# Learning from the Unexpected: Somato-Dendritic Innovations for Local Credit Assignment

**Anonymous authors — working ICLR 2027 draft**

> This is the evidence-bound manuscript source. It intentionally contains the
> failed biological and scaling gates. Author names, acknowledgements, and the
> venue template are left unset rather than inferred.

## Abstract

Local-learning models often identify activity in a feedback or apical
compartment with a teaching signal. That compartment can also carry ordinary
state and contextual traffic, so its raw activity need not point in a useful
learning direction. Motivated by the per-neuron somato-dendritic residuals
measured by Francioni and colleagues, we define the teaching variable as an
*innovation*: apical activity minus its neutral-period prediction from the same
neuron's somatic activity. We evaluate this operation on top of two inherited
credit pathways—node-perturbation-trained direct feedback and reciprocal
Kolen--Pollack plasticity—and attribute those pathways to prior work. Conditional
expectation makes the innovation the minimum-power residual within the
predictor's somatic information class, while a norm-matched raw control shows
that subtraction changes direction rather than merely gain. In a frozen
60-run intervention, raw and norm-matched apical signals fall to 10.38% and
10.31% MNIST accuracy under strong soma-predictable traffic, whereas innovation
retains 97.348%. Across a 12-fold increase in hidden depth on flattened
CIFAR-10, the learned-feedback backbone changes by -0.214 points while direct
feedback alignment loses early-layer alignment. On a standard ResNet-20, a
dynamic paired-neutral innovation rule reaches 91.584% mean CIFAR-10 test
accuracy across five untouched seeds, versus 91.388% for clean reciprocal
credit; the one-sided 95% upper bound on its deficit is 0.131 points. It uses
zero task-loss queries and 1.326 times the matched BP MAC estimate, but pays for
one instruction-off neutral observation per training example. A preregistered
synthetic BCI confirmation learns the task and causal sign yet fails outcome
vectorization and longitudinal prediction. The supported conclusion is
therefore algorithmic and narrow: neutral somato-dendritic innovation can
protect local credit from soma-predictable traffic and remain stable on
ResNet-20, without establishing a cortical learning rule or positive utility
from added standard-network depth.

## 1. Introduction

Credit assignment asks how a synapse or neuron should change given only a
distant behavioral outcome. Backpropagation solves this problem in artificial
networks by transporting exact reverse-mode derivatives, but its weight
transport, global computation graph, and update-locking requirements make it an
imperfect model of biological learning. Fixed feedback alignment (FA) and
direct feedback alignment (DFA) relax exact transport, while equilibrium
propagation, Forward--Forward, PEPITA, Dual Propagation, and dendritic or
burst-based models change the activity dynamics or phase structure of learning.
These approaches differ substantially in what is local, what is transported,
and what computational cost is hidden in a “phase.”

Compartmental models commonly separate basal feedforward activity from apical
feedback. This is a powerful architectural idea, but it leaves an identification
problem: feedback compartments carry state, context, prediction, and ordinary
coupling in addition to any instruction. Treating all apical activity as error
can therefore rotate a local update even when the feedback pathway itself is
well calibrated.

[Francioni et al. (2026)](https://doi.org/10.1038/s41586-026-10190-7)
provide a sharper empirical object. For each cortical neuron they model the
normal relation between somatic and distal dendritic event magnitudes and study
the residual. At population level those residuals carry information absent from
soma alone, including outcome and neuron-specific causal-role signatures. The
experiments establish a vectorized dendritic signal, but do not establish that
the residual directly updates synapses or that cortex implements
backpropagation.

We turn the residual operation itself into a falsifiable learning hypothesis:
use only the component of apical activity that is unexpected from the same
cell's neutral somatic state. We call this **Somato-Dendritic Innovation
Learning (SDIL)**. The credit pathway that supplies the instructional component
is deliberately modular. In small feedforward networks we train direct feedback
with causal node perturbations, following
[Lansdell, Prakash, and Kording (2020)](https://openreview.net/forum?id=ByeUBANtvB).
For the stable ResNet experiment we use reciprocal plasticity following
[Akrout et al. (2019)](https://papers.nips.cc/paper_files/paper/2019/hash/f387624df552cea2f369918c5e1e12bc-Abstract.html).
Neither mechanism is claimed as new.

Our contributions are:

1. a per-cell neutral innovation rule, with raw and per-example norm-matched
   controls that isolate subtraction from gain;
2. a conditional-projection analysis, a descent/gain boundary, and explicit
   perturbation variance and resource accounting;
3. frozen evidence that the innovation operation is load-bearing under
   soma-predictable traffic, including an independently confirmed ResNet-20
   endpoint; and
4. retained negative results showing where the proposal does not work:
   arbitrary top-down traffic, an unstable static ResNet predictor, a failed
   desired-velocity/online-control interpretation, and an untouched
   population-signature confirmation that fails its joint gate.

## 2. Somato-dendritic innovation learning

### 2.1 Local teaching variable

For hidden layer \(l\),

\[
u_l = W_l h_{l-1}, \qquad h_l = \phi(u_l).
\]

The apical compartment mixes an instruction \(s_l=A_lc_l\) with ordinary
traffic \(n_l\):

\[
a_l = s_l+n_l.
\]

A per-cell predictor is fitted when task instruction is absent:

\[
m_l(h_l) \approx \mathbb{E}[n_l\mid\mathcal{F}_{h_l},\mathrm{neutral}].
\]

The teaching variable is

\[
r_l=a_l-m_l(h_l).
\]

The implemented small-network predictor is diagonal affine,
\(m_{l,i}(h_{l,i})=p_{l,i}h_{l,i}+b_{l,i}\). This restriction matters:
traffic predictable only from other neurons or hidden contextual state cannot
be guaranteed to disappear.

With a static feedforward eligibility,

\[
\Delta W_l
=
\eta_W\left(r_l\odot\phi'(u_l)\right)h_{l-1}^{\mathsf T}.
\]

Every factor in this update is available at the synapse or its postsynaptic
cell: presynaptic activity, local activation gain, and the same cell's apical
innovation. Recurrent or spiking implementations can replace the instantaneous
eligibility with a local temporal trace; that extension is not evaluated here.

### 2.2 Two inherited instructional pathways

In the learned-direct-feedback experiments, occasional antithetic Rademacher
perturbations estimate a causal hidden-state direction. If
\(\xi_l\) is injected at layer \(l\) and \(L_+,L_-\) are the paired losses,

\[
q_l
=
-\frac{L_+-L_-}{2\sigma}\xi_l.
\]

The feedback map predicts this direction:

\[
\Delta A_l
=
\eta_A(q_l-A_lc_l)c_l^{\mathsf T}.
\]

This is learned synthetic feedback by node perturbation and is inherited from
Lansdell et al. It requires logical loss observations during calibration, which
we report separately from ordinary supervised loss computation.

The standard ResNet branch instead uses a modified Kolen--Pollack reciprocal
path. Forward and feedback synapses independently recompute matched local
activity products and use matched decay; neither path reads or copies the
other's weight tensor. This inherited mechanism eliminates task-loss queries
but adds a second reciprocal local correlation.

### 2.3 Dynamic neutral projection

A fixed neutral predictor was unstable in the ResNet mixed-traffic
intervention. Linearization exposes a multiplicative residual operator whose
positive modes can diverge even when the initial predictor sign is correct.
The successful ResNet variant retains a slow neutral predictor and adds a
paired instruction-off observation on every ordinary example. For each cell,

\[
e^0_l=a^0_l-m_l(h_l)
\]

is the remaining neutral residual, and the local affine projection coefficient
is

\[
q_l
=
\frac{\mathrm{Cov}(e^0_l,h_l)}
       {\mathrm{Var}(h_l)}.
\]

The stabilized instruction is the task-period apical signal after removing the
neutral mean and current affine soma coupling. The fit sees no task instruction,
loss, downstream weight, or reverse pass. It is nevertheless a real
instruction-off microphase: every neutral observation and its elementwise
arithmetic are counted, and we do not call this variant single-phase.

## 3. What residualization guarantees—and what it does not

Let \(n\) be neutral apical traffic and let
\(\mathcal{F}_h\) be the somatic information available to the predictor. The
conditional mean \(m(h)=\mathbb{E}[n\mid\mathcal{F}_h]\) obeys

\[
\mathbb{E}\langle n-m(h),g(h)\rangle=0
\]

for every square-integrable soma-measurable \(g\), and

\[
\mathbb{E}\|n-g(h)\|^2
=
\mathbb{E}\|n-m(h)\|^2+\mathbb{E}\|m(h)-g(h)\|^2.
\]

Thus the conditional mean is the unique minimum-power subtraction within the
chosen somatic information class. This is a standard projection identity, not
a new theorem. If the neutral traffic law is invariant and task apical
activity is \(a=s+n\), the innovation is \(r=s+n-m(h)\). The result says
nothing about nuisance independent of \(\mathcal{F}_h\), nor does it prove that
\(r\) is a gradient.

The norm-matched raw control uses
\(\alpha a\), where \(\alpha=\|r\|/\|a\|>0\) for each example. Since

\[
\cos(\alpha a,-g)=\cos(a,-g),
\]

positive gain matching cannot reproduce a directional benefit at a fixed
state. We still train the matched control end to end because gain changes later
states and optimization trajectories.

Finally, hidden-state alignment alone is insufficient. For complete parameter
gradient \(p=\nabla_\theta L\) and proposed update direction \(v\), a
\(\beta\)-smooth loss satisfies

\[
L(\theta+\eta v)-L(\theta)
\le
-\eta c\|p\|\|v\|
+\frac{\beta\eta^2}{2}\|v\|^2,
\]

where \(c=\langle-p,v\rangle/(\|p\|\|v\|)\). Descent requires direction, gain,
and curvature to agree. This distinction explains why some failed branches
end with nearly perfect feedback-weight cosine yet have already diverged.

## 4. Experimental protocol

We freeze advancement gates before opening the corresponding held-out
endpoint. Failed branches, dirty-provenance rejection, seed sets, and
validation/test boundaries remain in the repository. Exact hyperparameters,
hashes, and hardware-independent cost definitions are in the accompanying
manifests.

### Controlled traffic and depth

The primary necessity experiment trains depth-3, width-256 MNIST networks for
15 epochs across predictable-traffic ratios
\(\rho\in\{0,0.05,0.2,0.5\}\), three teaching signals, and seeds 0--4. The
signals are raw apical activity, per-example norm-matched raw activity, and
innovation.

The depth panel trains width-64 residual MLPs on flattened CIFAR-10 at hidden
depths 5, 10, 20, 30, and 60, with five paired seeds. BP is a nonlocal
reference; FA, DFA, and learned node-perturbation feedback are local-learning
comparators. Because accuracy does not improve with depth in this task, the
panel tests preservation and credit alignment rather than useful
representation depth.

### Standard ResNet confirmation

The standard-scale test uses a CIFAR ResNet-20 (\(6n+2\), width 16) trained for
200 epochs on all 50,000 training examples. D3 selects no confirmation seed:
it is a single validation-only endpoint. D4 then trains clean reciprocal credit
and dynamic innovation from scratch for untouched seeds 10--14, uses no
validation examples, and evaluates the 10,000-example test set once at the
endpoint. Both conditions use the same initialization/data seed pairing.

### Baselines and cost

In-repository controls include BP, FA, DFA, direct node perturbation,
Forward--Forward, PEPITA, canonical persistent-particle equilibrium
propagation, hierarchical FA, response-mirror variants, and reciprocal
Kolen--Pollack learning. We additionally audit author-code BurstCCN and Dual
Propagation runs under their native protocols. Native architectures,
preprocessing, selection semantics, and wall times are reported as context,
not placed on a purported equal-compute frontier.

We report logical task-loss observations, affine MAC estimates, separately
estimated elementwise work, forward-equivalent examples, paired neutral
observations, peak allocated memory, and wall time. A zero task-loss-query count
does not make neutral observations or local correlations free.

## 5. Results

### 5.1 Innovation is necessary under soma-predictable traffic

![Somato-dendritic innovation mechanism and controlled necessity experiment.](../results/figs/figure3_innovation.png)

**Figure 1: Controlled innovation necessity.** The committed figure renderer
audits all 60 records and displays mean and individual-seed outcomes.

At \(\rho=0\), all three signal rules coincide at 97.45%. At \(\rho=0.5\),
raw apical and norm-matched raw learning fall to 10.38% and 10.31%, whereas
innovation reaches 97.348%. The paired gain over norm-matched raw is
87.038 ± 0.607 points. Used-signal alignment remains positive for innovation
and becomes negative for both controls. The matched control rules out a
per-example magnitude-only explanation.

This intervention is deliberately strong and structured: traffic is generated
from the predictor's available somatic statistic. A separate broad endogenous
top-down intervention does not show uniform removal. The supported claim is
therefore conditional nuisance removal, not arbitrary contextual denoising.

### 5.2 Learned local credit preserves accuracy over depth in a controlled task

![Accuracy, BP gap, and early credit alignment across hidden depth.](../results/figs/figure2_scaling.png)

**Figure 2: Controlled depth preservation.** “Scaling” in this panel denotes
retention under a 12-fold increase in hidden depth, not a benefit from added
depth.

The learned-feedback backbone changes by -0.214 ± 0.349 accuracy points from
depth 5 to 60. Its paired one-sided test rejects a drop of at least one point
(\(p=0.0037\)). DFA changes by -0.870 ± 0.358 points and does not reject the
same margin (\(p=0.2310\)); its early-layer alignment falls from 0.514 to
0.047. SDIL-labelled no-traffic runs in this panel reduce to the inherited
Lansdell-style feedback learner and do not establish the novelty of
residualization.

![Local-learning Pareto frontier and exact-architecture EP comparison.](../results/figs/figure1_pareto.png)

**Figure 3: Accuracy and measured wall-time context.** The local frontier is
constructed only within the matched flattened-CIFAR protocol. The EP panel
matches forward architecture, examples, and epochs while retaining each
method's native preprocessing and dynamics.

Canonical EP is the strongest conceptual stability baseline in the repository
but is expensive in the audited implementation: at two hidden layers its mean
wall time is 17,530 s and mean test accuracy is 89.526%, versus 58.5 s and
97.516% for the feedforward local learner under the stated method-native
dynamics. These numbers are not a hardware-independent dominance theorem; they
make the measured cost mismatch explicit.

### 5.3 Dynamic innovation survives untouched ResNet-20 confirmation

![Paired ResNet-20 endpoint, layerwise signal alignment, and trajectory audit.](../results/figs/figure4_resnet_confirmation.png)

**Figure 4: Standard-ResNet confirmation.** All panels are regenerated from
the ten untouched D4 records, and the renderer refuses missing seeds,
protocol drift, dirty provenance, or disagreement with the frozen gate.

Dynamic innovation reaches 91.584% mean test accuracy versus 91.388% for clean
reciprocal credit. Its mean paired advantage is 0.196 points; the one-sided 95%
upper confidence bound on the clean-minus-dynamic deficit is 0.131 points,
well inside the frozen 2.5-point noninferiority margin. All five dynamic seeds
reach at least 91.51%, and mean early-third teaching alignment is 0.999687.

The raw apical direction is poorly aligned in early layers under four-times-RMS
traffic, whereas the projected innovation remains nearly collinear with the
negative hidden-state gradient. Reciprocal feedback tracks the forward path
throughout training rather than merely reaching an aligned endpoint.

The dynamic run uses 1.326 times the matched BP affine-MAC estimate, zero
logical task-loss queries, one paired neutral observation per ordinary example,
and 2.02 GiB mean peak allocated memory. On the same GTX 1080s its mean wall
time is 1.47 times paired clean KP. The result supports ResNet-20 robustness
under the audited traffic intervention. It does not support a ResNet-20-to-56
depth claim.

## 6. Biological-signature test and negative evidence

The original online-control/desired-velocity screen fails its frozen causal
sign and acute-control gates. We therefore constructed a separate
temporal-difference recovery that factorizes a slowly learned causal-role
vectorizer from within-episode performance dynamics. Its development screen
selects one learning rate before confirmation.

The untouched confirmation contains six task seeds and five model seeds per
task. It learns successfully: mean final performance is 99.531%, mean learning
gain is 90.451 points, the plasticity lesion has a 45.191-point half-margin,
role cosine is 0.9395, and all 30 records have the predicted positive sign
inversion. Residuals are also strongly decorrelated from soma, and their
correlation with error velocity exceeds that with error magnitude.

The joint biological gate nevertheless fails. Residual outcome decoding is
47.325%, 4.322 points below soma rather than above it, and early residuals do
not predict late somatic change (mean correlation -0.013). Surrounding-network
event accuracy also narrowly misses its frozen mean threshold. Thus the model
learns a causal-role temporal-difference plasticity signal without reproducing
the broader population outcome-vectorization and longitudinal signatures.
Because online control is disabled in this recovery, even a passed plasticity
gate would not establish an online desired-velocity controller.

These negatives constrain interpretation:

- we do not infer that dendritic residuals directly drive cortical plasticity;
- we do not infer that cortex implements BP;
- we do not claim arbitrary top-down traffic removal;
- we do not claim positive utility from adding standard ResNet depth; and
- we do not relabel task learning and sign inversion as a passed population
  signature.

## 7. Related work

FA replaces exact transpose transport with random feedback
([Lillicrap et al., 2016](https://doi.org/10.1038/ncomms13276)); DFA sends fixed
random output feedback directly to each hidden layer
([Nøkland, 2016](https://arxiv.org/abs/1609.01596)). Learned synthetic feedback
by causal perturbation is closest to SDIL's small-network instructional
backbone ([Lansdell et al., 2020](https://openreview.net/forum?id=ByeUBANtvB)).
Akrout et al.'s weight-mirror and modified Kolen--Pollack mechanisms are the
source of the stable reciprocal ResNet substrate.

Compartmental and burst-based approaches already establish that segregated
dendrites can coordinate local credit. These include segregated-dendrite
learning ([Guerguiev et al., 2017](https://doi.org/10.7554/eLife.22901)),
dendritic microcircuits
([Sacramento et al., 2018](https://papers.nips.cc/paper_files/paper/2018/hash/1dc3a89d0d440ba31729b0ba74b93a33-Abstract.html)),
and burst-dependent plasticity
([Payeur et al., 2021](https://doi.org/10.1038/s41593-021-00857-x)).
The recent BurstCCN preprint explicitly connects hierarchical dendritic credit
to the Francioni/Harnett observations
([Greedy et al., 2026](https://doi.org/10.64898/2026.06.16.732595)).
Consequently, “apical dendrites carry vector errors” and “a dendritic method
trains a convolutional network” are not our novelty claims.

Equilibrium propagation uses free and nudged energy-based relaxation
([Scellier and Bengio, 2017](https://doi.org/10.3389/fncom.2017.00024)).
Dual Propagation represents activity and error in dyadic states within one
inference phase
([Høier and Zach, 2023](https://proceedings.mlr.press/v202/hoier23a.html);
[Høier and Zach, 2024](https://openreview.net/forum?id=ui8ewXg1hV)).
PEPITA modulates the input with output error and uses a second forward
computation
([Dellaferrera and Kreiman, 2022](https://proceedings.mlr.press/v162/dellaferrera22a.html)).
Forward--Forward trains layer-local goodness on positive and negative data
([Hinton, 2022](https://www.cs.toronto.edu/~hinton/FFA13.pdf)).
SDIL differs in the variable it extracts from a mixed feedback compartment:
the instruction is the component unexpected from neutral soma, not raw
feedback, a two-state contrast, or an input perturbation.

## 8. Limitations and discussion

The central novelty is narrow. Conditional projection is standard, and both
instructional pathways are inherited. The empirical contribution is that
subtraction is load-bearing under a controlled mixed-channel intervention and
that the dynamic version remains stable at ResNet-20 scale.

The predictor's information class is a hard boundary. A diagonal per-cell
predictor cannot remove population-only or latent traffic. Neutral periods are
also an assumption: task-period fitting can absorb the soma-predictable part of
the teaching signal itself, while distribution shift can make a correct neutral
predictor wrong during behavior.

The paired-neutral controller improves stability but weakens a single-phase
biological interpretation and adds substantial wall time despite modest affine
MAC overhead. Hardware implementations may price local elementwise operations,
state storage, and phases differently from GPUs; this is why we report several
resource axes rather than one scalar cost.

The strongest standard result uses only ResNet-20. The separately frozen
ResNet-20/32/56 panel remains unopened because its biological prerequisite
failed. This preserves the declared accept-to-oral ordering but leaves positive
added-depth utility unresolved.

Finally, the synthetic BCI negatives are scientifically important. The
residual operation can be algorithmically useful without reproducing every
signature of cortical dendrites. A stronger biological paper needs a new
prediction and mechanism frozen independently of the failed outcome and
longitudinal metrics, ideally tested on the original event-level data rather
than engineered to pass the present synthetic task.

## 9. Reproducibility statement

Every publication-facing result is bound to source revision, exact seed set,
protocol, split, and evaluation boundary. Renderers regenerate figures from
raw records and write source-hash manifests. The complete mechanical audit is:

```bash
bash experiments/finalize_accept.sh
```

It rechecks the main figures, theoretical identities, local-rule mechanics,
baseline protocols, native-author records, standard-ResNet confirmation,
failed biological confirmation, and the sealed standard-depth boundary.