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{"type":"item.completed","item":{"id":"item_2","type":"agent_message","text":"```python\nimport numpy as np\nfrom scipy.linalg import svd, eigvals\nfrom threadpoolctl import threadpool_limits\n\ndef cosine(a,b):\n    return np.sum(a*b)/(np.linalg.norm(a)*np.linalg.norm(b)+1e-30)\n\nwith threadpool_limits(limits=2):\n    A=[]; B=[]; KB=[]\n    for l in range(4):\n        g=W[f\"ln1_w.{l}\"].astype(float); b=W[f\"ln1_b.{l}\"].astype(float)\n        for j in range(6):\n            sl=slice(64*j,64*j+64)\n            q=W[f\"W_q.{l}\"][sl].astype(float)\n            k=W[f\"W_k.{l}\"][sl].astype(float)\n            v=W[f\"W_v.{l}\"][sl].astype(float)\n            qg=q*g; kg=k*g; vg=v*g\n            for m in [qg,kg,vg]: m-=m.mean(1,keepdims=True)\n            A.append(qg.T@kg/8)\n            B.append(W[f\"W_o.{l}\"][:,sl].astype(float)@vg)\n            KB.append(kg.T@(q@b)/8)\n    print(\"L0H0 versus powers of L0H3 QK (weight products only)\")\n    C=np.eye(384)\n    for power in range(1,7):\n        C=C@A[3]\n        C/=np.linalg.norm(C)\n        print(power,round(cosine(A[0],C),4),round(cosine(A[0],C.T),4))\n    u,s,vt=svd(A[3],full_matrices=False)\n    Z=np.concatenate([u[:,:24],vt[:24].T],axis=1)\n    z,sz,_=svd(Z,full_matrices=False)\n    for rank in [16,24,32,40]:\n        P=z[:,:rank]\n        C3=P.T@A[3]@P; C0=P.T@A[0]@P\n        print(\"QK subspace rank\",rank,\"H0/H3 captured energies\",\n              np.round([np.linalg.norm(C0)**2/np.linalg.norm(A[0])**2,\n                        np.linalg.norm(C3)**2/np.linalg.norm(A[3])**2],3),\n              \"H0 vs H3^2\",round(cosine(C0,C3@C3),3),\n              \"commutator relative\",round(np.linalg.norm(C0@C3-C3@C0)/\n                  (np.linalg.norm(C0@C3)+np.linalg.norm(C3@C0)),3))\n    print(\"\\nShared L0 low-rank output space\")\n    T=np.concatenate([B[j] for j in [1,2,4,5]],axis=1)\n    U,ss,_=svd(T,full_matrices=False)\n    print(\"singular values\",np.round(ss[:12],3))\n    C=U[:,:2]\n    for i in range(24):\n        a=A[i]; kb=KB[i]\n        print(\"L%dH%d\"%(i//6,i%6),\n              \"Q-side/K-side 2D energy\",\n              np.round([np.linalg.norm(C.T@a)**2/np.linalg.norm(a)**2,\n                        np.linalg.norm(a@C)**2/np.linalg.norm(a)**2],3),\n              \"key-bias fraction\",round(np.linalg.norm(C.T@kb)**2/(np.linalg.norm(kb)**2),3),\n              \"2x2\",np.round(C.T@a@C,3).tolist(),\n              \"key-bias\",np.round(C.T@kb,3))\n    print(\"\\nL0H3 value spectrum\")\n    v=W[\"W_v.0\"][192:256].astype(float)*W[\"ln1_w.0\"]\n    v-=v.mean(1,keepdims=True)\n    u,s,vt=svd(v,full_matrices=False)\n    print(np.round(s,3))\n    for rank in [16,20,24,28,32]:\n        P=vt[:rank].T\n        print(\"Token-candidate subspace rank\",rank,\n              \"L3H3 QK@L0H3 OV trace/norm\",\n              round(np.trace(P.T@A[21]@B[3]@P)/np.linalg.norm(P.T@A[21]@B[3]@P),3))\n```\n"}}
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