path: root/TWO_STATE_BIAS_PROGRAM.md

# Two-state local learning under structured bias

## Active paper hypothesis

The working title remains:

> **Learning from the Unexpected: Somato-Dendritic Innovations for Local
> Credit Assignment**

The paper is no longer organized around clean-setting superiority or around
one feedback backbone. Its central hypothesis is:

> Local learners that update from a difference between two physical or neural
> states are robust to zero-mean noise only after averaging. A deterministic or
> state-dependent differential bias does not average away, eventually dominates
> the shrinking task signal, and becomes more damaging with optimization time,
> flat directions, task count, or the number of biased local populations. A
> neutral, per-cell prediction removes the identifiable component before it is
> consolidated into synapses.

SDIL is presented as a local debiasing plug-in for existing two-state learners,
not as a new optimizer on an accuracy--cost Pareto frontier. Comparisons use
matched budgets where possible and report unmatched overhead in a table.

“Two-state” includes equilibrium propagation (one recurrent network at free
and nudged equilibria), coupled learning, contrastive Hebbian learning, Dual
Propagation, and related positive/negative-state rules. It does not imply that
EP physically contains two networks. Some hardware implementations use two
matched physical copies, which creates an additional differential-mismatch
source.

## Harnett motivation and unchanged method

Francioni et al. do not identify raw distal dendritic activity as instruction.
They first remove the component predicted by the normal soma--dendrite
relationship and analyze the per-neuron residual. We apply that operation to a
local teaching channel.

For local state `z`, observed teaching signal `a`, and eligibility `e`:

```text
r = a - P(z)
Delta w = eta * r * e
```

On an instruction-off observation, the same local predictor uses:

```text
Delta P = eta_P * (a_neutral - P(z_neutral)) * features(z_neutral)^T
```

These equations are frozen. A backbone adapter may expose its local teaching
signal and eligibility, but it may not introduce sparse centered calibration,
oracle targets, copied clean updates, backpropagated gradients, or a new
backbone-specific controller and still call the result SDIL. Neutral
observations, state storage and arithmetic are charged. Baselines receive the
same observation budget when applicable.

Every adapter is also bound by `HARDWARE_LOCALITY_CONTRACT.md`: SDIL training
must execute with autograd disabled, and a stored local observation tuple must
reproduce its update without the model, task loss, labels or downstream
layers. Author code may use autograd as a native reference, but paper-facing
SDIL runs require an audited hand-written local update.

## Unified bias model

For local population or edge `l`, let the clean two-state teaching estimate be
`s_l`, locally observable neutral state be `z_l`, and measured estimate be

```text
a_l = s_l + b_l(z_l) + epsilon_l.
```

`epsilon_l` is conditionally zero-mean noise. `b_l` is a deterministic or
slowly drifting differential bias. It can arise from unequal physical copies,
sensor offsets, multiplier offsets, asymmetric state readout, or ordinary
state-dependent activity in a mixed dendritic compartment. A common offset
added identically to both states must cancel and is a negative control.

The claim is conditional. SDIL can remove only bias predictable from its local
neutral information class under a neutral-to-task invariance assumption. It
does not remove arbitrary noise, latent bias, or finite-nudge truncation error
unless that error is observable in the stated neutral channel.

## Theory program

The theory must predict experiments, not stop at the standard fact that a
conditional mean minimizes squared prediction error.

### Non-averaging

For repeated estimates `g_t + b + epsilon_t`, averaging `T` samples gives

```text
MSE(mean estimate, mean g) = ||b||^2 + Tr(Sigma) / T.
```

Noise vanishes with `T`; fixed bias does not. For distinct parameter blocks,
the squared norm of concatenated local bias is the sum of per-block squared
norms. Under a non-vanishing mean per-block bias, aggregate estimator bias
therefore grows linearly in squared norm with the number of biased populations.
This is an estimator statement, not yet a universal task-loss scaling theorem.

### Learning dynamics

Near a solution, use

```text
dot(theta) = -H(theta - theta_star) + b.
```

Positive-curvature modes converge to a displaced solution with displacement
`H^+ b`. Null-space bias produces linear drift `t * Pi_null b`. Alternating
tasks switch `H` and their solution sets, generating bias-dependent periodic
orbits. These quantities give predeclared predictions for error floors, cycle
span and forgetting.

With residual bias `delta=b-P(z)`, the same expressions replace `b` by
`delta`. Bounds must explicitly include predictor approximation error,
finite-sample error, drift rate and neutral-to-task distribution shift.

### Instruction preservation

State and prove the identification condition under which neutral regression
does not subtract instruction. Construct counterexamples for task leakage and
neutral/task shift. Empirically, those counterexamples are mandatory failure
controls.

### Prior-work boundary

Ghosh et al. (ICLR 2023) already study how gradient-estimator bias and variance
interact with network size, sparsity, gradient norm and curvature. Laborieux et
al. analyze finite-nudge EP bias; random beta sign cancels its first-order term
in expectation, centered EP removes it with an extra state, holomorphic EP
computes exact finite-amplitude derivatives, and Jacobian homeostasis targets
weight-asymmetry bias. Dillavou et al. already derive physical-bias-driven
null-space drift and introduce overclamping. Our theory must unify local
neutral identifiability with these learning dynamics; it cannot claim that
bias persistence, flat-direction drift, or generic conditional projection was
previously unknown.

## Evidence ladder

### P0: published physical evidence, no new learning claim

Reanalyze the raw experimental data released with Dillavou et al.:

- demonstrate deterministic, sign-consistent gate-voltage drift and measured
  nonzero differential offsets;
- reproduce error/cycle-span trends and standard-versus-overclamping figures;
- show that increasing the averaging window reduces measurement uncertainty
  around a nonzero drift rather than driving the drift estimate to zero;
- bind every number to Zenodo record `15692914`, release `v1.0.1`, source tree
  `maguzj-imperfect-learning-physical-systems-71b8d72`.

This stage establishes that the target failure exists in hardware. It does not
show that SDIL fixes it.

### P1: physical-model mechanism gate

Use the released small-network equations and measured bias vectors. Compare:

1. standard coupled learning;
2. same-RMS zero-mean noise;
3. constant per-edge calibration;
4. the authors' overclamping;
5. unchanged two-line SDIL;
6. oracle subtraction.

Before endpoints, freeze task pairs, bias measurements, predictor features,
neutral cadence and costs. Required plots are bias estimate versus averaging
window, null-space drift, cycle span, error floor and task forgetting. SDIL
must outperform constant calibration when bias is state-dependent and must be
competitive with overclamping after charging observations. Otherwise the
physical branch stops.

### B1: Dual Propagation adapter

Finish the already-frozen five-seed differential state-bias confirmation as a
supporting result. Then add a scale axis only after the same-path clean/raw
mechanics pass: miniCNN to VGG-style depth/width using the author code. Common
bias, same-RMS noise, constant calibration and oracle subtraction are required.
Artificial DP bias cannot be the only paper-facing evidence.

### B2: equilibrium propagation / DCHN adapter

Use author implementations and unchanged model/training hyperparameters. The
task ladder is FashionMNIST, SVHN, CIFAR-10 and, only after a passed gate,
CIFAR-100. The adapter acts at the local two-state teaching measurement, not
on a backpropagated gradient.

Required EP baselines depend on the bias source:

- random-sign beta is the same-cost baseline for finite-nudge first-order
  bias;
- centered EP is the extra-state low-variance reference;
- constant offset calibration and oracle subtraction target measurement bias;
- Jacobian homeostasis targets asymmetric dynamics;
- holomorphic EP is discussed or run only where its complex dynamics are a
  valid matched alternative.

Finite-nudge EP is a boundary test unless the unchanged SDIL observation model
actually identifies its bias. Do not design a new staged SDIL variant to beat
random-sign beta.

### B3: coupled learning and further backbones

The modern DCHN framework already contains positive, negative and centered EP
and coupled-learning variants on the same five datasets. After P1/B1/B2, use it
to test whether one frozen SDIL adapter transfers between EP and coupled
learning. Contrastive Hebbian learning or Forward--Forward is added only if the
same bias variable and neutral observation have an exact, auditable meaning.

## Cross-backbone matrix

Every backbone reports its native clean endpoint, biased raw endpoint, best
bias-specific baseline, SDIL and oracle. “Beat” means a paired advantage under
bias at matched architecture/data/training, together with no meaningful clean
regression, a matched observation protocol and disclosed implementation
overhead. It does not mean that SDIL must beat BP or centered EP on clean
accuracy.

| family | natural/independent bias | strongest required baseline | scale axis |
|---|---|---|---|
| physical coupled learning | measured device/update offset | overclamping, constant calibration | edges, task count, cycle period |
| Dual Propagation | differential state/readout mismatch | clean/raw DP, calibration | CNN depth/width |
| EP/DCHN | measurement offset; separately finite nudge | random-sign beta, centered EP | task difficulty, depth, relaxation |
| coupled-learning DCHN | state/readout mismatch | centered CpL, overclamping analogue | task difficulty, depth |

The same predictor family, optimizer rule and neutral schedule are frozen
across comparable digital backbones. Backbone-specific retuning of the
debiaser invalidates the “general operation” claim.

## Main causal matrix

At fixed corruption RMS cross:

- zero-mean noise versus fixed, state-dependent and slowly drifting bias;
- common-mode versus differential bias;
- low to high neutral predictability;
- matched versus shifted neutral/task distributions;
- zero versus controlled instruction leakage;
- raw, norm-matched raw, constant calibration, SDIL and oracle.

The central empirical claim passes only if performance is explained by neutral
predictability rather than by corruption magnitude, update clipping, stronger
nudging, extra observations, or a backbone-specific hyperparameter change.

## Paper order

1. Harnett motivation: biological analysis isolates an unexpected per-neuron
   dendritic component rather than treating raw dendritic activity as error.
2. Problem: two-state local learning subtracts large nearby quantities;
   differential structured bias survives averaging and dominates a shrinking
   task contrast.
3. Theory: non-averaging, displaced/flat-direction dynamics, neutral
   projection guarantee and failure conditions.
4. Real evidence: released physical-network measurements and predicted drift,
   cycles and forgetting.
5. Method: the unchanged two-line local innovation rule.
6. Cross-backbone tests: physical coupled learning, DP, EP and coupled-learning
   DCHNs, each against its own strongest correction.
7. Scope: no claim that all local learning fails under all bias, that Harnett
   proves plasticity, or that SDIL removes unobservable bias.

## Advancement and stop rules

Do not launch the full backbone matrix until P0 is reproduced and P1 shows that
the unchanged rule adds value beyond constant calibration and overclamping.
Stop this paper direction if:

- physical bias cannot be predicted from a genuinely local neutral variable;
- averaging, constant calibration or overclamping matches SDIL at lower cost;
- gains require a different predictor/controller for each backbone;
- the only positive results use bias generated directly from the predictor
  features;
- no predeclared scale variable amplifies raw bias damage;
- realistic neutral/task shift causes instruction removal without a detectable
  local certificate.

## Current status

- Literature and claim boundary: complete.
- Dillavou artifact: downloaded outside the NFS workspace to
  `/scratch/yurenh2/imperfect-learning-physical-systems-v1.0.1`; raw drift,
  bow-tie, big-network classification and overclamping data are present.
- Physical P0 descriptive reproduction: complete. Across the lowest six
  published periods, combined-error log slopes are
  `0.0619/0.2883/-0.0235` while squared-cycle-span slopes are
  `1.8374/1.7360/1.9468`; see `results/physical_bias/p0_summary.json`. This
  reproduces a nonzero rapid-switching error floor and an approximately
  constant low-period drift speed from real hardware. It is not an SDIL result.
- Dual Prop same-path confirmation: active/supporting, not a passed result.
- EP/CpL adapters: not implemented under this bias model.
- Current score for this new paper framing: 5/10 until P1 passes.