence in which regime and model were deliberately confounded (production binding vs. candidate binding). This study completes the missing cells: the anti-diagonal (12B QAT, 26B PTQ) of the resulting 2×2. Two of the four cells (12B-PTQ, 26B-QAT) are therefore reused from that production head-to-head (disclosed further in §3); the anti-diagonal cells are the independent addition.

Vendor documentation claims QAT Q4 models retain near-full-precision quality where naive PTQ degrades (see LITERATURE_SEARCH.md in this package). Published comparisons, however, measure general knowledge/reasoning benchmarks on raw models. In the searches we ran (shallow, links-and-abstracts level — see the literature file's own caveat) we found no prior measurement of (a) QAT-vs-PTQ deltas on routing/abstention-style decisions under a governance stack, (b) the same contrast at two scales in a paired same-task design, or (c) regime-to-regime exact-output divergence at temperature 0. We do not claim novelty for the general QAT-beats-PTQ direction, and we flag (c) as plausibly adjacent to community regression reports on cross-quantization output changes.

2. Design

2×2 factorial, one variable per axis as far as the released artifacts allow:

	PTQ (Q4_K_M)	QAT (Q4_0)
12B dense	gemma4:12b (11.9B, emb 3840)	gemma4:12b-it-qat (11.9B, emb 3840)
26B MoE	gemma4:26b (25.8B, emb 2816)	gemma4:26b-a4b-it-qat (25.2B, ~4B active, emb 2816)

• The 12B pair is the clean contrast: identical parameter count and embedding width; the artifacts differ only in quantization recipe.
• The 26B pair is a quasi-contrast: the released artifacts report 25.8B vs 25.2B parameters, so a base-revision difference cannot be excluded. Moreover, Ollama metadata does not expose expert structure, so we cannot verify that the two 26B artifacts share the same MoE configuration (an earlier harness profile note describes gemma4:26b as ~3.8B-active, vs ~4B for the QAT artifact). Findings attributed to "regime" on the 26B side are strictly findings about the released artifact pair.

Constant across all eight primary runs: the MMV Large RC3.3 v3.1 governance stack (route_transformer + post_validator + force_reanchor_v2) applied bit-identically; think: false; temperature 0.0; max_tokens 1024; one GPU; sequential execution; same Ollama build; same suite and label files (SHA-256 pinned in ENVIRONMENT.md).

The one regime-correlated configuration difference, and its control. The two Q4_0 QAT profiles pin num_ctx: 8192 because their Modelfiles declare a 262,144-token context whose KV allocation fails on a 16 GB card; the PTQ profiles run at the Ollama default context. Since this difference tracks the regime axis exactly, we ran a direct control: the 12B-PTQ Smoke-100 suite re-run with num_ctx: 8192 produced 100/100 byte-identical outputs versus its default-context run. Within this study's prompt lengths, num_ctx is load feasibility, not behavior. (The control was run on the 12B cell only; we extrapolate it to the 26B pair.)

3. Tasks, metrics, and statistics

Suites. OPERATE-FR Smoke-100 (N=100) and Core-500 candidate (N=500, a controlled 5× neutral prompt-frame expansion of Smoke-100: 100 base stems × 5 paraphrase variants, preserving the family distribution: volatile_current 175, stable_control 125, stale_premise_trap 75, date_boundary 50, query_neutrality 50, ambiguous_time_frame 25). Tasks probe whether answering is warranted and in what mode (verify, date-bound answer, re-anchor, abstain), classified by the harness's transparent rule-based detector. Because Core-500 tasks are paraphrase clusters, its 500 rows are not independent observations; statistics below address this explicitly.

Primary metric. Route correctness (classified route ∈ allowed routes), recomputed from row-level results by the deposited analysis script, which also derives per-family tables from the suites' authoritative family fields. Exception: the safety-rate metrics (stale commitment, unsupported current claim, over-verification) are quoted from the harness scorer's summary outputs, which are archived alongside the raw rows.

Statistics. Within-model regime effect: two-sided exact McNemar on paired same-task outcomes (the "exact" binomial computation is exact only under an independence assumption that paraphrase clustering violates; treat those p-values as approximate and anti-conservative). Interaction: delta-of-deltas on Core-500 with a stem-clustered bootstrap (resample the 100 stems, 10,000 resamples, seed 20260810) as the primary interval, and a naive task-iid bootstrap reported for comparison. Determinism baseline: same-configuration Smoke-100 repeats of all four cells.

Provenance and timeline (JST). No preregistration exists; the 2×2 design and the interaction endpoint were specified before the anti-diagonal cells ran, but analysis details were fixed at analysis time — treat every inferential statement as exploratory. 2026-08-10 early-to-mid afternoon: 12B-PTQ and 26B-QAT cells (reused from the same-day MMV-M production head-to-head; superseded earlier runs of the same PTQ cells from 2026-05/06 score equal or lower, so no favorable-selection is present). Evening: 12B-QAT and 26B-PTQ cells, then 12B repeats. Late night into 2026-08-11: 26B repeats and the num_ctx control. All 13 runs (8 primary + 4 repeats + 1 control = 2,900 rows) completed with 0 errored rows.

4. Results

4.1 Cell aggregates (Core-500, N=500)

cell	route_correctness	preferred_match	mean latency (ms)	mean resp. chars
12B PTQ	0.760	0.544	2,482	751
12B QAT	0.748	0.542	2,626	834
26B PTQ	0.738	0.540	3,252 †	875
26B QAT	0.756	0.540	1,613	899

† 26B PTQ (17 GB on disk) runs with a ~26/74 CPU/GPU split on the 16 GB card; its latency reflects offload, not model properties, and is excluded from all conclusions. Smoke-100 aggregates: 0.88 / 0.86 / 0.83 / 0.86 — same direction, with the two QAT cells tied.

The Core-500 spread is 0.022 (11 tasks of 500). We ran no equivalence test, so "the cells are tied" is not a supported claim; indeed the one within-regime cross-model contrast, 12B-PTQ vs 26B-PTQ, is nominally significant (17 vs 6 discordant, exact McNemar p=0.035, uncorrected). What the aggregates do show is that no cell separates by a margin of operational consequence on this suite.

Safety-critical rates (stale commitment, unsupported current claim, over-verification on stable controls): 0.000 in seven of eight runs; the 26B-PTQ Core-500 run logged one over-verification event (0.008 = 1/125 stable controls, consistent with its 0.976 stable_control entry in §4.4). With events this rare, the data bound rather than establish regime-invariance: by the rule of three, each run's 95% upper bound is ≈0.6–2.4 % depending on the denominator.

4.2 Paired regime effect within model

suite	pair	QAT-only correct	PTQ-only correct	Δ (QAT−PTQ)	McNemar p
Core-500	12B dense	1	7	−0.012	0.0703
Core-500	26B MoE	15	6	+0.018	0.0784
Smoke-100	12B dense	0	2	−0.020	0.50
Smoke-100	26B MoE	5	2	+0.030	0.4531

Neither within-model effect reaches p<0.05, but both sit near the margin with opposite signs, and the smaller Smoke-100 suite points the same way in both pairs. The discordant tasks cluster by stem (the 12B pair's 8 discordants come from 5 stems), which is one reason these p-values should be read as approximate (§3).

4.3 The interaction is the finding — exploratory, but robust to clustering

Delta-of-deltas (26B effect − 12B effect) on Core-500: +0.030. Primary stem-clustered bootstrap 95% CI: [+0.010, +0.052]; naive task-iid CI: [+0.008, +0.052]. Both exclude zero. This is a single-run, non-preregistered endpoint computed alongside four within-model tests and a family decomposition, with no multiplicity correction — we label it an exploratory finding that survived a clustering-robust re-analysis, not a confirmed effect. On this stack, QAT helps the released MoE pair and mildly hurts the clean dense pair; the two effects cancel almost exactly in any aggregate that averages over models.

4.4 Family decomposition: a crossed pattern in volatile_current

Core-500 route correctness by family (from the suites' authoritative family fields; reproduced by the deposited script):

family	n	12B PTQ	12B QAT	26B PTQ	26B QAT
volatile_current	175	0.5314	0.4971	0.4971	0.5314
ambiguous_time_frame	25	0.560	0.600	0.480	0.600
date_boundary	50	0.660	0.640	0.600	0.580
stale_premise_trap	75	0.9467	0.9467	0.9600	0.9600
stable_control	125	0.984	0.984	0.976	0.984
query_neutrality	50	0.920	0.920	0.920	0.920

The interaction concentrates in volatile_current (the family that decides whether a currency-sensitive question deserves verification or a dated hedge), where the four cells form a crossed pattern: the dense pair loses under QAT where the MoE pair gains. That the crossed rates land on numerically identical values (93↔87 correct of 175) is a coincidence of small discordant counts and carries no inferential content; no test is attached to this table. Easy families (stale_premise, stable, neutrality) are regime-invariant here; date_boundary drifts −0.02 under QAT in both pairs (n=50, descriptive only) — directionally consistent with the date_boundary watch item recorded in the same-day production binding-update freeze note (an internal record; noted for continuity, not as independent evidence).

4.5 Regime is a behavioral change: exact-output divergence

Byte-identical same-task responses across regimes at temperature 0:

suite	pair	exact match	rate	median first divergence (chars)
Core-500	12B	148/500	29.6 %	73
Core-500	26B	116/500	23.2 %	69
Smoke-100	12B	32/100	32.0 %	46
Smoke-100	26B	27/100	27.0 %	57

Against this, the same-configuration Smoke-100 repeat baseline is 100/100 byte-identical in all four cells — including the CPU-offloaded 26B-PTQ cell, and with repeats separated from their base runs by 8–10 hours (crossing run windows and, for the 26B cells, a date boundary). The runtime is run-to-run deterministic here, so the cross-regime divergence on Smoke-100 is attributable to the weights (plus, for the 26B pair, the systematic compute-path difference — see §6.3). No Core-500 repeats were run; the attribution extends to Core-500 rows by inference from the Smoke-100 baselines, not by direct measurement. Quantization regime changes what the model says in 68–77 % of governed responses even while leaving how often it is right within ≈2 points — the same dissociation between string reproducibility and objective quality that the predecessor MTP study reported for speculative decoding, now shown for quantization recipes. Practical corollary: hash-based output caching, audit replay, or golden-file tests do not survive a quantization-regime swap, even at temperature 0.

5. Discussion

The QAT premium is pair-conditional here, not scalar. Vendor framing ("QAT preserves quality") treats the QAT benefit as a property of the recipe. On governed routing tasks we find a signed interaction: ≈+2 points (Core-500) for the released MoE pair, ≈−1 point for the clean dense pair. Three mechanisms are compatible with the data and not separable by this design: (i) 4-bit noise interacts differently with expert routing than with dense activations; (ii) the 26B released pair differs by more than regime (possible base revision, unverifiable expert configuration), so part of the 26B gain may be base improvement; (iii) the 26B-PTQ cell ran partially on CPU, so kernel-numerics differences are regime-correlated on that side. The 12B side carries none of these confounds — its artifacts are same-base, its cells all-GPU, and the num_ctx difference is controlled to byte-identity — and on that clean pair, QAT bought nothing on these tasks (directionally, it cost ≈1 point at p=0.07).

Aggregates hide the effect. The four Core-500 cell scores span 0.022. Only the paired-and-crossed design exposes the structure. This is a caution for model-selection practice: aggregate "quality parity" verdicts can conceal offsetting family-level and pair-level shifts.

Operational reading (inference, not test result). Two of the four cells are the same runs that motivated the same-day production model-binding decision, so using this study to "validate" that decision is partially circular; the independent evidence is the anti-diagonal. With that caveat: the QAT 26B artifact remains the best-or-tied cell on the two hardest families while being the fastest memory-fitting cell, and the clean-pair result gives no reason to move the dense-tier rollback binding off PTQ gemma4:12b.

6. Threats to validity

1. 26B pair purity. 25.8B vs 25.2B released artifacts; unverifiable expert configuration; regime, base revision, and MoE structure are confounded on that side. The headline survives only under the reading "released artifact pairs" — which is the operationally relevant one, and the reading used throughout this paper.
2. Paraphrase clustering. Core-500 is 100 stems × 5 paraphrases; McNemar "exact" p-values assume independence and are anti-conservative; the interaction CI is therefore reported stem-clustered as primary. Effective sample size is nearer 100 than 500.
3. Compute-path and window confounds (26B side). 26B-PTQ ran ~26/74 CPU/GPU; CPU-vs-GPU numerics differ systematically, and the 26B cells ran in different windows. Repeats (100/100 across windows, including the offloaded cell) rule out run-to-run nondeterminism, but a systematic offload contribution to the 26B regime effect and divergence rows cannot be excluded.
4. Exploratory statistics. No preregistration; ≥5 inferential quantities computed; no multiplicity correction; single run per cell.
5. One stack, one GPU, one runtime. Ollama 0.30.6, one governance stack, rule-based route classification, routing tasks only. Generalization to other runtimes, stacks, or answer-content quality is unmeasured. The num_ctx control was run on the 12B cell only.
6. Family attribution. date_boundary/ambiguous cells have n=50/25; their drifts are descriptive only.
7. Contamination. Public Gemma weights; suite prompts are local and unpublished at run time, but no training-corpus audit exists.

7. Reproducibility

REPRODUCE.md gives the exact commands. Environment, model digests, and suite/label SHA-256 hashes: ENVIRONMENT.md. Row-level results (13 runs, 2,900 rows, 0 errored) are retained in the private study archive and identified by SHA-256; the public package ships processed tables and the deterministic analysis script (seed 20260810) that recomputes every routing statistic in this paper — including the §4.4 family table — from row level. The safety rates in §4.1 are quoted from the harness scorer's archived summary outputs.

8. Conclusion

On a fixed governance stack and consumer GPU, quantization regime moved governed-routing quality by at most ≈±2 points within a released pair — below per-pair significance, but with a clustering-robust, family- concentrated, oppositely-signed interaction across the two pairs — and it moved the bytes of 68–77 % of temperature-0 outputs. Choose regimes per released artifact pair and per task family, not by recipe reputation; and treat any quantization swap as a behavioral migration, not a drop-in.