# Mesa Phase 6 v3.2 — Top-k Neuron Mediation Result Note (Negative) This document records the Phase 6 v3.2 result for [`PHASE6_V32_SPEC.md`](PHASE6_V32_SPEC.md). v3.2 asked whether the entangled 5-dimensional basin-attractor subspace at `net.7` (established in v3 and characterized in v3.1) could be approximated by patching only the top-k most-contributing neurons. The spec included a smoke gate that, if failed, would deliberately stop the full k-sweep and record a negative result. Status: **smoke gate failed cleanly**. Z1 falsified by a wide margin. The full k-sweep was deliberately not run per the spec. v3.3 routes to non-linear neuron-attribution methods. ## 1. Summary Phase 6 v3.2 gives the program one tightly-bound negative result with a methodological lesson that stacks on v2's SAE-wrong-basis lesson: 1. **Top-k neuron-restricted patching does not deliver the v3 K=5 patch effect.** Even at top-32 (12.5% of net.7's neurons, capturing 33.6% of the aggregate L2 across PCs 1-5), the patch produces ~0% effect in both directions. The 5D subspace is **not linearly decomposable into top-k neuron contributions** — masking the delta to a subset of neurons does not deliver a proportional fraction of the mechanism. 2. **The mechanism is non-additive across the neuron substrate.** The patched neurons need the unmasked neurons to remain coordinated for the post-patch activation pattern to drive basin behavior; leaving 87.5% of neurons at their unpatched values interferes with the partial patch even though those neurons hold only ~66% of the subspace L2. 3. **Methodological lesson stacks with v2.** v2 said *feature- availability rankings (e.g., SAE features ranked by per-episode correlation) do not surface mechanism even at strong correlation*. v3.2 says *linear additive top-k neuron restriction does not surface mechanism even with the right basis*. Future Phase 6+ interpretability work in this regime should default to non-linear attribution methods. The cleanest v3.2 headline: **the entangled 5D basin subspace at `net.7` is implemented holistically across the layer's neuron substrate; linear additive top-k mediation is not a tractable lens for this circuit, and the gravity-claim mechanistic anchor stays at "5D entangled subspace" without further decomposition to a few specific neurons.** ## 2. Artifacts Harness: `training/mesa/phase6_v2_sae.py` subcommand `axis-m-neuron-mediation`. Smoke gate output: ``` results/mesa/phase6-v3-2-neuron-mediation/axis-m-cliff-pair/top-32/ patch.csv patch-aggregate.csv v1-vs-v3-comparison.csv neuron-ids-top-32.csv pc-l2-capture.csv manifest.json ``` PCA basis loaded from the v3.1 canonical reconstruction at `results/mesa/phase6-v3-1-validation/pca-basis/cliff-pca-net7-seed10000-n64-h200-k5.*`. Full k-sweep directories (k ∈ {8, 16, 32, 64, 256}) were **not created** — the smoke gate stopped the v3.2 sweep before they would have run. ## 3. Smoke Gate Outcome Smoke run: `--top-k 32 --seeds 8 --layer net.7 --pair cliff`. | metric | value | gate requirement | | --- | ---: | --- | | Top-32 captured L2 fraction (aggregate across PCs 1-5) | 0.3363 | (informational) | | P→C median patch_success | **−0.006** | ≥ 0.37 | | C→P median patch_success | +0.001 | (gate is P→C only) | The gate is one-sided on P→C per spec §3.4: if any direction concentrates, it should be the basin-inducing direction (per v3.1 Axis J showing basin-inducing generalizes more cleanly than basin-resisting). The P→C result of −0.006 is essentially zero — not a partial recovery, not a noisy positive trend, just a complete failure to deliver mechanism through the top-32 mask. **Per spec §3.4: stop. The full k-sweep is deliberately not run.** Per spec §12 Z1-falsifier branch: route v3.3 to non-linear attribution methods. ## 4. Mechanistic Interpretation The 33.6% L2 capture vs 0% patch effect contrast is the load-bearing pair of numbers. If the mechanism were *linearly distributed* across neurons (each neuron contributing patch effect proportional to its L2 share of the PCA basis), top-32 would deliver ~30-40% of patch success. Instead it delivers 0%. Two non-mutually-exclusive readings: - **Coordination reading.** The post-patch activation pattern works as a *whole*: the patched neurons need the unmasked neurons to be at their *patched* values too, or downstream weights' linear combinations across the layer produce action logits that don't reflect the intended subspace shift. Masking 87.5% of neurons leaves them at unpatched values, which interferes with the intended pattern at the patched neurons even though those unmasked neurons hold only ~66% of basis L2. - **Non-linear-readout reading.** The policy_head downstream of `net.7` may apply a Tanh + Linear transformation whose output is sensitive to *configurations* of net.7 activations rather than individual coordinates. Linear additive substitution in a 5D subspace works (v3 K=5); linear additive substitution restricted to a neuron subset doesn't because the same subspace shift, delivered partially, produces a different downstream configuration than the subspace shift delivered fully. Both readings predict that *non-linear* attribution methods — zero-ablation (per-neuron removal scored by behavioral cost), integrated gradients (per-neuron gradient credit along the integration path), or causal scrubbing (replacing activations with structurally- matched samples) — should produce different, more informative results. That is the v3.3 routing. ## 5. Reconciliation with v3.1 Axis K v3.1 Axis K reported per-PC top-32 L2-concentration in the range 0.377-0.663 (PC1 had the highest concentration; PCs 2-5 spanned the range). v3.2's aggregate top-32 captures 0.336 of total L2 across all five PCs. Why is 0.336 lower than the per-PC range's lower bound of 0.377? The per-PC top-32 mask is *different per PC* — PC1's top-32 neurons need not be the same as PC2's top-32. v3.2's aggregate ranking picks one fixed top-32 set by `Σ_i v_ij²`, which is the *intersection-ish* of the per-PC top-32 sets weighted by total contribution. A neuron that's #1 in PC2 but #200 in PC1/PC3/PC4/PC5 has low aggregate L2 even though it dominates PC2. The 0.336 / 0.377-0.663 numbers are therefore mutually consistent and do not conflict. v3.2's aggregate ranking is the *most parsimonious* single-mask version of "top neurons across all five directions"; it captures less L2 than any per-PC top-32 ranking but cleanly answers the v3.2 question of "does a single neuron subset mediate the v3 K=5 patch?" Alternative rankings — per-PC top-32 union, signed-L2 per PC, weighted by patch_success-per-PC — are v3.3 candidates if the program decides to revisit top-k mediation with a more sophisticated ranking. v3.2's clean failure suggests this is low-priority. ## 6. Methodological Lesson (stacks with v2) The Phase 6 program now has two stacked methodological lessons about mechanism-localization in this controller family: - **v2 lesson:** *Feature-availability rankings on a joint two-policy dataset return policy-identifier features rather than mechanism features.* SAE features with |corr| = 0.89 against `basin_pref_ intervened` produced zero patch effect because the correlation was dominated by between-policy mean differences rather than the causal-mechanism subspace. - **v3.2 lesson:** *Linear additive top-k restriction within the correct basis (PCA on per-step matched-seed diffs) still does not surface mechanism.* The basin-attractor circuit is implemented holistically across the neuron substrate; partial delivery of the subspace shift fails even when the basis is correct. Together these lessons say: for mechanism in this circuit, **non-linear attribution is mandatory; linear analysis methods (probes, SAE features, top-k subspace restriction, top-k neuron restriction) all fall short**. The result is preserved as a methodological note for future mesa-trap work and for any reviewer who reaches for the linear-interpretability toolkit first. ## 7. v3.3 Routing Per spec §12 Z1-falsifier branch: > v3.2 records the negative result: the 5D subspace is mediated by > a non-linearly-distributed neuron pattern that linear top-k > ablation can't reproduce. > v3.3 routes to non-linear attribution methods: zero-ablation > attribution scores per neuron, integrated gradients on net.7 → > action logits, or causal scrubbing. Three candidate v3.3 axes, in order of compute-tractability: 1. **Axis N — Zero-ablation attribution.** For each neuron j ∈ {0..255}, set neuron j's activation to zero at the patch step (analogous to dropout at a single neuron), rerun the v3 K=5 patch battery, measure how much patch_success drops. The "critical" neurons are those whose ablation drops patch_success most. Compute: 256 neurons × 8-16 seeds × 4 forwards ≈ ~15-30 minutes wall-clock. This is the dual of v3.2: instead of asking "which neuron subset is *sufficient*," ask "which neurons are *necessary*." Critical-neuron sets often differ from high-contribution sets in non-linear systems. 2. **Axis O — Integrated gradients on net.7 → action logits.** Standard gradient-based attribution. For each (seed, step), compute gradient of action logit w.r.t. net.7 activation, integrate from a baseline (zero or matched-protected activation), sum per-neuron credit. Compute: ~10 minutes with PyTorch autograd. Surfaces per-step neuron credit independent of the patching apparatus; tests whether basin-resisting and basin-inducing have different gradient-attribution structure. 3. **Axis P — Causal scrubbing.** Replace `net.7` activations with structurally-matched samples drawn from a hypothesized circuit model (e.g., "the basin attractor is implemented as a downstream readout that gates on the projection along PC2"). More work; more informative when there's a specific hypothesis to test. v3.3.1 candidate after Axis N / Axis O surface targets. Recommended v3.3 sequencing: Axis N first (cheapest, dual to v3.2, direct comparison possible), then Axis O if Axis N surfaces no critical neurons. ## 8. Open Edges v3.2 closed cleanly but left two questions worth flagging for v3.3: - **Does the directional asymmetry from v3.1 carry into zero-ablation attribution?** v3.1 Y4 confirmed P→C and C→P have statistically different patch_success structure. If zero-ablation attribution surfaces different critical-neuron sets for P→C vs C→P, that generalizes the asymmetry to neuron-level mechanism. - **What is the relationship between aggregate-L2-rank and zero-ablation-rank?** v3.2 ranked neurons by L2; v3.3 Axis N will rank by ablation-cost. If the two rankings disagree substantially, that's a strong sign the L2-rank metric is misleading for this circuit and future interpretability work should default to ablation-based ranking. These are v3.3 questions; not v3.2's to answer. ## 9. Versioning - **v3.2 (2026-05-12)** — initial pin and negative result. Smoke gate ran with `--top-k 32 --seeds 8 --pair cliff`. Top-32 captured 33.6% of aggregate L2, delivered −0.006 P→C / +0.001 C→P median patch_success. Z1 falsified. Full k-sweep deliberately not run per spec §3.4. v3.3 routes to non-linear attribution methods (Axis N zero-ablation as first move).