A local signal clears the wall
2026-06-27 · the second positive · experiment DD
The prior round isolated the missing ingredient: abstraction needs credit assignment, not better wiring. It named the prize: can a local gradient keep the win inside the online, local, bounded regime? This round answers it on the exact same harness. Add two new ways for the hidden layer to learn, and a probe on text it never saw. A broadcast neuromodulatory scalar fails. A per-unit local signal clears the wall. The diagnosis sharpens from "credit assignment" to "per-unit credit assignment."
The question
DC left a clean prize. Hold one network fixed, swap only the update rule, and the gradient builds the abstract space while the no-gradient rule does not, so the wall was credit assignment, not topology. But DC's winning arm was global backprop, the oracle: online and single-pass, yet global and non-local, the kind of learning the program's four laws forbid. It proves the target exists. It is not a learner we would ship.
So the question for DD was the constructive one. The brain does credit assignment without backprop's weight transport. Can a biologically plausible, local rule do enough of it to build an abstract space while staying inside online, single-pass, bounded? If yes, the program has a candidate learner, not just a measuring stick.
What we tried
We reused DC's harness without changing a line of it. The same small network: a context window of the last five characters, through the program's random sparse encoder, through one hidden layer, to a next-character prediction. The same strict online regime: one character at a time, single pass, no epochs, no shuffling. The same three probes, imported verbatim. Four arms differ only in how the hidden layer learns.
- GRAD, online backprop. DC's global oracle, the measuring stick.
- HEBB, Oja, no gradient anywhere. The no-credit floor.
- THREE-FACTOR, neuromodulated Hebbian: the Oja step scaled by a single broadcast surprise/precision scalar. This is the count-native "top-down control burst," the same scalar everywhere, the precision-weighted form the literature reaches for.
- FEEDBACK-ALIGNMENT, fixed-random-feedback per-unit credit. A global error is projected back through a fixed random matrix, so each hidden unit gets its own credit signal with no weight transport. Local, biologically plausible.
And one new measurement: a transfer abstraction score, probed on a disjoint held-out slice of text the model never trained on. The neuroscience says abstraction is the thing that generalizes to unseen cases, so we report transfer CCGP beside the within-slice score, at every arm.
What happened
The four arms split exactly along the per-unit line.
| bits-per-char | CCGP within (v/c) | CCGP transfer (v/c) | word-position (transfer) | |
|---|---|---|---|---|
| raw-input baseline | n/a | 0.302 | 0.339 | 0.503 |
| GRAD (oracle) | 3.81 → 3.26 | 0.507 | 0.489 | 0.642 |
| HEBB (Oja) | ~flat 4.13→4.29 | 0.378 | 0.335 | 0.366 |
| THREE-FACTOR (broadcast) | ~flat 4.08→4.29 | 0.256 | 0.306 | 0.353 |
| FEEDBACK-ALIGNMENT (per-unit) | 4.05 → 3.50 | 0.412 | 0.407 | 0.581 |
Read it as three findings.
The broadcast third factor fails. THREE-FACTOR lands on top of HEBB: at or below the raw-input baseline on the abstraction score, word-position CCGP collapsed, no improvement in bits-per-char. A single scalar broadcast to every unit cannot tell each one how to change; it can only scale an unsupervised Oja step up or down. This is exactly Lindsay 2017's lesson in our harness: a neuromodulator alone is not the carrier of credit.
A per-unit local signal clears the wall. FEEDBACK-ALIGNMENT drops bits-per-char from 4.05 to 3.50 (real learning) and lifts the abstraction score to about 0.41 both within and on transfer, word-position to 0.58, approaching the global oracle's 0.49. With no weight transport, with a fixed random feedback matrix, staying inside online, local, and bounded. So abstraction is reachable inside the program's laws. But it needs per-unit credit, not a scalar.
Transfer tracks within. For every arm the transfer score sits right next to the within-slice score (GRAD 0.49/0.51, FA 0.41/0.41). The arms that build an abstract space inside one slice also carry it to text they never saw, which is the definition of abstraction, and a reassurance that the within-slice probe was measuring the right thing all along, not a confound.
The lesson
A globally-broadcast neuromodulatory scalar does not build an abstract space; it only scales an unsupervised step. A per-unit local credit signal does, drawing close to the global-backprop oracle while staying online, local, and bounded. DC's "credit assignment" sharpens to per-unit credit assignment.
This is the second positive of the line and the constructive one. DC proved a gradient can build the abstract space with an oracle the program would never ship. DD shows a shippable class of learner can do most of it: feedback alignment, and with it target propagation, e-prop, predictive coding with a learned dictionary, anything that hands each unit its own credit. The named prize, an online, local, bounded learner that abstracts, is now in reach rather than in principle.
The honest caveats
- One architecture, one probe. Still the context-window network and one abstraction score, as in DC. It shows what within a fixed topology clears the wall; it does not yet show it on the full stack.
- The error is still global, the wiring is not. Feedback alignment broadcasts a global error and projects it through a fixed random matrix. So the credit each unit receives is per-unit and the wiring is local with no weight transport, while the error signal itself is global. Biologically plausible, not yet the fully local ideal.
- The absolute scores are modest. FA reaches ~0.41, close to but under the oracle's ~0.49. The result is the direction and the mechanism (per-unit beats broadcast, decisively) more than a finished number.
The frontier
DD answers DC's prize and sharpens the next question to a point. We now know abstraction wants per-unit credit. The open question is the one the neuroscience has been pointing at all along: per-unit credit on what pathway, delivered how biologically? Wutz 2018 says abstraction is built by a top-down process, so the natural move is to carry the per-unit credit down a real top-down (apical) pathway, the same wire that primes the level below, gated by precision for when it fires. That fuses the priming track and the credit track into one mechanism, on a stacked network where altitude can finally mean something. That is the next experiment.
Lineage
Grew from the head-to-head that found the missing ingredient, whose harness, probes, and online regime DD reuses verbatim so the four arms are directly comparable, and whose named next step (test a biologically-plausible local gradient) DD runs. The mechanisms are feedback alignment (fixed random feedback, no weight transport) and the neuromodulated three-factor rule; the framing is Lindsay 2017 (a neuromodulator alone is not the carrier) and the Wójcik transfer refinement (abstraction emerges under generalization, hence the held-out probe).
Led to the apical fusion that makes abstraction climb: per-unit credit ridden down a real top-down pathway, gated by precision, on a two-level stack.
Thread: abstraction, and online learning without counting. The second positive, a candidate shippable learner, where DC had only an oracle.