# Oral-A-v3: vectorizer-space causal calibration

## Status and claim boundary

Oral-A-v1 failed full ResNet training and Oral-A-v2 failed its frozen-forward
early-layer causal-capture gate. Both outcomes remain failed. The post-v2
oracle audit showed that learned channel-subspace calibration reached only
`0.007209` early-third alignment, versus `0.023966` for the same vectorizer
family fit directly to exact causal targets on a disjoint batch. V3 changes
only this diagnosed regression interface: it estimates the A/G matrix target
directly in the vectorizer parameter subspace rather than estimating
per-example channel coefficients and regressing them afterward.

V3 remains forward-only. Each direction uses the same two antithetic task-loss
queries, K1/every-4 cadence, output-error context, channel-gated teaching field,
local forward-weight eligibility, and no weight transport. No V3 GPU endpoint
was observed before this protocol and its executable selectors were committed.
The CIFAR-10 test set and seeds 10--14 remain untouched.

## V3-0: exact mechanics and matched variance

`experiments/conv_local_smoke.py` must verify before any endpoint:

- the vectorizer-space estimator mean has cosine above `0.95` and norm ratio
  in `[0.90,1.10]` to the exact A/G target;
- at batch 128, its matched one-query MSE is below 25% of the
  channel-coefficient-then-regress estimator's MSE;
- no-BatchNorm and BatchNorm antithetic JVP relative errors are below `2e-6`;
- implemented A/G updates agree with the analytic delta rule to absolute error
  below `1e-14`;
- every legacy convolutional/local-eligibility check remains green.

This mechanics gate passed before V3-1 opened: cosine `0.969283`, norm ratio
`1.048876`, MSE ratio `0.0338103`, JVP errors `1.61e-10` and `1.98e-10`, and
delta-rule error `5.42e-20`.

## V3-1: frozen-forward causal-capture gate

Use the identical V2 initial-state protocol: seed-0 ResNet-20, first 10,000
development-training examples, batch 128, zero-initialized channel-gated A/G,
400 feedback-only minibatches, K1, `sigma=0.01`, perturbation seed 1000, and a
fixed 64-example exact-gradient audit. Forward weights, readout, BN state, and
BN affine parameters remain bitwise fixed.

Run one matched V2 channel-subspace reference at `eta_A=0.01` and V3
vectorizer-subspace candidates at `eta_A in {0.01,0.1,1.0}`. Select V3 by
maximum early-third teaching/negative-gradient cosine, then maximum all-layer
cosine, then lower rate. V3 advances only if all four records are finite and:

1. selected V3 early-third alignment is at least `0.01`;
2. selected V3 all-layer alignment is at least `0.05`;
3. selected V3 early-third alignment exceeds the matched V2 reference by at
   least `0.01`;
4. selected V3 reaches at least 60% of the independently measured
   channel-gated family oracle (`0.60 * 0.0239658 = 0.0143795`).

The absolute-improvement condition is the binding anti-threshold-shopping
rule: given V2's audited `0.007209`, V3 must reach approximately `0.017209`,
not merely cross the old `0.01` threshold. No extra rate, warmup length,
direction count, or feedback initialization is added after observation.

## V3-2: full ResNet-20 validation gate

Only after V3-1 passes, run one 200-epoch seed-0 model on all 45,000
development-training examples. Copy the failed v1 schedule exactly: hidden LR
`0.03`, output LR `0.1`, momentum `0.9`, weight decay `1e-4`, and 10x drops at
epochs 100 and 150. Use selected V3 `eta_A`, 400 feedback-only warmup steps,
and vectorizer-space K1/every-4 calibration. No recovery branch follows.

Against the frozen BP (`91.62%`) and DFA (`33.06%`) records, V3 must have every
metric finite, finish within 5 points of BP and at least 2 points above DFA,
retain early-third alignment at least `0.05`, and use no more estimated MACs
than BP. Failure closes V3 without test evaluation.

## V3-3: untouched confirmation and score rule

Only a V3-2 pass permits a new ResNet-20/32/56, seeds 10--14 confirmation with
one final test evaluation per run and no depth-specific tuning. Its gate is
identical to V2/V1: finite 45-run panel, SDIL within 2 points of BP at every
depth, at least 2 points above DFA at depth 56, depth-20-to-56 degradation no
worse than -2 points, retained early alignment, and a hardware-independent
Pareto point.

V3-0/V3-1 cannot raise the strict ICLR score. A complete V3-2 pass moves the
forecast from 5 to 6; oral-level scale requires V3-3.

## Audited outcome (2026-07-22)

All four V3-1 records were finite and shared clean source commit `612196a`.
The frozen selector chose `eta_A=0.01`. The matched alignment endpoints were:

| estimator | early-third alignment | all-layer alignment |
|:--|--:|--:|
| V2 channel subspace | 0.007209 | 0.052740 |
| V3 vectorizer subspace | 0.007139 | 0.062579 |

V3 improves the all-layer mean by `0.009839`, mostly through middle and late
blocks, but does not improve the binding early-layer endpoint. It fails the
`0.01` absolute early threshold, the `+0.01` matched improvement, and the 60%
family-oracle threshold; only the all-layer check passes. Rates `0.1` and `1.0`
reduce early alignment further to `0.004804` and `0.002234`.

The calibration MSE/power values are not compared across V2 and V3 because
their metric spaces differ. The valid common endpoint is exact hidden-gradient
alignment. V3-1 status is **failed**; V3-2 was not launched, no test endpoint
or confirmation seed was touched, and the reviewer score remains 5/10.

The negative result rules out coefficient-then-regress variance as the sole
early-layer bottleneck. Direct matrix estimation works exactly and lowers
matched synthetic variance, yet the real early signal remains unchanged. The
next mechanism must add informative hierarchical/high-level context or remove
the remaining cross-layer/parameter-space noise, not repeat this rate grid.