# Rain EP Dillavou-Imperfection Matrix

## Question

Can a local neutral predictor remove a fixed hardware update offset without
using a larger EP nudging voltage?

The primary corruption is the model in Dillavou et al., Eq. (7).  Every local
parameter update receives a fixed, unknown, parameter-specific offset after
the two-state EP estimate has been formed:

\[
g^{\rm measured}_i = g^{\rm EP}_i + B_i.
\]

`B_i` is fixed across examples, epochs, and beta signs.  Its RMS is specified
relative to the first clean local update only to set a reproducible simulation
scale.  This normalization is not visible to the learner.  The optional
state-drift ratio is zero in all exact-model experiments.

The correction is local and uses no backpropagation.  With the teaching input
disabled, the update circuit exposes `B_i`.  The predictor stores this neutral
measurement and subtracts it from subsequent updates.  Under the strictly
constant model, constant calibration and SDIL innovation are expected to
coincide.  A difference between them is neither predicted nor claimed.

## Frozen author protocol

- author repository: `rain-neuromorphics/energy-based-learning`;
- revision: `6b253fd8a5d267535f58ab79992256ef10031ceb`;
- endpoint: `experiments/rain_ep_bias_train.py`;
- network protocol: `comparative32`;
- FashionMNIST with the author's 32x32 augmentation;
- author ConvHopfieldEnergy32 architecture, gains and per-layer rates;
- beta 0.25, 15 training relaxation iterations, 60 inference iterations;
- batch size 100 and 100-epoch cosine schedule.

## S0 development screen

S0 uses only a fixed training/holdout split with 10,000 training and 2,000
holdout examples.  One epoch selects a non-catastrophic offset magnitude from
the frozen grid `0.003, 0.01, 0.03, 0.1`.  The same wave includes clean PEP,
random-sign beta, centered EP, and one SDIL arm.  S0 is development evidence
and is never reported as a final result.

## Confirmation matrix

After S0 freezes one offset magnitude, the full author horizon compares:

| EP estimator | no offset | raw offset | constant calibration | SDIL |
|---|---:|---:|---:|---:|
| positive beta | yes | yes | yes | yes |
| random beta sign | yes | yes | no | no |
| centered EP | yes | yes | no | no |

An oracle subtraction arm checks implementation correctness.  A large-beta
EP sweep is reported as a strong-clamp proxy but is not called overclamping:
Dillavou overclamping also changes the output force and update duration, so a
beta sweep alone is not the published method.

The exact constant model establishes the hardware failure and the limit of
beta centering.  It cannot establish an advantage over ordinary local offset
calibration.  Any claimed SDIL advantage requires a separately labeled
state-dependent extension or real measured device drift.