# O0-CRP-037 · Cross-Architecture Perspective Distillation — Scientific Record

**Semantic name:** SIM-CRP-003c · Cross-Architecture Compression (Nearest-Neighbor Memory Observer)
**Record class:** SIMULATION
**Program:** Contact and Revelation (CRP-001)
**Non-drift question:** PERSPECTIVE
**Version:** 1.0.0
**Date:** 2026-07-30
**Status:** PARTIAL_MEMORY_SIGNAL (preregistered verdict)
**Preregistration:** [preregistration.md](preregistration.md) (frozen v1.0.0, 2026-07-30)

---

## Claim-status banner

```
CLAIM STATUS   : PARTIAL_MEMORY_SIGNAL (preregistered)
EVIDENCE TYPE  : COMPUTATIONAL SIMULATION · Nearest-Neighbor Memory Observers
PHYSICAL VALID : NONE
INDEPENDENT REP: THIS IS CROSS-ARCHITECTURE REPLICATION OF CRP-035 v1.2 F2

SUPPORTED:
- NNMO exhibits an immediate compression cliff: BC_TV drops from 1.000 (N0
  full memory) to 0.459 (N1 10 centroids), a loss of 0.541.
- The N1..N4 plateau (BC_TV = 0.43-0.46) indicates that whatever behavior
  survives compression is preserved with essentially the same fidelity at
  4 to 10 retained memory items — the FIRST compression is the costly one.
- Even minimal memory retention (N4: one argmax-reward action) lifts
  behavior modestly above the random-parameter baseline (gap 0.136 TV,
  0.146 AM), showing that some identity signal survives 200-to-1 memory
  compression.
- CROSS-ARCHITECTURE FINDING: CRP-035 v1.2 F2 (high-capacity component
  carries identity) generalizes across architectures, but the DEGREE of
  compression tolerance is highly architecture-dependent. Parameterized
  observers (CRP-035) preserve BC_TV = 0.892 at L4 compression;
  memory-based observers (CRP-037) drop to BC_TV = 0.459 at analogous
  N1 compression, despite N1 retaining MORE numeric information (~100
  numbers vs 32 for L4).

NOT ESTABLISHED:
- Any preregistered "clean cliff to random" behavior — N4 remains above
  random baseline by ~0.14 TV.
- That memory-based observers universally require exact-memory retention;
  followups with different memory clustering (CRP-037-R1) will characterize
  the cliff shape.
- Any generalization to observer architectures other than linear-bandit
  parameter or nearest-neighbor memory. A Bayesian PP observer test is
  registered as CRP-037-R2.
- Any philosophical claim about identity or perspective.
```

---

## Abstract

Preregistered cross-architecture replication of CRP-035 v1.2's F2 finding
(weights carry identity in a linear-bandit observer). Instead of a
parameterized observer whose decision rule uses learned parameters, this
study uses a Nearest-Neighbor Memory Observer (NNMO) whose decision rule
uses stored `(context, action, reward)` triples DIRECTLY: at each context,
the observer kernel-weights the k nearest stored contexts, votes by action,
and applies softmax with a per-observer temperature.

Six compression levels (N0..N5) progressively summarize the memory: full
memory → 10 k-means centroids → 4 per-action centroids → per-action mean
reward vector → single argmax-reward action → empty memory. NNMO has no
learned parameters other than memory, so this compression pipeline directly
probes what happens when the observer's ONLY identity carrier is
progressively summarized.

Confirmatory n = 30, 200 held-out contexts, adversarial random-parameter
and cross-observer baselines. Runtime: 1629 s.

Key findings:

- Full-memory BC = 1.000 (identity gate passes).
- N1 (10 k-means centroids, ~100 retained numbers): BC_TV = 0.459 vs
  random 0.298 (gap 0.161). **A single compression step already drops BC
  to less than half its starting value.**
- N1..N4 plateau at BC_TV ≈ 0.43-0.46 with random-baseline gaps of
  0.14-0.17. The compression is essentially binary in this architecture:
  either you keep all of memory, or the fine-grained behavioral fidelity
  is lost.
- N5 (empty memory): BC_TV = 0.349, exactly the random baseline.
- CROSS-ARCHITECTURE: at analogous "keep the high-capacity component"
  compression, parameterized observers (CRP-035 L4) preserve BC_TV = 0.892
  while memory-based observers (CRP-037 N1) preserve only 0.459 — a
  0.43 gap despite N1 retaining more numeric information.

Verdict: **PARTIAL_MEMORY_SIGNAL** (preregistered). Full memory is required
for high behavioral fidelity in NNMO, but modest signal survives extreme
compression down to a single action.

## 1. Historical and conceptual background

CRP-035 v1.2 found that in a linear-bandit observer, the per-action weight
matrix `W ∈ R^{d×K}` carries essentially all identity-relevant behavioral
signal: L4 compression (W preserved, preferences discarded) gave
BC_TV = 0.892 vs random 0.282.

This finding is architecture-dependent by construction: linear-bandit
observers have identity in their weight parameters because that is where
learning is stored. A memory-based observer whose decision rule uses stored
experience directly could have a very different compression profile.

CRP-037 tests this: same environment class, same measurement pipeline,
GENUINELY different observer architecture.

## 2. Source-claim audit

No new philosophical source claim. CRP-037 is a mechanistic sub-question
of CRP-035's PERSPECTIVE branch.

## 3. Research question

For an observer whose decision rule uses stored `(context, action, reward)`
triples directly via nearest-neighbor kernel voting, at what level of
memory compression does behavior collapse to a random baseline?

## 4. Operational definitions

Inherited from CRP-035 v1.1/v1.2 §3 (BC_TV, BC_AM, SR, VP, PS).

## 5. Formal model

**Nearest-Neighbor Memory Observer (NNMO).** State
$\theta = (M, k, \sigma, \tau, \text{id})$ where:

- $M$: FIFO memory of up to 200 `(x, a, r)` triples
- $k \in \{3, 5, 7, 10\}$: number of neighbors used per decision
- $\sigma \in [0.5, 2.0]$: kernel bandwidth
- $\tau \in [0.15, 0.5]$: softmax temperature
- id: stable identifier

Decision rule: for context $x$, find $k$ nearest neighbors from $M$ by
Euclidean distance, kernel-weight them by $w_i = \exp(-d_i^2 / 2\sigma^2)$,
compute per-action $\hat{Q}(a) = \sum_{i \in kNN, a_i=a} w_i r_i / \sum_{i \in kNN, a_i=a} w_i$,
and apply $\pi(a | x) = \text{softmax}(\hat{Q} / \tau)$.

No parameters other than memory are updated during training. `k`, `\sigma`,
`\tau` are per-observer constants sampled at instantiation.

Training environment: identical to CRP-035 v1.2 (linear-Gaussian rewards
per action). 200 training episodes populate memory.

## 6. Methods

Confirmatory sample: **n=30 observers**, seeds 18000..18029. Environment
seeds 18500..18529. Eval context seed 19000 (N=200 contexts). Probe seed
19500 (N=500 probes). VP env seeds 20000..20049 (N=50 envs × 20 episodes).

Compression pipeline (six levels): full memory → 10 k-means centroids →
4 per-action centroids → per-action mean rewards → argmax(reward) →
identifier only.

Random-parameter baseline at each level uses NNMOs with randomly-drawn
memories of matching size.

## 7. Results

| Level | Retained | BC_TV | BC_AM | BC_cos | SR | VP | PS | BC_TV_random | BC_AM_random | BC_TV_cross | BC_AM_cross |
|---|---|---:|---:|---:|---:|---:|---:|---:|---:|---:|---:|
| **N0** | Full memory (~200 triples) | **1.000** | **1.000** | 1.000 | 1.000 | 1.000 | 1.000 | 0.297 | 0.238 | 0.270 | 0.248 |
| **N1** | 10 k-means centroids | 0.459 | 0.434 | 0.525 | 0.067 | 0.545 | 0.330 | 0.298 | 0.250 | 0.275 | 0.246 |
| N2 | 4 per-action centroids | 0.445 | 0.414 | 0.538 | 0.133 | 0.212 | 0.261 | 0.299 | 0.260 | 0.294 | 0.247 |
| N3 | per-action mean r | 0.445 | 0.414 | 0.538 | 0.133 | 0.207 | 0.261 | 0.270 | 0.234 | 0.294 | 0.247 |
| N4 | argmax(reward) — 1 action | 0.430 | 0.414 | 0.478 | 0.133 | 0.240 | 0.186 | 0.294 | 0.268 | 0.276 | 0.247 |
| N5 | identifier only | 0.349 | 0.268 | 0.565 | 0.033 | 0.008 | 0.000 | 0.349 | 0.268 | 0.349 | 0.268 |

Random gaps at each level:

| Level | BC_TV - random | BC_AM - random | Interpretation |
|---|---:|---:|---|
| N0 | 0.703 | 0.762 | Full identity signal |
| N1 | 0.161 | 0.184 | Modest signal above random |
| N2 | 0.146 | 0.154 | Modest signal above random |
| N3 | 0.175 | 0.181 | Modest signal above random |
| N4 | 0.136 | 0.146 | Modest signal above random |
| N5 | 0.000 | 0.000 | Random baseline (by construction) |

### 7.1 Preregistered verdict application

Applied verdict rules from preregistration §8 in order:

1. **MEASUREMENT_FAILURE** — BC_TV(N0) = BC_AM(N0) = 1.000 · PASS.
2. **METRIC_SATURATION** — BC_TV_cross(N0) = 0.270, BC_AM_cross(N0) = 0.248 · PASS.
3. **MEMORY_CARRIES_IDENTITY_IN_NNMO** — H1: BC(N0) >= 0.95 ✓ AND
   BC(N4) - BC_random(N4) < 0.10. **FAILS** — gap is 0.136 TV, 0.146 AM
   (both > 0.10). Rule does not fire.
4. **PARTIAL_MEMORY_SIGNAL** — BC(N4) - BC_random(N4) >= 0.10 on either
   metric. **FIRES** — gaps of 0.136 TV and 0.146 AM.
5. Rule 3 fires before rule 5, so no COMPRESSION_CLIFF verdict.

**Preregistered verdict: PARTIAL_MEMORY_SIGNAL.**

### 7.2 Cross-architecture comparison

Direct comparison of "keep the high-capacity component" compression across
two observer architectures:

| Observer | Level | Description | Retained numbers | BC_TV | BC_TV_random | Gap |
|---|---|---|---:|---:|---:|---:|
| CRP-035 v1.2 linear-bandit | L4 | W matrix + τ | 32 (+ τ) | **0.892** | 0.282 | **0.610** |
| CRP-037 NNMO | N1 | 10 k-means centroids | ~100 (+ k, σ, τ) | **0.459** | 0.298 | **0.161** |

Despite N1 retaining MORE numeric information than L4, it preserves MUCH
LESS behavior. The identity carrier is not just "high-capacity component"
— it is "high-capacity component that IS the decision rule."

In CRP-035, W is directly used to compute Q values via a compact linear
function; it captures the full learned policy in 32 numbers. In CRP-037,
memory is used via nearest-neighbor interpolation over stored triples;
compressing memory to 10 centroids destroys the interpolation ability
even though the centroids themselves preserve gross action structure.

### 7.3 Additional observations

- **Plateau at N1..N4.** BC_TV stays in [0.43, 0.46] across all
  intermediate compression levels. Once the first compression step is
  taken, further compression loses little. This is different from CRP-035
  v1.2 where BC declined smoothly from L4 (0.892) through L5 (0.458) to
  L6 (0.326). NNMO's compression is essentially step-shaped.

- **VP breakdown at N2 and N3.** Value preservation drops sharply from
  N1 (0.545) to N2/N3 (0.21). Even though BC_TV plateaus, VP breaks.
  This is because per-action means (N2, N3) don't discriminate reward
  magnitudes well across actions, so the compressed observer picks
  reasonable actions less often over long horizons.

- **SR spike at N2/N3.** Self-recognition is HIGHER at N2/N3 (0.13) than
  at N1 (0.07). This is likely because forced per-action centroids
  (N2 always has one centroid per action) produce fingerprints that are
  more distinguishable across observers than the noisier N1 centroids.
  Documented but not the primary finding.

## 8. Uncertainty

Per-observer means with SEMs in `results/summary_confirmatory.json`. All
random-gap effects are >0.14 TV / >0.14 AM with SEM around 0.02.

## 9. Limitations

- Single memory-based observer architecture. Other memory-based schemes
  (episodic memory + LTM, dynamic prototypes, replay buffers) may compress
  differently.
- Single environment class (linear-Gaussian rewards) — same as CRP-035.
- N1's compression uses simple k-means; smarter compression schemes
  (learned prototypes, sketch data structures) may preserve more behavior.
- The cross-architecture finding depends on the specific NNMO decision
  rule; a different kernel (e.g. RBF over context+action) might preserve
  more information under compression.

## 10. Alternative interpretations

- **N1 loses more than L4 because it loses interpolation ability, not
  because it has less "identity."** A single centroid represents many
  contexts; compressing 200 items to 10 discards the fine-grained action
  boundaries in context space. In CRP-035, W preserves those boundaries
  by construction (linear function).
- **N1 could preserve more with better clustering.** If k-means were
  replaced with a learned prototype-selection method, N1 might approach
  L4's fidelity. This would move the story from "memory-based observers
  cliff" to "compression quality matters."
- **The N0-to-N1 cliff might depend on training regime.** 200 episodes of
  training produces a specific memory distribution; longer training would
  produce more redundant memory and might compress better.

## 11. Replication procedure

```
cd research/studies/O0-CRP-037/src
python run_study.py --phase exploratory   # ~30 s
python run_study.py --phase confirmatory  # ~30 min
python summarize.py confirmatory
```

## 12. Code and data manifest

- `preregistration.md` (v1.0.0)
- `src/nnmo.py` — NNMO observer implementation
- `src/nn_compressors.py` — 6 compression operators
- `src/run_study.py` — driver
- `src/summarize.py` — result-table printer
- `results/summary_exploratory.json`
- `results/summary_confirmatory.json`

## 13. Relationship to the philosophical archive

**Conceptual provenance is not empirical support.** CRP-037 tests a
mechanistic sub-question. Its indirect contribution: it establishes that
"identity carriers" are architecture-dependent. The philosophical claim
"perspective survives distillation" cannot be evaluated by any single
observer architecture; each architecture answers only "identity survives
under THESE compression rules for THIS decision procedure."

## 14. Registered follow-ups

- **O0-CRP-037-R1** — Vary `k_c` in {3, 5, 10, 20, 50} to characterize
  the compression cliff shape.
- **O0-CRP-037-R2** — Third architecture: Bayesian PP observer.
- **O0-CRP-037-R3** — Adversarial memory contamination: replace some
  triples with random noise; measure BC vs contamination rate.

## 15. References

- CRP-035 v1.2, CRP-036 v1.0.
- Sutton & Barto, 2018 (contextual bandit background).
- MacQueen, 1967 (k-means).
- Cover & Hart, 1967 (nearest-neighbor classification).

## 16. Revision history

| Version | Date | Change |
|---|---|---|
| 1.0.0 | 2026-07-30 | Preregistration frozen and code drafted. Exploratory (n=6) and confirmatory (n=30) executed. Verdict: PARTIAL_MEMORY_SIGNAL. Cross-architecture comparison to CRP-035 v1.2 L4 documented. |