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+# 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.
+
+“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.
+
+## 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 and an explicit cost coordinate. 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 reproduction: not yet complete.
+- 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.
+