# SDIL — results log (audited sections report n; timan107 GTX-1080 / ep_pascal)

## 2026-07-21 audit and version boundary

Git was initialized after inheriting the project. The original code/results are preserved at
`215acff`. The following audit findings changed the canonical implementation:

1. `49b86d6`: residual-block local updates now include the branch Jacobian
   `res_alpha=1/sqrt(depth)`. The omission preserved cosine direction but inflated update norms by
   `sqrt(depth)`, confounding cross-depth optimization comparisons.
2. `5255166`: the Harnett baseline is now a per-neuron affine soma-dendrite fit
   `ahat_l = p_l * h_l + b_l`, rather than a dense population map. This follows the paper's
   per-cell least-squares somatic-event to dendritic-event relation.
3. `c2769e6`: causal perturbation targets and predicted residuals are measured on the same
   pre-update network state.
4. `0f107d1` / `e0bfdfd`: simultaneous hidden-layer perturbations reduce calibration from
   quadratic to linear depth work; batching directions makes the reduction visible in GPU wall
   time. `66e3034` fixes diagnostics so raw-apical ablations report the signal actually used.
5. `2f3f44d`: the raw-apical control can be matched per sample to the innovation norm. This
   separates subtraction/direction from a trivial update-magnitude explanation.
6. `6093fe5` / `d6a00aa`: FA, PEPITA, Forward-Forward, and EP were reimplemented against their
   papers and reference code. EP uses persistent free particles; deep PEPITA requires an explicit
   learning rate; FA now logs the signal actually transported through its fixed feedback path.

All older `deepres_*` files predate item 1. Their alignment directions remain informative, but
their accuracy and stability should not be pooled with the corrected runs below.

## Method
SDIL (Somato-Dendritic Innovation Learning), a local non-backprop rule inspired by Harnett 2026.
Per hidden layer l:
- forward: `u_l = W_l h_{l-1}`, `h_l = φ(u_l)`
- apical feedback `a_l = A_l c` (c = output error e = softmax−onehot, broadcast)
- default per-neuron predictor `ĥ_l = p_l ⊙ h_l + b_l`; teaching signal `r_l = a_l − ĥ_l`
- three-factor update `ΔW_l = η (r_l ⊙ φ'(u_l)) h_{l-1}^T`
- `A_l` LEARNED by amortized node perturbation (q_l ≈ −∇_{h_l}L, forward-only, no weight transport)
- `P_l` learned on neutral (c=0) periods only, so it strips the soma-predictable nuisance
  without eating the teaching signal.

The scalable perturbation mode injects independent Rademacher interventions at all hidden layers
in the same antithetic forward evaluations. Cross-layer interference adds variance but averages to
zero; it trains all `A_l` using `O(depth)` rather than `O(depth^2)` forward work.

Distinct from the failed `~/sdrn` (fixed-random feedback + post-hoc residualization) and from
Dual Prop / DFA / FA: the feedback pathway is *learned by causal perturbation*, so the residual is
aligned by construction rather than being a random projection.

## Critical fix
Node-perturbation estimator must divide by σ, not σ² (with δ=σξ, ĝ = δ·ΔL/σ² = ξ·ΔL/σ ⇒ ‖q‖≈‖∇L‖).
The σ² bug made the teaching signal ~100× too large ⇒ effective LR ~100× ⇒ SDIL stalled. Cosine is
magnitude-invariant so alignment looked fine while optimization blew up. Fixing it turned SDIL from
"worse than DFA everywhere" to "matches DFA on MNIST, beats it on FMNIST/CIFAR". (Codex independently
flagged the same σ-scale issue.)

## Verified narrow depth scaling (CIFAR-10, width 64, 5 epochs, five seeds)

Mean ± sample SD. Alignment is the mean per-sample cosine over the earliest third of hidden layers
at the final checkpoint. SDIL uses simultaneous perturbations with 16 batched directions.

| depth | method | test acc (%) | early-third alignment | wall time (s) |
|------:|:-------|-------------:|----------------------:|--------------:|
| 30 | BP | 41.908 ± 0.697 | — | 29.8 ± 1.3 |
| 30 | FA | 38.158 ± 0.517 | 0.593 ± 0.014 | 26.9 ± 1.9 |
| 30 | DFA | 36.988 ± 0.524 | 0.087 ± 0.007 | 23.4 ± 0.8 |
| 30 | SDIL | 41.198 ± 0.523 | 0.366 ± 0.007 | 47.8 ± 1.4 |
| 60 | BP | 41.624 ± 0.781 | — | 58.4 ± 1.0 |
| 60 | FA | 38.428 ± 0.387 | 0.577 ± 0.011 | 49.8 ± 1.8 |
| 60 | DFA | 36.898 ± 0.444 | 0.047 ± 0.005 | 47.6 ± 5.6 |
| 60 | SDIL | 41.246 ± 0.323 | 0.336 ± 0.013 | 96.4 ± 12.4 |

The paired SDIL−DFA accuracy gap is `4.210 ± 0.426` points at d30 and
`4.348 ± 0.554` at d60. SDIL wall time grows 2.02x when depth doubles, so the batched simultaneous
calibration removes the former superlinear depth cost. Its accuracy is depth-stable and remains
within 0.71 points of BP at d30 and 0.38 points at d60. Flattened CIFAR itself is depth-flat here, so
these runs establish preservation rather than positive accuracy scaling.

DFA's early-layer direction nearly halves with depth. Residual FA does **not** show that failure:
its identity skips transport most of the state gradient exactly, leaving cosine near 0.58–0.59.
Nevertheless FA plateaus around 38.3%, roughly three points below SDIL. Thus the supported claim is
not “all FA signals lose directional alignment”; direction, signal scale, serial transport, and
optimization efficiency must be separated.

## Harnett-specific residualization (MNIST, d3/w256, 15 epochs, five seeds)

The matched-raw control preserves the raw apical direction but rescales every sample to the
innovation's norm.

| nuisance rho | raw apical acc (%) | matched raw acc (%) | residual acc (%) |
|-------------:|-------------------:|--------------------:|-----------------:|
| 0.00 | 97.450 ± 0.046 | 97.450 ± 0.046 | 97.450 ± 0.046 |
| 0.05 | 96.438 ± 0.077 | 96.980 ± 0.148 | 97.382 ± 0.154 |
| 0.20 | 95.512 ± 0.150 | 95.974 ± 0.144 | 97.370 ± 0.083 |
| 0.50 | 10.380 ± 0.548 | 10.310 ± 0.633 | 97.348 ± 0.133 |

At zero nuisance all three signals are identical. As normal soma-dendrite coupling grows, raw
feedback degrades and eventually reaches chance; residual learning stays at 97.35–97.45%. Matching
the raw signal's norm recovers only part of the low-rho loss and does nothing at rho=0.5. The strong
result therefore depends on subtracting the soma-predictable component, not merely clipping or
normalizing an oversized update. This is the most direct evidence that the Harnett-specific
innovation operation is algorithmically necessary.

## Legacy accuracy (pre-audit implementation)
| task                         | BP        | DFA   | SDIL          |
|------------------------------|-----------|-------|---------------|
| MNIST  d3 / d5 / d7 / d10    | 98.3      | 97.3 / 97.2 / 97.1 / 96.8 | 97.4 / 97.3 / 97.1 / 97.1 |
| FashionMNIST d3 / d5 / d7 / d10 | 88–89  | 86.3 / 87.1 / 86.2 / 86.9 | 88.4 / 87.6 / 87.3 / 88.1 |
| CIFAR-10 (no-BN residual) d5/10/20 | 44.2 / 44.8 / 45.5 | 40.6 / 39.9 / 37.4 | 42.4 / 42.6 / 42.4 |

SDIL matches DFA on easy MNIST and **beats DFA on FashionMNIST (+1–2 pts) and CIFAR (+2 to +5 pts)**.
On CIFAR the SDIL−DFA gap GROWS with depth (+1.8 → +2.7 → +5.0 at d5/10/20): DFA degrades with depth,
SDIL holds.

## Legacy credit assignment / depth utility
Per-layer alignment cos(r_l, −∇_{h_l}L), early-third average, CIFAR no-BN residual:
| depth | DFA early-align | SDIL early-align |
|-------|-----------------|------------------|
| 5     | 0.55            | 0.83             |
| 10    | 0.36            | 0.86             |
| 20    | 0.25            | 0.88             |
| 30    | 0.19            | 0.87             |

DFA's teaching signal to early/deep layers collapses toward random (~0.05–0.19) as depth grows;
SDIL stays ~0.85 and is depth-invariant. This is the "does credit reach early layers" metric that
DFA fails and SDIL passes — the core advantage.

## Paper-faithful non-backprop baselines

`PETITE` in the initial request is treated as **PEPITA**. Implementations and hyperparameters were
checked against the [FA paper](https://www.nature.com/articles/ncomms13276),
[PEPITA paper](https://proceedings.mlr.press/v162/dellaferrera22a.html) and
[author code](https://github.com/GiorgiaD/PEPITA),
[Forward-Forward paper](https://www.cs.toronto.edu/~hinton/absps/FFXfinal.pdf) and
[reference implementation](https://github.com/mpezeshki/pytorch_forward_forward), and the
[EP paper](https://www.frontiersin.org/journals/computational-neuroscience/articles/10.3389/fncom.2017.00024/full)
and [author code](https://github.com/bscellier/Towards-a-Biologically-Plausible-Backprop).

Native protocol results are not an equal-compute comparison:

| method | architecture | budget | n | last test acc (%) | wall time (s) |
|:-------|:-------------|:-------|--:|------------------:|--------------:|
| PEPITA | d3/w256 | 60 epochs | 5 | 91.094 ± 0.214 | 89.2 ± 3.5 |
| Forward-Forward | d3/w256 | 15 epochs/layer | 5 | 93.558 ± 0.232 | 68.2 ± 0.8 |
| EP | d1/w500 | 25 epochs | 2 | 97.040 ± 0.269 | 839.8 ± 78.4 |

PEPITA uses its two forward presentations, He-uniform initialization, shared 10% dropout mask, and
an explicit deep-network learning rate of 0.001. Forward-Forward trains greedy local goodness layers
and has no classifier readout. EP uses the original hard-sigmoid energy dynamics, random beta sign,
20 free steps, 4 nudged steps, layer rates `[0.1, 0.05]`, and persistent free particles for the fixed
first 50k examples. This corrected EP is the strongest baseline and is also by far the most expensive.

### EP exact-architecture comparison

All methods below use d1/w500, the same first 50k MNIST examples, and 25 epochs. EP retains its
native raw-pixel energy protocol; BP/DFA/SDIL retain the shared z-score/tanh feedforward protocol.
Forward parameter count is 397,510 for every row.

| method | n | last test acc (%) | best test acc (%) | wall time (s) |
|:-------|--:|------------------:|------------------:|--------------:|
| BP | 2 | 98.190 ± 0.014 | 98.215 ± 0.007 | 15.1 ± 0.9 |
| DFA | 2 | 97.620 ± 0.071 | 97.690 ± 0.099 | 9.9 ± 0.1 |
| EP | 2 | 97.040 ± 0.269 | 97.220 ± 0.283 | 839.8 ± 78.4 |
| SDIL | 2 | 97.510 ± 0.028 | 97.570 ± 0.028 | 15.4 ± 0.4 |

SDIL is 0.47 points above EP on last-epoch mean and about 54.5x faster in wall time. This establishes
that SDIL does not lose to the strongest baseline in the exact shallow architecture. It is **not**
evidence of a unique scaling advantage: DFA is also strong on this easy d1 MNIST problem, and only
two EP seeds have been run. At similar forward-parameter count but d3/w256, SDIL and EP are tied
within noise (97.13% vs 97.04% last-epoch mean), again with a ~26x wall-time advantage for SDIL.

## How to run
`experiments/run.py --mode {bp,dfa,sdil} --dataset {mnist,fmnist,cifar10} --depth D --residual {0,1} --act {tanh,gelu,silu,relu}`
Batteries: `experiments/run_v2.sh <ds> "<depths>" <res> <act> "<seeds>" <ep> <pfx>`.
Canonical local baselines: `experiments/baseline_sweep.sh`; original d1 EP:
`experiments/ep_original_sweep.sh`; EP comparison: `experiments/ep_matched_sweep.sh`.
Audited aggregate tables: `experiments/analyze_verified.py`.
Smoke/mechanism checks: `experiments/smoke.py` and `experiments/baseline_smoke.py`.

## Open items

- Compare simultaneous calibration at fixed loss-evaluation budgets and sweep directions
  (4/8/16/32).
- Validate SDIL on a genuinely depth-necessary compositional task and a CNN; flattened CIFAR does
  not gain accuracy with depth.
- Diagnose why residual FA has high directional cosine but lower accuracy: log update-norm ratios,
  parameter-space cosine, and serial feedback latency/cost.
- Increase EP and exact-architecture comparisons from two to five seeds. If compute permits, run the
  author's d2 EP schedule (60 epochs, 150 free steps, 6 nudged steps) rather than inventing a cheap
  deep-EP approximation.
- Tune SDIL schedules using a held-out validation split, never the test trajectory, then freeze the
  protocol before expanding the EP comparison.
- Extend PEPITA and Forward-Forward beyond shallow MNIST before making any scaling claim about them.