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
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
|
# Residual response-mirror baseline protocol
## Status and method boundary
Estimate-then-average WM passed its frozen capture gate but missed the short
accuracy gate by under one point. Its final feedback/forward cosine plateaued
near 0.81 in the deepest convolutional group despite frequent local probes.
The diagnosed issue is stationary estimator noise: a fresh finite-sample W
estimate is noisy even when Q already equals W.
Residual response mirroring (RRM) is a substantive update-rule change, not a
new cadence/batch/rate branch of failed WM. For each local Gaussian probe it
compares the observed forward child response with Q's predicted response and
updates from their difference. At Q=W, every individual stochastic update is
zero. The observation and update remain separated; the update never reads a
forward parameter. RRM is still inherited local predictive weight estimation,
not SDIL or Harnett-specific novelty.
A mechanics-only synthetic-image pilot was used to bound the mirror-rate grid.
No CIFAR development-prefix alignment or validation/test endpoint was observed
before this protocol and its executable selector were committed.
## RRM-0: mechanics gate
The convolutional smoke suite must verify:
- exact-symmetry response-residual fraction below `1e-14` for every probe;
- exact-symmetry parameter-update RMS below `1e-14`;
- changing all forward parameters after observations are fixed changes the
feedback update by exactly zero;
- all prior hierarchical and local-gradient checks remain green.
This passes at response-residual fraction `3.08e-17`, update RMS `2.75e-18`,
and forward-parameter independence error exactly zero.
## RRM-1: frozen-forward capture gate
Copy WM-1 exactly: seed-0 ResNet-20, random feedback scale 1, frozen 10k
development prefix, 64-example exact-gradient audit, convolutional mirror batch
1, Gaussian noise standard deviation 1, mirror seed 3000, 20 observations, and
no forward/readout/BatchNorm update. Record fixed HFA and cross
`eta_M in {0.03,0.1,0.3}`. Select early alignment, then all-layer alignment,
then lower rate.
All four records must be finite, and selected RRM must reach early alignment
0.65, all-layer alignment 0.70, mean feedback/forward cosine 0.93, norm ratios
in `[0.5,1.5]`, and zero task-loss queries. No extra observation, rate, batch,
noise, cadence, or layer-specific setting follows a failure.
## RRM-2: short accuracy gate
Only an RRM-1 pass opens two 10k-example, 20-epoch ResNet-20 validation jobs.
Copy WM-2 exactly: hidden LR `{0.03,0.1}`, output LR 0.1, batch 128, cosine
decay, no warmup, momentum 0.9, weight decay `1e-4`, 20 mirror warmup
observations, then one batch-1 observation every 16 task updates. The extra Q
response-prediction convolution is charged explicitly.
Select accuracy, then total MACs/rate. Both records must be finite; selected
RRM must reach 65%, lie within 10 points of matched BP 74.94%, retain early
alignment 0.50, use zero task-loss queries for feedback learning, and cost no
more than 1.15x matched BP MACs. Failure closes RRM.
## RRM-3: conditional full baseline
Only an RRM-2 pass opens one 200-epoch seed-0 validation run, copying selected
settings and the A1 epoch-100/150 step drops on all 45,000 development-training
examples. It must be finite, reach 88%, retain early alignment 0.50, and cost
at most 1.15x BP. It does not authorize test access. A pass instead freezes the
same scalable substrate for a raw-versus-innovation mixed-traffic experiment.
RRM is a baseline throughout. RRM-1/RRM-2 cannot raise the reviewer score;
only a later load-bearing innovation result on top of it can do so.
## Audited RRM-1 outcome
The frozen-forward capture gate passed on source revision `18aff5b`. The full
rate sweep is retained rather than reporting only the selected record:
| method / rate | early alignment | all-layer alignment | feedback/forward cosine | norm range |
|:--|--:|--:|--:|:--|
| fixed HFA | -0.000263 | 0.011279 | 0.001614 | [0.959, 1.055] |
| RRM 0.03 | 0.075016 | 0.235001 | 0.622965 | [0.695, 0.792] |
| RRM 0.10 | **0.665070** | **0.730253** | **0.953680** | **[0.884, 1.018]** |
| RRM 0.30 | 0.003489 | 0.053744 | 0.740396 | [0.999, 30.132] |
The preregistered selector chooses `eta_M=0.1`. All records have finite
reported metrics, and the selected record passes every alignment, cosine,
norm, and zero-query check. Its 20 observations cost `2.4458e9` MACs. The
high-rate instability remains visible and is not used to widen the rate grid.
RRM-2 is therefore opened at the frozen selected rate.
Relative to normalized estimate-then-average mirroring at the same selected
rate and observation count, residual mirroring improves early alignment by
`0.218929`, all-layer alignment by `0.188094`, and feedback/forward cosine by
`0.038200`. This is evidence that removing estimator noise at the fixed point
matters. It remains inherited local predictive weight estimation, so the
strict reviewer score stays `5/10`.
## Audited RRM-2 outcome
The frozen short accuracy gate passed on source revision `6206483`:
| hidden LR | validation accuracy | early alignment | all-layer alignment | feedback/forward cosine |
|--:|--:|--:|--:|--:|
| 0.03 | 62.32% | 0.999604 | 0.999692 | 0.999970 |
| 0.10 | **65.08%** | **0.999128** | **0.999377** | **0.999902** |
The accuracy selector chooses hidden LR 0.1. It clears the 65% gate by only
0.08 points and lies 9.86 points below matched BP at 74.94%, clearing the
within-10-point gate by 0.14 points. Both runs are finite. The selected run
uses zero task-loss queries, 119 mirror events, `2.4256703e13` MACs
(`0.9969x` matched BP), 1.731 GB peak allocated memory, and 93.0 s on a GTX
1080. Every frozen RRM-2 check passes, so RRM-3 opens without changing the
selected mirror rate, cadence, or hidden learning rate.
The nearly exact directional and weight cosines do not erase the short-horizon
accuracy gap. This makes the result more useful as a strict baseline: direction
alone is not a surrogate for trajectory equivalence, especially when feedback
tracks changing forward weights at discrete intervals. Because RRM is inherited
predictive weight estimation, this pass does not change the reviewer score.
## Audited RRM-3 outcome
The sole frozen full run from source revision `8a5c104` fails decisively:
| metric | RRM-3 | frozen requirement/reference |
|:--|--:|--:|
| validation accuracy | **10.00%** | at least 88%; BP is 91.62% |
| validation loss | **NaN** | finite |
| early / all-layer endpoint alignment | 0.877435 / 0.848738 | early at least 0.50 |
| endpoint feedback/forward cosine | 0.999998 | diagnostic only |
| feedback/forward norm range | [1.000157, 1.002447] | diagnostic only |
| MAC ratio to BP | 0.996857x | at most 1.15x |
| task-loss queries for feedback | 0 | exactly 0 |
The task trajectory, not the endpoint tracking snapshot, identifies the
failure. Mean training loss grows from `2.6107` at epoch 1 to a peak of
`1.5808e16` at epoch 92 and remains `9.6549e15` at epoch 100. Stepwise learning
rate drops subsequently reduce it to `8.9503e13` by epoch 200 without restoring
the classifier. Thus an almost perfect final Q/W cosine and controlled norm do
not certify that feedback tracked the fast task-weight trajectory when the
destructive updates occurred.
The ideal recurrence in `THEORY.md`,
`E_(m+1)=(1-eta_M)E_m-U_m`, explains the audit: intermittent tracking error is
driven by cumulative forward motion between mirror events, but a quiet or
low-rate tail can erase endpoint error geometrically. RRM-3 therefore closes
without cadence/rate rescue, opens no innovation experiment, touches no test
seed, and leaves the strict reviewer score at 5/10.
|
