fidelity factorial arms (randk / noises0 / hidden-capacity) + pre-registration item 15

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

scripts/loop_common.py

@@ -180,6 +180,17 @@ class ParcaeAdapter(RecurrentAdapter):
             return self.A_diag().max().item()
 
 
+class NoisyMergeAdapter(MergeAdapter):
+    """MergeAdapter with noise s0 (factorial cell: isolates the initial
+    state; everything else identical to the standard merge)."""
+
+    def init_state(self, e):
+        n = torch.randn_like(e.float())
+        n = n * (e.float().norm(dim=-1, keepdim=True)
+                 / (n.norm(dim=-1, keepdim=True) + 1e-6))
+        return n.to(e.dtype)
+
+
 class TiedAlphaAdapter(nn.Module):
     """Merge with LEARNED per-dim constant alpha, B tied to (1-a):
         x = (1-a)*e + a*s_hat + MLP([e;s_hat]),  a = sigmoid(a_hat)