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{"type":"item.completed","item":{"id":"item_2","type":"agent_message","text":"```python\nimport numpy as np\nfrom scipy.linalg import svdvals, eigvals\nfrom threadpoolctl import threadpool_limits\nthreadpool_limits(limits=2)\n\nd = 384\nP = np.eye(d) - np.ones((d,d))/d\nA, B = {}, {}\nfor l in range(4):\n    scale = np.asarray(W[f\"ln1_w.{l}\"],float)\n    for h in range(6):\n        s = slice(64*h,64*(h+1))\n        q,k,v = [np.asarray(W[f\"W_{n}.{l}\"][s],float) for n in [\"q\",\"k\",\"v\"]]\n        o = np.asarray(W[f\"W_o.{l}\"][:,s],float)\n        A[l,h] = P @ (scale[:,None]*(q.T@k)*scale[None,:]) @ P\n        B[l,h] = o @ (v*scale[None,:]) @ P\n\nprint(\"L0 per-head V and O singular values (first 35)\")\nfor h in range(6):\n    s = slice(h*64,(h+1)*64)\n    for name,a in [\n        (\"V\",np.asarray(W[\"W_v.0\"][s],float)),\n        (\"Vscaled\",np.asarray(W[\"W_v.0\"][s],float)*W[\"ln1_w.0\"][None,:]),\n        (\"O\",np.asarray(W[\"W_o.0\"][:,s],float))]:\n        print(h,name,np.round(svdvals(a)[:35],3))\n\nprint(\"\\nSigned key-composition trace: sqrt(d)*tr(A_B B_A)/(||A_B||F ||B_A||F)\")\nprint(\"Columns are L0H0..L0H5. Large positive values are a matching-circuit clue, not an attention measurement.\")\nfor l in range(1,4):\n    for h in range(6):\n        a=A[l,h]\n        vals=[np.sqrt(d)*np.trace(a@B[0,k])/(np.linalg.norm(a)*np.linalg.norm(B[0,k]))\n              for k in range(6)]\n        print(f\"L{l}H{h}\",np.round(vals,3))\n\nprint(\"\\nStrongest signed composition traces over all earlier heads\")\nfor l in range(1,4):\n    for h in range(6):\n        a=A[l,h]\n        vals=[]\n        for m in range(l):\n            for k in range(6):\n                b=B[m,k]\n                z=np.sqrt(d)*np.trace(a@b)/(np.linalg.norm(a)*np.linalg.norm(b))\n                vals.append((z,f\"L{m}H{k}\"))\n        vals.sort(reverse=True)\n        print(f\"L{l}H{h}\",[(n,round(z,3)) for z,n in vals[:4]])\n\nprint(\"\\nL0 QK/V subspace overlap\")\nfor h in range(6):\n    a=A[0,h]\n    vals=[]\n    for k in [1,4,5]:\n        s=slice(64*k,64*(k+1))\n        v=(np.asarray(W[\"W_v.0\"][s],float)*W[\"ln1_w.0\"][None,:])@P\n        _,_,vt=np.linalg.svd(v,full_matrices=False)\n        u=vt[:28].T\n        vals.append((k,round(np.linalg.norm(a@u)**2/np.linalg.norm(a)**2,3),\n                     round(np.linalg.norm(u.T@a)**2/np.linalg.norm(a)**2,3)))\n    print(f\"L0H{h}\",vals)\n\nprint(\"\\nAffine key-prior coefficient norm from ln1_b, relative to bilinear Frobenius norm\")\nfor l in range(4):\n    scale=np.asarray(W[f\"ln1_w.{l}\"],float)\n    bias=np.asarray(W[f\"ln1_b.{l}\"],float)\n    for h in range(6):\n        s=slice(64*h,64*(h+1))\n        q,k=[np.asarray(W[f\"W_{n}.{l}\"][s],float) for n in [\"q\",\"k\"]]\n        c=P@(scale*(k.T@(q@bias)))\n        print(f\"L{l}H{h}\",round(np.linalg.norm(c),3),\n              round(np.linalg.norm(c)/np.linalg.norm(A[l,h]),3))\n```"}}
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