A number you already have, for free, predicts which tensors will hurt

This entire analysis — the full 40+ hour cascaded measurement, the YAQA Hessian correction, every chart on this page — runs on a single Apple M3 Max, 128GB RAM (Mac15,9). As far as this project's own research has been able to establish, it is the first port of YAQA's rounding-error correction to Apple's MLX framework. That claim is a stated goal of the work, not an independently audited record — it is written here as motivation, not as a verified fact the way the numbers below are.

The danger score is coded so lower means more dangerous (see "The setup, in one paragraph" above). P0 (the baseline plan, built purely from isolated KL, before this cascade ever ran) correlates negatively with it — Pearson -0.23, Spearman -0.36 — which is the sensible direction: as danger score drops (more dangerous), isolated KL rises (more real risk). The Hessian's dangerous-tensor calls agreed with the old isolated baseline. The moment the first real cascade round ran (P1), that flips to positive: Pearson +0.17, Spearman +0.16 — the backwards direction. A positive correlation here means the tensors the Hessian calls safe (spread-out curvature) are the ones showing up with higher real, compounding risk, while the ones it flags dangerous turn out comparatively less risky once cascading effects are actually measured. As of the most recent real data on this live run (P3, n=496), it reads Pearson +0.17, Spearman +0.17. (See the layer-coverage caveat below before reading anything into that sign specifically. A separate, earlier real run used an accidental 8-window flat calibration instead of this project's real N=24 stratified calibration — kept only as an archived, non-canonical historical record, not a comparison baseline for the number above; see HESSIAN_STORY_COMPLETE_ROUND.html.)

There is a real, separately-established finding (see this project's V6.4 competition doc) that pushing the whole model's average bit budget below roughly 4.30-4.40 BPW causes weighted ΣKL to explode even while raw ΣKL rises gently -- that is a real, validated, aggregate result about how much total compression the model can absorb before quality collapses. It does not tell you which specific tensor is "the" fragile one. The historical early-QKV floor treated a large isolated-KL reading at an early layer as proof that tensor was intrinsically fragile -- but isolated testing measures a single perturbation propagating through every remaining full-precision layer, so an early perturbation gets more downstream depth to be amplified through no matter which tensor carries it. That is a real, checkable artifact (confirmed above: the single highest isolated-KL tensor in this exact model, in both the old and new calibration data, is layer 0's own linear_attn.out_proj) -- and it is a different mechanism from cascaded compounding, not the same one. Cascaded measurement is not immune to a similar caution: it tells you real risk keeps growing with depth once earlier layers are actually quantized, but attributing that growth to any one tensor "in isolation" still overstates what an aggregate KL number can support -- much like tracing a single neuron's causal role from a whole brain's behavior change. What both signals robustly agree on: middle bit-tiers empty out toward the extremes (see the flow diagram below), and the smallest average bit budget the model tolerates before serious degradation sits close to that same 4.30-4.40 BPW boundary either way.

One specific claim worth checking rather than assuming: that BF16 protection concentrates at the network's boundaries (embedding-adjacent start, lm_head-adjacent end). In this exact plan it does not -- Q16 tensors appear at every one of the 64 layers with no positional clustering (mean layer number 31.5 for Q16 versus 30.4 for Q4, statistically indistinguishable), lm_head itself is assigned Q4, and embed_tokens is not even in the 497-tensor optimizable set to begin with (excluded by pipeline design, never a measured decision). The real, supported pattern is protection by tensor role (see Finding 2 above), not by depth position.

P0's raw/weighted KL sums come from the old isolated measurement's own scale; P1 onward come from the cascaded measurement's scale. These are not directly comparable in magnitude for the reason established elsewhere on this page (isolated KL structurally underrates risk, worse the deeper into the model you go) — compare bit-tier counts across stages, not the raw KL numbers, for an apples-to-apples read.

No — the real numbers say the opposite. The fraction of tensors that stay in the exact same tier climbs sharply from one transition to the next (see the list above): most of the churn happens once, moving away from the old isolated-KL baseline, and then rapidly settles. That's convergence toward a stable allocation shape, not noise — consistent with what Finding 4 on the archived, accidental 8-window flat-calibration page showed for a fully finished run (kept as a historical record only, not a comparison baseline).

An earlier version of this chart reused this project's existing 74-point V3.3 sweep (V3_3_APPLES_TO_APPLES_0005) as a stand-in, with P0 marked separately since it used different calibration. That sweep was traced back to the vendor optiq convert tool's own flat calibration (concatenate-all-domains) -- confirmed by the command in archive/DRAFT_PROMPT.md and by the vendor package containing zero "stratified" code anywhere. This project had only ever run V3.3 once against the real stratified checkpoint before (the single matched P0 point) -- never the full sweep. This chart is that real sweep, generated fresh against Qwen3.8-27B-heretic-ara-OptiQ-5bpw_CLEAN_STRATIFIED/sensitivity_checkpoint.json, same solver, same validation, same output schema as the original -- see run_Qwen38_V3_3_frontier_STRATIFIED_CONTINUE_ON_FAILURE.sh.

Both floors were built on a solid, measured root cause: early-region isolated-KL rankings are far noisier. What isn't documented anywhere in this project is why. This investigation found a real, checkable mechanism: isolated testing perturbs one tensor and leaves every other layer at full BF16, so an early perturbation has far more downstream, untouched, nonlinear depth left to be amplified through than a late one -- confirmed directly (the single highest isolated-KL tensor in this exact model, in both the old flat and new stratified calibration data, is layer 0's own linear_attn.out_proj, roughly 7-12x the median). If a tensor's isolated-KL score is substantially driven by how much amplification runway is left downstream rather than its own intrinsic fragility, ranking tensors against each other within the early region would naturally scramble far more often than in late layers, where there is almost no runway left to distort the ranking. That is a plausible causal explanation for the 34.4%-vs-1.3% split, not a replacement for it.

A solver that needs zero hand-tuned regional floors because its own objective already reflects real cascaded risk. Testable, not aspirational: re-run the two historical incidents that motivated V3.2 and V3.3 -- the V3.1 matched-budget IFEval drop and the V3.2 matched-BPW MMLU drop -- under a cascaded-informed objective with both floors disabled, and check whether the same bad trades still get made. If they don't, the floors become redundant rather than load-bearing, and can be removed or kept purely as a cheap safety net rather than the primary correction. If they still get made, that is real, useful evidence the depth-position floors are catching something the role/cascade signal alone still misses -- also a real answer, just the other one.

This measurement runs in rounds because a single cascaded pass measures every tensor against a specific upstream context -- which bit-width each earlier tensor is assumed to already have. The real bit-width plan computed FROM that measurement can end up disagreeing with the context it was measured against. When it does, a new round automatically starts, re-measuring using the new plan as the updated context, and stops once a round's own output agrees with what it assumed (or a round cap is hit). Every round this run has completed or is currently working through is shown below, separately -- so you can see for yourself whether later rounds broadly agree with earlier ones (converging) or keep shifting (not yet converged), instead of only ever seeing the most recent one.

It isn't a perfect predictor — a Pearson correlation of +0.17 means real, useful signal, not a guarantee. The Spearman rank correlation (+0.17) matters here specifically because it only cares about ordering, not the raw KL scale — so it reads the same whichever calibration mode produced these numbers. Both agree: you can look at data you already have, for free, and get a real head start on which tensors are worth worrying about, before spending 40+ hours finding out the hard way.

When you're deciding where to spend extra bits, this says: favor Query and the attention-input tensors everywhere in the model. You can more safely push Key and attention-output tensors to lower bits, everywhere. That's a real, structural rule you can apply right now — no more waiting on the full run to tell you the same thing layer by layer.

The deeper into the model you go, the more the old, isolated-testing method was underselling the real risk. Every model you've built so far — including this one — used a bit-allocation plan built from that old method. This chart is direct, real evidence that plan is leaving real quality on the table, and it gets worse the deeper you look.

This is a simple linear fit on a real but partial, noisy sample (R²=0.03 — Finding 1's own scatter shows this isn't a tight line). Treat the predicted table as informed triage, not certainty: a real ranking signal to look at before the run gets there, not a substitute for the actual measurement once it arrives.