# Rain EP Released-Drift Profile

## Scope

This protocol asks whether a local affine predictor adds value beyond a local
intercept when hardware update bias changes with the adaptive parameter state.
It is a controlled neural-network transfer of a shape measured in released
physical traces. It is not a reproduction of the resistor hardware and is not
labeled as a real-hardware neural-network result.

The source is the committed analysis
`results/physical_bias/p0_state_dependence.json`, derived from Zenodo record
15692914, release v1.0.1. For each of four measured edges, the report supplies
an affine offset, local gate-voltage slope, and the gate range visited in the
retained drift traces. The transfer profile divides both the offset and the
slope times observed gate range by the RMS of the four offsets. This freezes
the following dimensionless values without a task-accuracy fit:

- offsets: `0.93562, 1.60206, -0.10014, 0.74026`;
- full-range state variations: `0.52595, 0.31317, 0.38320, -0.04782`.

Neural parameters are deterministically assigned these four profiles. Their
initial local update-offset RMS is set by `bias_ratio`; parameter displacement
in units of that tensor's initial parameter RMS maps through `tanh` to the
measured state-range coordinate. This mapping preserves the measured relative
state dependence but does not claim that resistor gate volts equal neural
weight units.

## Local observation contract

At a neutral probe, the teaching input to the local update circuit is disabled.
The corrector receives the resulting measured circuit output at its current
parameter state. It is not given an externally calibrated coefficient. An
intercept-only predictor and affine SDIL receive identical probes. All
parameters probe in parallel, so probe count is independent of parameter count;
each parameter stores its own predictor coefficients.

## R0 development screen

R0 begins only after `dillavou_c0` finishes. It uses the same 10,000/2,000
training-only split as development, batch size 128, one epoch, fixed bias ratio
1.0, and the released affine profile. Eight cells run:

1. clean positive EP;
2. raw released-profile bias;
3. intercept-only, one initial probe;
4. affine SDIL, one initial probe;
5. intercept-only, one initial probe then every 10 steps;
6. affine SDIL with the same probes;
7. intercept-only, one initial probe then every 50 steps;
8. affine SDIL with the same probes.

R0 is a mechanics/development screen. A useful result requires affine SDIL to
have lower held-out residual bias and higher task accuracy than the matched
intercept-only arm. Final evidence additionally requires multiple seeds, a
frozen probe cadence, measurement noise/quantization, and the strong-clamp
baseline.

R0 did not pass this gate. Clean positive EP reached 53.2% after one epoch and
the raw released-profile arm reached 40.0%. With only the initial probe,
intercept and affine predictors were exactly matched at 49.9%. At cadence 10,
affine SDIL reached 49.9% versus 44.8% for the intercept, but its final relative
residual was higher (`9.51e-4` versus `5.95e-4`). At cadence 50, affine SDIL
had a slightly lower residual (`7.42e-3` versus `7.55e-3`) but lower accuracy
(47.1% versus 48.4%). No cadence improved both mechanism and task performance,
so R0 is ambiguous negative development evidence and is not promoted. The
stable centered-EP backbone identified by C0 is required before further task
confirmation.

The paper-facing decision is based on downstream accuracy, not residual-bias
diagnostics. Reinterpreted on that basis, R0 supplies one positive cadence
(49.9% affine versus 44.8% intercept at cadence 10) and one negative cadence
(47.1% versus 48.4% at cadence 50). This cadence sensitivity and the single
unstable positive-EP run make R0 inconclusive rather than a mechanism gate.

## R1 centered-EP screen

R1 freezes cadence 10 from the only positive R0 downstream comparison and
moves to the stable centered estimator. On the same 10,000/2,000 development
split, one epoch compares centered clean, fixed raw/intercept/SDIL, released-
profile raw/intercept/SDIL, and a released-profile oracle. Downstream holdout
accuracy is the only selection endpoint. Residual diagnostics are retained
only to catch implementation errors.

R1 used 10,000 FashionMNIST training examples and a disjoint 2,000-example
holdout drawn from the official training set, one epoch, one fixed seed, and
the author's comparative ConvHopfieldEnergy32 network. Holdout accuracy was:

| hardware condition | correction | accuracy |
|---|---|---:|
| no hardware bias | none | 46.00% |
| constant per-parameter bias | none | 10.00% |
| constant per-parameter bias | intercept-only | 45.45% |
| constant per-parameter bias | affine SDIL | 45.45% |
| released state-dependent profile | none | 32.70% |
| released state-dependent profile | intercept-only, cadence 10 | 43.85% |
| released state-dependent profile | affine SDIL, cadence 10 | 42.35% |
| released state-dependent profile | exact oracle subtraction | 46.00% |

The constant-offset rows are an implementation sanity check only. Because the
neutral observation is exact, measuring a strictly constant offset once and
subtracting it is already oracle correction; the matching intercept and SDIL
rows contain no scientific advantage. The only substantive R1 comparison is
the state-dependent profile. There, affine SDIL is 1.50 percentage points
below the matched intercept tracker and 3.65 points below exact oracle
subtraction. No residual-bias diagnostic can override this accuracy result.

## R2 paired-seed accuracy check

R2 repeated the state-dependent cadence-10 comparison for four network
initializations while keeping the data split and every other R1 setting fixed.
The paired holdout accuracies were:

| seed | intercept-only | affine SDIL | SDIL minus intercept |
|---:|---:|---:|---:|
| 1988 | 43.85% | 42.35% | -1.50 points |
| 1989 | 42.45% | 38.60% | -3.85 points |
| 1990 | 36.65% | 36.10% | -0.55 points |
| 1991 | 48.30% | 47.75% | -0.55 points |
| mean | 42.81% | 41.20% | -1.61 points |

Affine SDIL lost all four paired comparisons. The one-epoch state-dependent
claim is therefore negative. The remaining accuracy question is whether the
affine predictor needs a longer trajectory to learn the state relation; R3
tests that question on full-data ten-epoch trajectories.

## R3 full-data trajectories

R3 used all 60,000 FashionMNIST training examples, the official 10,000-example
test set, ten epochs, and two paired initializations. The hardware bias was the
released state-dependent profile, not the constant-offset sanity check. The
intercept tracker and affine SDIL received the same exact neutral observation
every ten parameter updates. Final test accuracy was:

| seed | clean/oracle | raw | intercept tracker | affine SDIL | SDIL minus intercept |
|---:|---:|---:|---:|---:|---:|
| 1988 | 88.67% | 10.00% (nonfinite after epoch 3) | 84.52% | 83.13% | -1.39 points |
| 1989 | 88.80% | 10.00% (nonfinite after epoch 2) | 86.02% | 87.22% | +1.20 points |
| mean | 88.74% | 10.00% | 85.27% | 85.18% | -0.10 points |

Both local correction methods prevent the raw state-dependent failure, but
affine SDIL does not have a consistent accuracy advantage: it wins one pair,
loses one pair, and is 0.095 percentage points lower on the two-seed mean. The
predeclared endpoint is final accuracy, so its temporarily higher intermediate
or best accuracy is not substituted for this result. Two further paired seeds
are required to narrow the comparison, but R3 itself is mixed/negative for an
SDIL-over-intercept claim.

## R4 four-seed aggregate

R4 added seeds 1990 and 1991 under the identical full-data protocol. Their
final clean/raw/intercept/SDIL accuracies were 86.93/10.00/83.56/84.37% and
83.17/10.00/83.37/85.72%, respectively. Raw became nonfinite after three and
one epochs. SDIL beat the intercept tracker by 0.81 and 2.35 points on these
seeds.

Across all four full runs, final clean/raw/intercept/SDIL accuracy averages
86.89/10.00/84.37/85.11%. The paired SDIL-minus-intercept differences are
-1.39, +1.20, +0.81, and +2.35 points, for a +0.74-point mean with a
1.56-point sample standard deviation. This is directionally positive but not
decisive: the gain changes sign and is small relative to seed variation. It
also compares against a costly tracker that receives a fresh exact local probe
every ten updates. The next experiment freezes equal small upfront probe
budgets and then removes further probes, testing whether state prediction
improves accuracy when repeated recalibration is unavailable.

## R5 equal upfront probe budgets

R5 gave the intercept tracker and affine SDIL exactly the same first
2/4/8/16 neutral observations, then disabled all further probes. It used the
10,000/2,000 centered-EP development split for one epoch. Holdout accuracy was:

| upfront probes | intercept tracker | affine SDIL | SDIL minus intercept |
|---:|---:|---:|---:|
| 2 | 43.75% | 44.05% | +0.30 points |
| 4 | 41.30% | 38.10% | -3.20 points |
| 8 | 44.90% | 44.30% | -0.60 points |
| 16 | 45.45% | 44.00% | -1.45 points |

The present normalized-LMS affine predictor does not turn a small matched
upfront calibration budget into a reliable downstream advantage. Three of
four budgets lose to retaining the last measured intercept. This closes
cadence/probe-budget tuning for the current predictor; further work must change
the local identification rule and then re-enter through a new development
screen rather than scaling this implementation.

## R6 local least-squares development screen

R6 changed only the affine predictor's local identification rule from
normalized LMS to online least squares. Each parameter stores its own running
state/measurement statistics; it receives no label, clean update, generated
bias coefficient, or nonlocal value. The matched upfront-probe experiment was
then repeated on the same seed and split:

| upfront probes | intercept tracker | least-squares SDIL | SDIL minus intercept |
|---:|---:|---:|---:|
| 2 | 43.75% | 44.65% | +0.90 points |
| 4 | 41.30% | 45.35% | +4.05 points |
| 8 | 44.90% | 46.10% | +1.20 points |
| 16 | 45.45% | 45.90% | +0.45 points |

Least-squares SDIL wins all four equal-budget comparisons. At four probes it
recovers 45.35% versus 41.30% for the tracker and a 46.00% clean/oracle
reference from R1. This is positive development evidence, not confirmation;
the four-probe point is frozen for the next paired-seed check.

## R7 frozen four-probe seed check

R7 repeated the selected four-probe least-squares setting for four paired
initializations. Holdout accuracy was:

| seed | intercept tracker | least-squares SDIL | SDIL minus intercept |
|---:|---:|---:|---:|
| 1988 | 41.30% | 45.35% | +4.05 points |
| 1989 | 31.85% | 30.45% | -1.40 points |
| 1990 | 34.50% | 33.10% | -1.40 points |
| 1991 | 46.40% | 44.20% | -2.20 points |
| mean | 38.51% | 38.28% | -0.24 points |

The selected result does not replicate: least-squares SDIL loses three of the
four pairs and is lower on average. The per-update correction diagnostic is
small in every seed, but that diagnostic cannot override downstream accuracy.
R7 therefore rejects the four-upfront-probe claim and closes this predictor
setting rather than promoting the favorable seed-1988 development result.