Add Vast multi-seed findings for action-symmetry cycle 2

experiments/mess3_reward_state_action_symmetry_cycle_2/battery/findings.md

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+# Cycle 2 battery — Vast multi-seed findings
+
+Five seeded full-battery runs (`seeds 42–46`) on Vast RTX 4090 boxes
+(`delay=0`, `700k` env steps, experiment SHA `e0c9ac5`, harness
+`fcccfa9`). Flash/RunPod results from the prior attempt were abandoned.
+
+Compact results live on the `results` branch under
+`experiments/mess3_reward_state_action_symmetry_cycle_2/battery/results/mess3-as-c2-seed{42..46}-*/`.
+Seed 42 also completed a full B2 durability upload; seeds 43–46 had compact
+results recovered before slow CN egress finished hashing/uploading checkpoints.
+
+## Final probe MSE (all seeds)
+
+| seed | variant_1 | variant_2 | variant_3 |
+|-----:|----------:|----------:|----------:|
+| 42 | 0.002860 | 0.005516 | 0.000648 |
+| 43 | 0.003313 | 0.004761 | 0.000662 |
+| 44 | 0.000731 | 0.004546 | 0.000437 |
+| 45 | 0.002858 | 0.004386 | 0.000861 |
+| 46 | 0.003018 | 0.005538 | 0.003780 |
+| **mean±std** | **0.00256±0.00104** | **0.00495±0.00054** | **0.00128±0.00141** |
+
+## Filtered comparison (non-collapsed / non-outlier runs)
+
+Keep policies that did not hard-collapse to a single action (plus all v1):
+**v1 all seeds**, **v2 seed 45 only**, **v3 seeds 42–45**.
+
+| arm | n | mean final MSE | range |
+|-----|--:|---------------:|------|
+| v3 (42–45) | 4 | **0.00065 ± 0.00017** | 0.00044–0.00086 |
+| v1 (all) | 5 | **0.00256 ± 0.00104** | 0.00073–0.00331 |
+| v2 (45) | 1 | **0.00439** | — |
+
+Roughly: **v3 ≈ 4× better than v1**, and **v1 ≈ 1.7× better than mixed v2**.
+
+## Final-checkpoint greedy action mix
+
+`greedy_action_fractions` = `[noop, pos, neg]` from final probes:
+
+| variant | typical mix | notes |
+|---------|-------------|-------|
+| 1 | ~0 / 100 / 0 | always hard-argmax **positive** (5/5) |
+| 2 | ~6 / 94 / 0 | almost always **positive**; seed 45 ~27/73/0 |
+| 3 | ~21 / 42 / 38 | mixed ~26/37/37 on seeds 42–45; seed 46 ~0/61/39 |
+
+So v1/v2 mostly collapse to “always positive”; only v3 keeps a real action mix
+(on the retained seeds). Oracle policies differ by variant
+(`v1: +++`, `v2: ++noop`, `v3: +−noop`).
+
+## Takeaways
+
+1. On the filtered set, **variant 3 remains clearly best** for belief MSE.
+2. **Variant 2 is worst**, and when it does not fully collapse (seed 45) MSE is
+   still ~0.0044.
+3. **Variant 1** sits in between and is always action-collapsed to positive.
+4. Ranking on retained runs: **3 ≪ 1 < 2**.
+
+See `multi_seed_summary.json` for machine-readable aggregates and run IDs.

experiments/mess3_reward_state_action_symmetry_cycle_2/battery/multi_seed_summary.json

@@ -0,0 +1,172 @@
+{
+  "study": "mess3_reward_state_action_symmetry_cycle_2",
+  "provider": "vast",
+  "seeds": [
+    42,
+    43,
+    44,
+    45,
+    46
+  ],
+  "run_ids": {
+    "42": "mess3-as-c2-seed42-20260729T002732Z",
+    "43": "mess3-as-c2-seed43-20260729T002921Z",
+    "44": "mess3-as-c2-seed44-20260729T004248Z",
+    "45": "mess3-as-c2-seed45-20260729T005231Z",
+    "46": "mess3-as-c2-seed46-20260729T010051Z"
+  },
+  "experiment_ref": "e0c9ac503cad2cbb65a3f40865f8369f4acc8419",
+  "library_ref": "fcccfa94a3a30bc24d53cf7eca76d3d1c82f9e4f",
+  "note": "Compact results recovered to results branch. Seed42 also completed B2 durability upload; seeds43-46 B2 uploads aborted after compact recovery due to slow CN egress.",
+  "per_seed": [
+    {
+      "seed": 42,
+      "run_id": "mess3-as-c2-seed42-20260729T002732Z",
+      "variant_1_mse": 0.002860448046062251,
+      "variant_1_fine_mse_ratio": 12.858605450944093,
+      "variant_2_mse": 0.005515727495577958,
+      "variant_2_fine_mse_ratio": 12.240160060105984,
+      "variant_3_mse": 0.000647866496178273,
+      "variant_3_fine_mse_ratio": 1.5147507618478806
+    },
+    {
+      "seed": 43,
+      "run_id": "mess3-as-c2-seed43-20260729T002921Z",
+      "variant_1_mse": 0.0033132448592615533,
+      "variant_1_fine_mse_ratio": 14.530551281067257,
+      "variant_2_mse": 0.004760574112606016,
+      "variant_2_fine_mse_ratio": 10.255646104866631,
+      "variant_3_mse": 0.0006618247894507844,
+      "variant_3_fine_mse_ratio": 1.5457587853513888
+    },
+    {
+      "seed": 44,
+      "run_id": "mess3-as-c2-seed44-20260729T004248Z",
+      "variant_1_mse": 0.000730985640257047,
+      "variant_1_fine_mse_ratio": 3.2750994597996663,
+      "variant_2_mse": 0.004546089070409274,
+      "variant_2_fine_mse_ratio": 9.876359929171711,
+      "variant_3_mse": 0.0004370410097976952,
+      "variant_3_fine_mse_ratio": 1.0446271038613808
+    },
+    {
+      "seed": 45,
+      "run_id": "mess3-as-c2-seed45-20260729T005231Z",
+      "variant_1_mse": 0.0028582732543088658,
+      "variant_1_fine_mse_ratio": 12.823862347161601,
+      "variant_2_mse": 0.0043861679756017615,
+      "variant_2_fine_mse_ratio": 15.466828138256021,
+      "variant_3_mse": 0.0008611550886762781,
+      "variant_3_fine_mse_ratio": 2.056207350525793
+    },
+    {
+      "seed": 46,
+      "run_id": "mess3-as-c2-seed46-20260729T010051Z",
+      "variant_1_mse": 0.0030175494619106465,
+      "variant_1_fine_mse_ratio": 13.981054994024134,
+      "variant_2_mse": 0.00553842590738169,
+      "variant_2_fine_mse_ratio": 12.045445835596635,
+      "variant_3_mse": 0.0037798704606170786,
+      "variant_3_fine_mse_ratio": 6.659647097932064
+    }
+  ],
+  "aggregate": {
+    "variant_1": {
+      "mean_final_mse": 0.002556100252360073,
+      "stdev_final_mse": 0.0010369646544970753,
+      "min_final_mse": 0.000730985640257047,
+      "max_final_mse": 0.0033132448592615533,
+      "n": 5
+    },
+    "variant_2": {
+      "mean_final_mse": 0.00494939691231534,
+      "stdev_final_mse": 0.0005438804066042359,
+      "min_final_mse": 0.0043861679756017615,
+      "max_final_mse": 0.00553842590738169,
+      "n": 5
+    },
+    "variant_3": {
+      "mean_final_mse": 0.001277551568944022,
+      "stdev_final_mse": 0.0014068641212186086,
+      "min_final_mse": 0.0004370410097976952,
+      "max_final_mse": 0.0037798704606170786,
+      "n": 5
+    }
+  },
+  "filtered_selection": {
+    "variant_1_seeds": [
+      42,
+      43,
+      44,
+      45,
+      46
+    ],
+    "variant_2_seeds": [
+      45
+    ],
+    "variant_3_seeds": [
+      42,
+      43,
+      44,
+      45
+    ],
+    "rationale": "Retain all v1; v2 only non-collapsed seed 45; v3 drop outlier seed 46"
+  },
+  "filtered_aggregate": {
+    "variant_1": {
+      "mean_final_mse": 0.002556100252360073,
+      "stdev_final_mse": 0.0010369646544970753,
+      "min_final_mse": 0.000730985640257047,
+      "max_final_mse": 0.0033132448592615533,
+      "n": 5,
+      "values": [
+        0.002860448046062251,
+        0.0033132448592615533,
+        0.000730985640257047,
+        0.0028582732543088658,
+        0.0030175494619106465
+      ]
+    },
+    "variant_2": {
+      "mean_final_mse": 0.0043861679756017615,
+      "stdev_final_mse": 0.0,
+      "min_final_mse": 0.0043861679756017615,
+      "max_final_mse": 0.0043861679756017615,
+      "n": 1,
+      "values": [
+        0.0043861679756017615
+      ]
+    },
+    "variant_3": {
+      "mean_final_mse": 0.0006519718460257577,
+      "stdev_final_mse": 0.00017326937386526962,
+      "min_final_mse": 0.0004370410097976952,
+      "max_final_mse": 0.0008611550886762781,
+      "n": 4,
+      "values": [
+        0.000647866496178273,
+        0.0006618247894507844,
+        0.0004370410097976952,
+        0.0008611550886762781
+      ]
+    }
+  },
+  "final_greedy_action_fractions": {
+    "note": "[noop, pos, neg] from final_probe",
+    "variant_1_mean": [
+      0.0,
+      1.0,
+      0.0
+    ],
+    "variant_2_seed45": [
+      0.275,
+      0.725,
+      0.0
+    ],
+    "variant_3_seeds_42_45_approx": [
+      0.26,
+      0.37,
+      0.37
+    ]
+  }
+}