For layer l, fit a local predictor during neutral observations and form the innovation:
Then update each forward weight with information available at that neuron:
There is no reverse-mode differentiation, backward computation graph, or transport of transposed forward weights. The feedback direction can come from causal perturbations or a reciprocal local-feedback network. The new operation is the per-neuron subtraction, not the feedback backbone.
Five paired seeds were run at every depth. SDIL improves as the network gets deeper and remains close to exact backpropagation (BP).
| Method | ResNet-20 | ResNet-32 | ResNet-56 | ResNet-56 cost / BP |
|---|---|---|---|---|
| SDIL | 91.584 | 92.254 | 92.760 | 1.331× |
| BP | — | — | 92.632 | 1.000× |
| Clean reciprocal feedback | — | — | 92.670 | — |
| DFA | — | — | 30.850 | — |
Numbers are mean test accuracy in percent. Every SDIL seed improves from ResNet-20 to ResNet-56; the mean gain is 1.176 points. Its early-layer teaching direction has 0.999423 cosine agreement with the exact descent direction.
With strong activity-predictable interference, raw feedback and a magnitude-matched raw control reach 10.38% and 10.31% accuracy. SDIL reaches 97.35%. Across five seeds, its paired gain over the magnitude-matched control is 87.038 ± 0.607 points. Matching signal size does not explain the result; subtraction changes the direction used for learning.
In a new author-code Dual Prop screen, activity-dependent bias makes raw learning nonfinite in epoch 1 at all three strengths. Innovation remains finite and reaches 71.10%, 70.18%, and 68.96%, within 0.90 points of exact bias subtraction. The core comparison passes, but the complete development gate fails its clean/common endpoint controls.
In the matched author-code VGG16 comparison, SDIL reaches 90.70% validation accuracy in 1.24 h. Dual Prop reaches 92.38% in 5.97 h. Clean reciprocal feedback reaches 90.86% in 1.08 h. SDIL is much cheaper than Dual Prop at similar accuracy, but it does not beat every method on clean data.