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# Oral-A-v4: causal calibration of hierarchical feedback maps
## Status and claim boundary
The output-error-only V2/V3 feedback families failed their frozen early-layer
causal-capture gates. A held-out oracle then showed that ordinary downstream
activations are not enough, whereas gated 3x3 maps of the actual residual-DAG
child error fields can reconstruct early credit almost exactly. Fixed random
hierarchical FA subsequently improved the matched short ResNet-20 endpoint to
43.52% from DFA's 37.16%, but failed its frozen 50% full-run gate.
V4 is the first trainable use of that diagnosed spatial hierarchy. Every
feedback convolution consumes its local child teaching field. One independent
Rademacher tensor is drawn in each feedback-parameter space; all induced parent
fields are injected in a single antithetic pair, and the scalar task-loss
derivative estimates each edge's causal target moment. The locally computed
prediction moment is subtracted before updating Q/R. Forward weights are never
copied or read by the learning rule, and no reverse-mode differentiation is
used.
Recursive learned feedback is not claimed as the Harnett-specific novelty.
V4 is an engineering prerequisite for a later hierarchical innovation model
and must be compared with fixed HFA, learned FA/weight mirroring, and BurstCCN.
The frozen Oral-A-v1 failure remains failed; V4 cannot retroactively open A4.
No V4 GPU endpoint was observed before this protocol and its selector were
committed. CIFAR-10 test and confirmation seeds 10--14 remain untouched.
## V4-0: mechanics gate
Before any endpoint, `experiments/conv_local_smoke.py` must verify:
- the simultaneous BatchNorm-coupled antithetic JVP to relative error below
`2e-6`;
- under an audit-only symmetric Q=W and R=-Wout-transpose copy, every predicted
local feedback moment equals its exact causal delta-rule target to relative
error below `2e-12`;
- the symmetric hierarchical field and local parameter update continue to
reproduce exact BP under the pre-existing thresholds;
- all legacy convolutional checks remain green.
This gate passed with JVP error `6.16e-10`, delta-rule relative error
`2.30e-16`, hidden-field relative error `4.97e-16`, and parameter-update
absolute error `1.49e-8`. Actual training never makes the symmetric copy.
## V4-1: frozen-forward causal-capture gate
Use seed-0 ResNet-20, the first 10,000 development-training examples, batch
128, the frozen 45k/5k split, random hierarchical feedback scale 1, one
direction, `sigma=0.01`, perturbation seed 1000, and a fixed 64-example exact
gradient audit. Forward weights, readout, BatchNorm state, and affine
parameters remain bitwise fixed.
Record one uncalibrated HFA reference and calibrate Q/R for 400 feedback-only
minibatches at `eta_A in {0.1, 1.0, 10.0}`. Select maximum early-third
teaching/negative-gradient cosine, then maximum all-layer cosine, then lower
rate. V4-1 passes only if all four records are finite and the selected method:
1. reaches early-third alignment at least `0.05`;
2. reaches all-layer alignment at least `0.10`;
3. exceeds the matched uncalibrated HFA early alignment by at least `0.04`;
4. keeps every feedback/forward audit norm ratio in `[0.1, 3.0]`.
The norm gate is audit-only and prevents a scale explosion from being hidden
by cosine. No extra rate, query count, initialization, warmup, normalization,
or per-layer schedule is added after endpoints are observed.
## V4-2: bounded short accuracy gate
Only a V4-1 pass opens a 10k-example, 20-epoch ResNet-20 validation screen.
Copy A2b exactly: batch 128, cosine decay, no warmup, momentum 0.9, weight decay
`1e-4`, output LR 0.1, and hidden LR `{0.03, 0.1}`. Use the V4-1-selected
feedback rate, 400 feedback-only warmup minibatches, then K1/every-4 joint
calibration. Select validation accuracy, then lower MACs/rate.
Advance only if both runs are finite, selected V4 reaches at least 60%, exceeds
fixed HFA's 43.52% by at least 10 points, retains early alignment at least
0.05, and does not exceed `1.5x` exact-BP estimated MACs. Failure closes V4
without a full run or an expanded grid.
## V4-3: full validation and confirmation rule
Only a V4-2 pass opens one 200-epoch seed-0 validation run on all 45,000
development-training examples. Copy the selected hidden rate, output rate 0.1,
400-step feedback warmup, K1/every-4 joint calibration, and the A1 step drops
at epochs 100/150. It must be finite, finish within 5 points of BP 91.62%, beat
DFA 33.06% and fixed HFA 43.52% by at least 2 points, retain early alignment
0.05, and remain within `1.5x` BP MACs. There is no recovery branch.
A complete V4-3 validation pass may move the strict reviewer forecast from 5
to 6 and permits a new, separately frozen hierarchical-SDIL residualization
test. It does not itself establish Harnett-specific novelty. Only after that
innovation test passes may an independent ResNet-20/32/56 confirmation be
specified; no test endpoint is authorized by V4-1 or V4-2.
## Audited outcome (2026-07-22)
V4-1 failed. The uncalibrated reference has early/all-layer alignment
`-0.000263/0.011279`. At `eta_A=0.1`, 400 causal calibration events move these
to only `-0.000180/0.017336`; feedback norms remain controlled. At `eta_A=1`,
early/all alignment is `0.000348/0.007922`, but the maximum feedback/forward
norm ratio explodes to `58.48`. The `eta_A=10` feedback state becomes
nonfinite. Mean prediction/target cosine is at most `0.000668` across the
finite learned candidates.
Consequently the selected finite candidate fails all four substantive gates,
and the four-record finite gate also fails. Each learned record used exactly
800 logical batch-loss queries and estimated `1.2254e13` MACs before any task
weight update. V4-2 and V4-3 are not launched, test remains untouched, and the
reviewer score remains 5/10.
The result falsifies this simultaneous global-task-scalar estimator at the
frozen budget; it does not falsify the representational value of hierarchy.
Further rate or query-budget tuning of V4 is prohibited. A next branch must
change the information source, for example by using a locally observed child
response as in learned FA/weight-mirroring controls, rather than estimating
267,904 feedback parameters from the same global scalar projection.
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