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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\nfrom threadpoolctl import threadpool_limits\nthreadpool_limits(limits=2)\nnp.set_printoptions(precision=3,suppress=True,linewidth=160)\n\nA=[]; B=[]; kbias=[]\nfor l in range(4):\n    for j in range(6):\n        sl=slice(64*j,64*(j+1))\n        qr=W[f\"W_q.{l}\"][sl].astype(float)\n        kr=W[f\"W_k.{l}\"][sl].astype(float)\n        vr=W[f\"W_v.{l}\"][sl].astype(float)\n        g=W[f\"ln1_w.{l}\"].astype(float)\n        q=qr*g; k=kr*g; v=vr*g\n        q-=q.mean(axis=1,keepdims=True)\n        k-=k.mean(axis=1,keepdims=True)\n        v-=v.mean(axis=1,keepdims=True)\n        o=W[f\"W_o.{l}\"][:,sl].astype(float)\n        o-=o.mean(axis=0,keepdims=True)\n        A.append(q.T@k/8)\n        B.append(o@v)\n        kbias.append(k.T@(qr@W[f\"ln1_b.{l}\"])/8)\n\nu4,s4,v4=svd(B[4],full_matrices=False,check_finite=False)\nu5,s5,v5=svd(B[5],full_matrices=False,check_finite=False)\nuP,sP,vP=svd(np.concatenate([A[1],A[1].T,A[5],A[5].T],axis=1),\n             full_matrices=False,check_finite=False)\nbases={\n    \"uniform-head-write3\":u4[:,:3],\n    \"uniform-head-read3\":v4[:3].T,\n    \"H5-value-read27\":v5[:27].T,\n    \"H5-value-write27\":u5[:,:27],\n    \"L0-H1H5-QK-shared20\":uP[:,:20],\n}\nprint(\"L0H4 effective OV singular values:\",s4[:12])\nprint(\"Basis pair overlaps, normalized by smaller rank:\")\nnames=list(bases)\nprint(names)\nprint(np.array([[np.linalg.norm(bases[a].T@bases[b])**2/min(bases[a].shape[1],bases[b].shape[1])\n                 for b in names]for a in names]))\n\nfor name,U in bases.items():\n    print(\"\\n\",name,\": QK query-energy/key-energy; bias-vector energy\")\n    for i in range(24):\n        a=A[i]; z=kbias[i]\n        print(\"L%dH%d %.3f %.3f %.3f\"%(i//6,i%6,\n              np.linalg.norm(U.T@a)**2/np.linalg.norm(a)**2,\n              np.linalg.norm(a@U)**2/np.linalg.norm(a)**2,\n              np.linalg.norm(U.T@z)**2/(np.linalg.norm(z)**2+1e-30)))\n\nprint(\"\\nPairwise cosine of bias-derived key coefficients across all heads\")\nZ=np.stack(kbias);Z/=np.linalg.norm(Z,axis=1,keepdims=True)\nfor i in range(24):\n    row=Z@Z[i];row[i]=-2\n    idx=np.argsort(-row)[:4]\n    print(\"L%dH%d\"%(i//6,i%6),\n          [(\"L%dH%d\"%(k//6,k%6),round(float(row[k]),3))for k in idx])\n```\n"}}
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