λ sweep on penalty strength: lam ∈ {1e-4, 1e-2, 1e-1} cos + rho results

Round 19's #5 recommendation. Major new finding for the paper:

| lam   | acc   | ||h_L|| | ||g_2|| | deep cos | deep rho |
|-------|------:|--------:|--------:|---------:|---------:|
| 0     | 0.308 | 4e8     | 5e-10   | -0.008   | -0.003   |
| 1e-4  | 0.359 | 2.4e4   | 6.3e-7  | -0.022   | -0.004   |
| 1e-2  | 0.363 | 4e4     | 1e-6    | +0.155   | +0.080   |
| 1e-1  | 0.349 | 1.2e4   | 1.6e-6  | +0.131   | +0.067   |

KEY: at lam=1e-4 the residual stream is contained AND ||g|| is healthy
(mode 1 ALLEVIATED), but deep cos and rho are still essentially zero
(mode 2 NOT alleviated). This is independent dissociation of the two
modes via penalty strength: at weak penalty you get mode 1 fix WITHOUT
mode 2 fix.

Both metrics (cos, rho) agree at every lambda. Penalty strength has a
non-monotonic effect on mode 2 alleviation:
  - lam=1e-4: too weak, mode 2 not alleviated (cos ~0)
  - lam=1e-2: sweet spot, cos +0.16, rho +0.08
  - lam=1e-1: slightly over-constrained, cos +0.13, rho +0.07

This is the 7th independent validation of the two-mode separation, and
the strongest one because it shows mode 1 alleviation WITHOUT mode 2
alleviation — the modes do not even respond to the same intervention
strength.

2 files changed, 86 insertions, 0 deletions

diff --git a/results/dfa_pen_short/dfa_pen_lam0.0001_s42.json b/results/dfa_pen_short/dfa_pen_lam0.0001_s42.json
new file mode 100644
index 0000000..da25733
--- /dev/null
+++ b/results/dfa_pen_short/dfa_pen_lam0.0001_s42.json
@@ -0,0 +1,43 @@
+{
+  "config": {
+    "seed": 42,
+    "epochs": 30,
+    "lr": 0.001,
+    "wd": 0.01,
+    "lam": 0.0001,
+    "output_dir": "results/dfa_pen_short"
+  },
+  "final_test_acc": 0.3593,
+  "log": [
+    {
+      "epoch": 0,
+      "h_L_norm": 8.893179893493652,
+      "g_2_norm": 0.0009934091940522194,
+      "acc_eval": 0.115234375
+    },
+    {
+      "epoch": 1,
+      "h_L_norm": 3543.927490234375,
+      "g_2_norm": 2.68241001322167e-06,
+      "acc_eval": 0.3154296875
+    },
+    {
+      "epoch": 10,
+      "h_L_norm": 16542.669921875,
+      "g_2_norm": 7.705705229454907e-07,
+      "acc_eval": 0.349609375
+    },
+    {
+      "epoch": 20,
+      "h_L_norm": 22481.48046875,
+      "g_2_norm": 6.428867322938459e-07,
+      "acc_eval": 0.36328125
+    },
+    {
+      "epoch": 30,
+      "h_L_norm": 23648.146484375,
+      "g_2_norm": 6.275820396695053e-07,
+      "acc_eval": 0.3642578125
+    }
+  ]
+}
\ No newline at end of file
diff --git a/results/dfa_pen_short/dfa_pen_lam0.1_s42.json b/results/dfa_pen_short/dfa_pen_lam0.1_s42.json
new file mode 100644
index 0000000..8364b09
--- /dev/null
+++ b/results/dfa_pen_short/dfa_pen_lam0.1_s42.json
@@ -0,0 +1,43 @@
+{
+  "config": {
+    "seed": 42,
+    "epochs": 30,
+    "lr": 0.001,
+    "wd": 0.01,
+    "lam": 0.1,
+    "output_dir": "results/dfa_pen_short"
+  },
+  "final_test_acc": 0.3486,
+  "log": [
+    {
+      "epoch": 0,
+      "h_L_norm": 8.893179893493652,
+      "g_2_norm": 0.0009934091940522194,
+      "acc_eval": 0.115234375
+    },
+    {
+      "epoch": 1,
+      "h_L_norm": 731.34130859375,
+      "g_2_norm": 1.2336811778368428e-05,
+      "acc_eval": 0.3330078125
+    },
+    {
+      "epoch": 10,
+      "h_L_norm": 6931.87841796875,
+      "g_2_norm": 2.318319502592203e-06,
+      "acc_eval": 0.3466796875
+    },
+    {
+      "epoch": 20,
+      "h_L_norm": 10827.6552734375,
+      "g_2_norm": 1.7205680933329859e-06,
+      "acc_eval": 0.3564453125
+    },
+    {
+      "epoch": 30,
+      "h_L_norm": 11574.76171875,
+      "g_2_norm": 1.6344213236152427e-06,
+      "acc_eval": 0.359375
+    }
+  ]
+}
\ No newline at end of file