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{"type":"item.completed","item":{"id":"item_1","type":"agent_message","text":"```python\nimport numpy as np\nfrom scipy.linalg import svd\nfrom threadpoolctl import threadpool_limits\n\nwith threadpool_limits(limits=4):\n    A, B = {}, {}\n    for l in range(4):\n        g = W[f\"ln1_w.{l}\"].astype(float)\n        for j in range(6):\n            sl = slice(j*64,(j+1)*64)\n            q = W[f\"W_q.{l}\"][sl].astype(float)*g\n            k = W[f\"W_k.{l}\"][sl].astype(float)*g\n            v = W[f\"W_v.{l}\"][sl].astype(float)*g\n            q -= q.mean(1,keepdims=True)\n            k -= k.mean(1,keepdims=True)\n            v -= v.mean(1,keepdims=True)\n            A[l,j] = q.T@k/8\n            B[l,j] = W[f\"W_o.{l}\"][:,sl].astype(float)@v\n    print(\"Key-path matching: tr(QK_l @ OV_0)/(||QK_l||F ||OV_0||F)\")\n    for l in range(1,4):\n        for j in range(6):\n            a=A[l,j]\n            print(f\"L{l}H{j}\",np.round([np.trace(a@B[0,h])/\n                   (np.linalg.norm(a)*np.linalg.norm(B[0,h])) for h in range(6)],4))\n    print(\"\\nLargest matching compositions across all preceding heads:\")\n    for l in range(1,4):\n        for j in range(6):\n            a=A[l,j]\n            scores=[]\n            for m in range(l):\n                for h in range(6):\n                    b=B[m,h]\n                    z=np.trace(a@b)/(np.linalg.norm(a)*np.linalg.norm(b))\n                    scores.append((z,f\"L{m}H{h}\"))\n            print(f\"L{l}H{j}\",[(h,round(z,4)) for z,h in sorted(scores,reverse=True)[:4]])\n\n    print(\"\\nL0H3 OV spectrum after LN scale/centering\")\n    u,s,vt=svd(B[0,3],full_matrices=False)\n    print(np.round(s[:64],4))\n    print(\"L0H0 OV spectrum\")\n    print(np.round(svd(B[0,0],compute_uv=False)[:48],4))\n\n    print(\"\\nMLP0 input-weight Gram coupling between current-token and H3-written subspaces\")\n    f=W[\"W_fc.0\"].astype(float)*W[\"ln2_w.0\"].astype(float)\n    f-=f.mean(1,keepdims=True)\n    gram=f.T@f\n    for r in (12,16,20,24,28,32):\n        basis=vt[:r].T\n        t=basis.T@gram@B[0,3]@basis\n        z=np.linalg.eigvals(t)\n        z=z[np.argsort(abs(z))[::-1]][:10]\n        print(\"rank\",r,\"eigs\",np.round(z,3))\n\n    print(\"\\nLater-head QK on H3's read-to-write circuit (r=24)\")\n    basis=vt[:24].T\n    for l in range(1,4):\n        for j in range(6):\n            t=basis.T@A[l,j]@B[0,3]@basis\n            sy=(t+t.T)/2\n            ev=np.linalg.eigvalsh(sy)\n            print(f\"L{l}H{j}\",np.round([\n                  np.linalg.norm(t),np.trace(t),\n                  np.linalg.norm(sy)**2/(np.linalg.norm(t)**2+1e-30),\n                  ev[-1],ev[0]],4))\n```\n"}}
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