1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
|
# Endogenous shared-feedback feasibility protocol
## Question and claim boundary
The existing clean-task scaling results cannot identify an SDIL scaling
contribution. When reciprocal Kolen--Pollack (KP) feedback contains only the
instructional field, the neutral predictor is zero and SDIL is exactly clean
KP. Adding an otherwise unused nuisance field and removing it establishes
robustness, not innovation-enabled scaling.
This protocol tests a different system constraint before any further scaling
claim is allowed: one apical pathway must carry both task-required contextual
feedback during inference and an instructional field during learning. The
ordinary component is therefore present with no bias or nuisance intervention,
and disabling it must damage the task. SDIL may advance only if neutral-period
prediction separates instruction from that shared field. A clean/oracle KP
condition is retained as an upper bound, but it receives a separate
instruction-only observation that the shared-path conditions do not receive.
Passing this feasibility screen is not a scaling result and cannot change the
review score. A later depth or architecture experiment may be opened only by
the frozen gate below.
## S0 contextual task and architecture
Each example contains two independent standard-normal features `x0,x1` and a
balanced binary context `z`. The target is `1[x0 > 0]` when `z=0` and
`1[x1 > 0]` when `z=1`. Input features alone have a 75% Bayes ceiling because
the context is independent and unavailable on the basal input path.
The student is a two-hidden-layer width-64 tanh network. Context enters every
hidden population only as a fixed random apical field
```text
n_l(z) = C_l onehot(z)
u_l = W_l h_(l-1) + n_l(z)
h_l = tanh(u_l).
```
`C_l` is drawn once with elementwise standard deviation `1/sqrt(2)` and is
identical across conditions. There is no context input to the basal stream or
readout. The output is a two-class linear readout. Removing `n_l(z)` at
evaluation is the required context lesion.
Forward and reciprocal weights use independently initialized modified-KP
updates with equal momentum and decay. For population `l`, let `t_l` be the
instructional field transported by its reciprocal path. The measured shared
apical field is generated by the forward computation itself:
```text
a_l = n_l(z) + t_l.
```
No traffic ratio, additive offset, measurement error, or generated nuisance is
introduced.
## Conditions
All conditions share examples, minibatch order, initial forward/reciprocal
weights, fixed context projections, optimizer, and forward computation.
1. `oracle`: use the separately observed instruction-only field `t_l`.
2. `raw_shared`: use the shared field `a_l` directly.
3. `innovation`: fit a per-cell affine neutral predictor
`n_hat_li = p_li h_li + b_li` from instruction-off observations and use
`a_l - n_hat_l`.
4. `matched_raw`: preserve the direction of `a_l` but match its per-example
norm to the innovation, ruling out a magnitude-only explanation.
The predictor sees context-bearing forward states and neutral apical activity,
but no label, loss, instructional field, oracle difference, or downstream
weight. A fixed 512-example training-only neutral set is observed before each
epoch. These observations and their extra forward work are counted.
## Frozen development screen
Use 8,192 generated training examples and an independently generated balanced
2,048-example validation set, batch size 128, 40 epochs, model/data seed 3101,
SGD momentum 0.9, hidden/output learning rate 0.03, reciprocal learning rate
0.03, and weight decay `1e-4`. There is no learning-rate, context-scale,
predictor-rate, width, depth, or epoch grid. Validation is evaluated only at
the endpoint. No test split is generated in S0.
Before the task run, deterministic mechanics tests must establish:
- identical forward outputs and parameters across all four conditions;
- exact context removal in the context lesion;
- zero instructional observations during neutral predictor fitting;
- `raw_shared = n + t`, oracle recovery under exact subtraction, and exact
per-example norm matching;
- reciprocal updates do not read or copy forward weights or updates;
- the zero-context limit makes oracle, raw, matched raw, and innovation
identical when the predictor is zero.
S0 passes only if all mechanics checks pass and the single frozen run satisfies
all of:
- oracle validation accuracy is at least 90%;
- the oracle context lesion loses at least 10 accuracy points;
- neutral context RMS is nonzero in every hidden population;
- raw shared feedback is at least 5 points below oracle or becomes nonfinite;
- innovation is at least 5 points above raw and no more than 3 points below
oracle;
- innovation is no more than 2 points from exact generated-context subtraction;
- matched raw remains at least 3 points below innovation;
- the neutral predictor explains at least 80% of per-cell context variance on
average and leaves at most 25% of raw context RMS;
- all predictor reports contain zero task-instruction observations.
Failure closes this realization without tuning it. Passing permits one new,
separately committed useful-depth protocol. That protocol must demonstrate a
BP/oracle benefit from depth, a growing raw shared-path deficit, recovery by
innovation, context lesions, and an explicit accounting of the extra clean-KP
instruction wire. Injected-bias or clean-KP scaling results cannot substitute
for those checks.
|
