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# Three-part paper evidence
## One-sentence claim
Somato-dendritic innovation is a local correction for predictable teaching-
channel error. It transfers across digital local learners, preserves coupled
learning as the number of imperfect components grows, and can be implemented
with local sampling and subtraction in a hardware-realistic CLLN.
The method remains:
```text
r = a - P(z)
Delta w = eta * r * eligibility
```
`P` is fitted from instruction-off local observations. It receives no task
gradient, device constant, downstream weight, or BP signal.
## Part 1: additive digital correction
The first part asks whether the same operation can be attached to an existing
learning rule without replacing that rule.
| Digital learner | Task and repetitions | Clean | Raw imperfection | Static calibration | SDIL | Status |
|:--|:--|--:|--:|--:|--:|:--|
| Dual Propagation | CIFAR-10 miniCNN, 5 seeds | 82.86% | 9.40% | — | 82.92% | Passed frozen confirmation |
| Equilibrium Propagation | FashionMNIST ConvHopfield, 5 seeds | 76.26% | 31.38% | 67.90% | 74.52% | SDIL beats raw in every seed; strict gate failed because one seed favors calibration |
| Digital coupled learning | released ring tasks, size ladder pilot | reported by size | 37.5–62.5% error | 2.5–30.0% error | 0–7.5% error | Full confirmation running |
| Overclamped coupled learning | released ring tasks, size ladder pilot | 0–2.5% error | 25–50% error | — | 0–2.5% error | Clean-only time constant selected before biased endpoints |
Sources:
- `results/contrastive_bias/c1_gate.json`
- `results/ep_bias/c1_gate.json`
- `results/coupled_ladder/p1_imperfection_pilot.json`
- `results/coupled_ladder/p1_bias_baseline_pilot.json`
- `results/coupled_ladder/p1_overclamp_selected_pilot.json`
The Dual Propagation result establishes strong transfer. The EP result shows
transfer with a visible remaining clean gap and seed variance. Coupled learning
adds a system where the local variables map directly to circuit measurements.
## Part 2: scaling digital coupled learning
The periodic grid ladder uses side lengths `4, 8, 12, 16, 24, 32`, or 32 to
2,048 learnable edges. Every method receives the same released task, tiled
initial gate field, and component draw. Size-dependent update exposure is
selected from ideal coupled learning only.
Pilot final classification error:
| Edges | Clean | Same-RMS noise | Raw | Static calibration | SDIL |
|--:|--:|--:|--:|--:|--:|
| 32 | 0.0% | 0.0% | 50.0% | 2.5% | 0.0% |
| 128 | 0.0% | 0.0% | 62.5% | 2.5% | 0.0% |
| 288 | 2.5% | 5.0% | 52.5% | 2.5% | 2.5% |
| 512 | 2.5% | 10.0% | 47.5% | 5.0% | 2.5% |
| 1,152 | 2.5% | 17.5% | 50.0% | 10.0% | 7.5% |
| 2,048 | 2.5% | 22.5% | 37.5% | 30.0% | 2.5% |
The raw learner has a large error floor at every size. Static calibration works
on small grids and degrades on larger grids. Relative to static calibration,
SDIL reduces the pilot excess-error growth slope by 88.1%; the paired
task-bootstrap slope-difference interval is positive. At 2,048 edges, SDIL
closes the full raw-to-clean final-error gap and reaches stable zero error on
80% of task runs, versus 0% for raw and static calibration.
The tuned overclamp pilot gives the same structural result. Clean overclamping
ends at 0–2.5% error across the ladder. Imperfect overclamping ends at 25–50%,
while overclamping plus SDIL ends at 0–2.5%. SDIL therefore combines with the
strong-clamp correction.
The publication figure and data are:
- `results/figs/figure_clln_scaling_pilot.pdf`
- `results/coupled_ladder/p1_scaling_analysis.json`
- `results/coupled_ladder/p1_scaling_source.csv`
The mechanism statement is now explicit in `THEORY.md`. For a local
state-dependent component error, conditional subtraction removes at least as
much mean-square bias as a constant calibration. Residual component power adds
with edge count. In a local quadratic objective, persistent residual bias
produces an exact displaced optimum with excess objective
`0.5 * delta^T H^+ delta`; the classification ladder tests whether this local
effect reaches the downstream task endpoint.
The pilot has five task clusters and one component draw per task and size. The
running confirmation contains all 40 released tasks, three new component draws,
six sizes, and five core methods: 3,600 training trajectories. Its outputs are
`results/coupled_ladder/p2_confirm_side{4,8,12,16,24,32}.json`.
## Part 3: hardware-realistic simulation
This part uses the nonlinear conductance law, periodic 4-by-4 topology,
released Figure-5 tasks and initial gates, Appendix-C component imperfections,
and explicit local voltage-square updates.
The untouched confirmation uses 40 tasks and three new component draws, or 120
trials per method:
| Method | Mean classification error | Zero-error trials |
|:--|--:|--:|
| Clean CLLN | 0.00% | 100.00% |
| Raw imperfect CLLN | 25.42% | 18.33% |
| Static calibration | 1.35% | 92.50% |
| Clean overclamping | 0.00% | 100.00% |
| Imperfect overclamping | 5.42% | 85.83% |
| SDIL | 0.00% | 100.00% |
| Overclamping + SDIL | 0.00% | 100.00% |
The local CDS/autozero circuit model then adds sampling gain mismatch,
pedestal mismatch, noise, and stale refresh. Ideal CDS and the combined mild
refresh-every-four condition retain 0% error. The combined strong condition
has 0.55% mean error and 96.88% zero-error trials. A 0.1 V/s pedestal mismatch
has 0.63% error; a 0.25 V/s mismatch has 4.45% error and marks the simulated
failure boundary.
Sources:
- `results/physical_bias/p11_nonlinear_hardware_confirmation.json`
- `results/physical_bias/p11_nonlinear_hardware_confirmation_gate.json`
- `sdil/physical_grid.py`
- `results/physical_bias/p5_full_grid_bias_crossover.json`
- `results/physical_bias/p9_grid_correlated_autozero_key_results.json`
- `results/physical_bias/p8_spice_autozero_primitive.json`
- `results/figs/figure_physical_hardware_evidence_confirmation.pdf`
- `results/physical_bias/p12_hardware_evidence_analysis.json`
The hardware claim is: the full update is simulated with published device
equations and nonideal local sampling, and its primitive sample/subtract path
has a SPICE check. A fabricated-chip demonstration remains future work.
## Main figures
1. Method and transfer across Dual Propagation, EP, standard CLLN, and
overclamped CLLN.
2. Digital CLLN scaling: final error, stable success, and learning curves.
3. Hardware-realistic CLLN: raw, calibration, overclamping, SDIL, and
nonideal-CDS robustness.
4. Mechanism boundary: matched noise, state dependence, sampling mismatch,
and refresh interval.
## Remaining gates
1. Complete and audit the 3,600-trajectory digital ladder confirmation.
2. Run the selected overclamp pair on the full task/device confirmation panel.
3. Rebuild the digital transfer and scaling figures from confirmation data;
the hardware-realistic figure is complete.
4. Audit every manuscript number
against its source JSON.
|
