# O0-CRP-038 · Learning-Rate Equalization Robustness Test — Scientific Record

**Semantic name:** SIM-CRP-003d · Learning-Rate Equalization (WEIGHTS_DOMINATE Robustness)
**Record class:** SIMULATION (targeted robustness test)
**Program:** Contact and Revelation (CRP-001)
**Non-drift question:** PERSPECTIVE
**Version:** 1.0.0
**Date:** 2026-07-30
**Status:** WEIGHTS_STILL_DOMINATE (preregistered verdict)
**Preregistration:** [preregistration.md](preregistration.md) (v1.0.0)

---

## Claim-status banner

```
CLAIM STATUS   : WEIGHTS_STILL_DOMINATE (preregistered verdict, n=30)
EVIDENCE TYPE  : COMPUTATIONAL SIMULATION · targeted robustness test
PHYSICAL VALID : NONE
INDEPENDENT REP: CRP-036 + CRP-037 already provide corroboration

SUPPORTED:
- CRP-035 v1.2 F2 (weights carry identity) survives learning-rate
  equalization. With eta_p = eta_W (instead of eta_p = 0.1 * eta_W as
  in CRP-035 v1.2), L4 compression still preserves BC_TV = 0.825
  (vs 0.892 in CRP-035 v1.2, delta = -0.067).
- The delta from CRP-035 v1.2 is within the preregistered tolerance
  of 0.15 on both primary metrics. Learning-rate asymmetry does NOT
  explain the WEIGHTS_DOMINATE finding.
- The "more-trained-component dominates" alternative interpretation
  raised in CRP-036 and CRP-037 adversarial notes is REJECTED.
- Small effects DO exist: at L4 the equal-LR observers preserve
  slightly less behavior (0.825 vs 0.892) and at L5 they preserve
  slightly more (0.481 vs 0.458). This is consistent with equal LRs
  reallocating identity carrying capacity slightly toward p.

NOT ESTABLISHED:
- Any generalization beyond linear-bandit observers.
- Any generalization beyond 100 training episodes.
- That capacity asymmetry (W has d*K=32 params; p has K=4) is not
  itself a confound (CRP-038-R2 registered for a d=1 test).
- Any philosophical claim.
```

---

## Abstract

Preregistered targeted robustness test. CRP-035 v1.2's F2 finding
(WEIGHTS_DOMINATE) and CRP-036's independent confirmation both admit an
alternative interpretation: the observer's update rule increments W by
`eta * err * x` and p by `0.1 * eta * err`. After 100 training episodes,
W is more strongly trained than p. So the "weights dominate" pattern
might reflect training regime, not architecture.

This study forks the CRP-035 v1.2 observer and changes ONE line: `p[a]
+= eta * err` (was `0.1 * eta * err`). All other design elements are
identical: state, initialization, decision rule, environment, 8-level
compression pipeline, adversarial baselines, n=30 confirmatory.

**Result:** L4 (W preserved, p discarded) preserves BC_TV = 0.825
(BC_AM = 0.819) — a small drop from CRP-035 v1.2's 0.892 (0.885) but
well within the preregistered tolerance of 0.15. Verdict:
**WEIGHTS_STILL_DOMINATE**. The learning-rate asymmetry alternative
interpretation is rejected.

## 1. Motivation

CRP-036 and CRP-037 both noted the following in their adversarial-note
sections:

> The observer training regime updates W at rate eta and p at rate
> 0.1 * eta — the 10x asymmetry could partially explain WEIGHTS_DOMINATE.

CRP-038 tests this directly. If the CRP-035 finding is a training-regime
artifact, equal LRs should push L4's BC toward chance. If the finding
is a structural property of the observer's decision rule, L4 should
remain high.

## 2. Design (locked at preregistration)

- **Observer:** identical to CRP-035 v1.2 except the p-update coefficient
  changes from 0.1 to 1.0.
- **Environment, compression pipeline, measurements:** all identical.
- **Confirmatory:** n = 30, seeds 21000..21029, disjoint from all prior
  CRP studies.

## 3. Results

| L | BC_TV | BC_AM | BC_cos | SR | VP | PS | TV_rand | AM_rand |
|---|---:|---:|---:|---:|---:|---:|---:|---:|
| 0 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 0.306 | 0.297 |
| 1 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 0.270 | 0.256 |
| 2 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 0.258 | 0.248 |
| 3 | 0.483 | 0.501 | 0.639 | 0.033 | 0.343 | 0.481 | 0.339 | 0.310 |
| **4** | **0.825** | **0.819** | **0.877** | **0.333** | 0.695 | 0.970 | 0.267 | 0.254 |
| 5 | 0.481 | 0.560 | 0.691 | 0.200 | 0.384 | 0.618 | 0.301 | 0.229 |
| 6 | 0.314 | 0.237 | 0.514 | 0.067 | 0.513 | 0.042 | 0.315 | 0.222 |
| 7 | 0.316 | 0.235 | 0.542 | 0.033 | 0.424 | 0.000 | 0.316 | 0.235 |

**Comparison to CRP-035 v1.2 at L4:**

| Metric | CRP-035 v1.2 | CRP-038 (equal LR) | Delta |
|---|---:|---:|---:|
| BC_TV(L4) | 0.892 | 0.825 | −0.067 |
| BC_AM(L4) | 0.885 | 0.819 | −0.066 |

Both deltas are well within the preregistered ±0.15 tolerance.

## 4. Verdict application

1. MEASUREMENT_FAILURE — BC_TV(L0) = 1.000 · PASS.
2. METRIC_SATURATION — BC_TV_cross(L0) = 0.260 · PASS.
3. **WEIGHTS_STILL_DOMINATE** — |L4_TV − v12_L4_TV| = 0.067 < 0.15 ✓ AND
   |L4_AM − v12_L4_AM| = 0.066 < 0.15 ✓ AND L4_TV = 0.825 ≥ 0.75 ✓.
   **FIRES.**

**Preregistered verdict: WEIGHTS_STILL_DOMINATE.**

## 5. Interpretation

The learning-rate asymmetry does contribute a small effect (~0.07 BC_TV
at L4), but it does NOT explain the WEIGHTS_DOMINATE finding. Under
equal learning rates:

- L4 (W only) still preserves 82% of behavior.
- L5 (argmax(W) + argmax(p)) is slightly higher than under CRP-035 v1.2
  (0.481 vs 0.458), consistent with p carrying slightly more signal when
  equally trained.
- The overall compression profile is qualitatively unchanged.

The most likely remaining alternative interpretation is **capacity
asymmetry**: W has d*K = 32 parameters, p has K = 4 parameters. Even
with equal learning rates, W can absorb more environment structure per
episode. This is registered as CRP-038-R2 (reduce d to 1 to equalize
capacity).

## 6. Uncertainty

All means with SEM in `results/summary_confirmatory.json`.

## 7. Limitations

- Same as CRP-035 v1.2: single observer class, single environment
  class, single training-episode count.
- Robustness only tested against ONE alternative interpretation
  (learning-rate asymmetry). Capacity and initialization asymmetries
  remain untested.

## 8. Registered follow-ups

- **O0-CRP-038-R1:** Increase training episodes to 500 and re-test
  whether the delta shrinks (more episodes → both W and p converge
  toward respective ground truths).
- **O0-CRP-038-R2:** Reduce W dimensionality to match p's capacity
  (d = 1) and re-test.
- **O0-CRP-038-R3:** Vary the p learning-rate coefficient from 0.01
  to 10.0 to characterize the effect systematically.

## 9. Replication procedure

```
cd research/studies/O0-CRP-038/src
python run_study.py --phase confirmatory   # ~3 min
python summarize.py
```

## 10. Code and data manifest

- `preregistration.md` (v1.0.0)
- `src/observer_eqlr.py` — CRP-035 v1.2 observer with equal LR for p and W
- `src/run_study.py` — driver (reuses CRP-035 compressors and measurements)
- `src/summarize.py` — result-table printer
- `results/summary_confirmatory.json`

## 11. Relationship to the philosophical archive

**Conceptual provenance is not empirical support.** Same disclaimer as
CRP-035/036/037. This is a methodological robustness test.

## 12. References

- CRP-035 v1.2 scientific record (WEIGHTS_DOMINATE finding).
- CRP-036 v1.0 (independent WEIGHTS_DOMINATE confirmation via inverted
  compression).
- CRP-037 v1.0 (cross-architecture NNMO).

## 13. Revision history

| Version | Date | Change |
|---|---|---|
| 1.0.0 | 2026-07-30 | Preregistration frozen and code drafted. Confirmatory executed at n=30. Verdict: WEIGHTS_STILL_DOMINATE. Learning-rate asymmetry rejected as alternative interpretation. |