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{"type":"item.completed","item":{"id":"item_1","type":"agent_message","text":"```python\nimport numpy as np\nfrom threadpoolctl import threadpool_limits\nthreadpool_limits(4)\n\ng0=W[\"ln1_w.0\"].astype(float)\nv=W[\"W_v.0\"][192:256].astype(float)*g0\no=W[\"W_o.0\"][:,192:256].astype(float)\nB=o@v\nT=np.linalg.svd(v,full_matrices=False)[2][:20].T\ncoords=np.array([21,39,58,99,184])\nprint(\"Counter-coordinate blocks and induction-path diagnostics\")\nfor l in range(1,4):\n    g=W[f\"ln1_w.{l}\"].astype(float)\n    b=W[f\"ln1_b.{l}\"].astype(float)\n    for j in range(6):\n        s=slice(64*j,64*(j+1))\n        q=W[f\"W_q.{l}\"][s].astype(float)\n        k=W[f\"W_k.{l}\"][s].astype(float)\n        A=(q*g).T@(k*g)/8\n        r=(q@b)@(k*g)/8\n        C=T.T@A@B@T\n        eig=np.linalg.eigvals(C)\n        sym=np.linalg.eigvalsh((C+C.T)/2)\n        print(\"L%dH%d\"%(l,j),\n              \"A21,21=%.3f col21energy=%.3f row21energy=%.3f r21=%.3f\"%\n              (A[21,21],np.sum(A[:,21]**2)/np.sum(A*A),np.sum(A[21]**2)/np.sum(A*A),r[21]),\n              \"token-path tr/norm=%.3f positive_sym=%d/20\"%\n              (np.trace(C)/(np.linalg.norm(C)+1e-12),sum(sym>0)),\n              \"sym_extrema\",np.round([sym[0],sym[-1]],3))\n        if j in [0,3,4]:\n            print(\"A block rows/cols\",coords.tolist())\n            print(np.round(A[np.ix_(coords,coords)],3))\n\nprint(\"\\nL0 QK/OV effective ranks\")\nfor j in range(6):\n    s=slice(64*j,64*(j+1))\n    A=(W[\"W_q.0\"][s]*g0).T@(W[\"W_k.0\"][s]*g0)/8\n    B=W[\"W_o.0\"][:,s]@(W[\"W_v.0\"][s]*g0)\n    for name,M in [(\"QK\",A),(\"OV\",B)]:\n        sv=np.linalg.svd(M,compute_uv=False)\n        energy=np.cumsum(sv**2)/np.sum(sv**2)\n        print(\"L0H%d %s\"%(j,name),\"rank90/95/99\",np.searchsorted(energy,[.90,.95,.99])+1)\n```\n"}}
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