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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\nprint(\"Last MLP output singular values:\")\nfor l in [0,3]:\n    sv=np.linalg.svd(W[f\"W_proj.{l}\"].astype(float),compute_uv=False)\n    print(\"L\",l,np.round(sv[:48],4))\n\nprint(\"\\nL0 head singular-vector coordinate structure\")\nAs=[];Bs=[]\ng=W[\"ln1_w.0\"].astype(float)\nfor j in range(6):\n    s=slice(64*j,64*(j+1))\n    q=W[\"W_q.0\"][s].astype(float); k=W[\"W_k.0\"][s].astype(float)\n    A=(q*g).T@(k*g)/8\n    B=W[\"W_o.0\"][:,s].astype(float)@(W[\"W_v.0\"][s].astype(float)*g)\n    As.append(A); Bs.append(B)\n    ua,sa,va=np.linalg.svd(A,full_matrices=False)\n    ub,sb,vb=np.linalg.svd(B,full_matrices=False)\n    print(\"L0H%d\"%j)\n    for label,z in [(\"QK left1\",ua[:,0]),(\"QK right1\",va[0]),(\"OV left1\",ub[:,0]),(\"OV right1\",vb[0]),(\"OV left2\",ub[:,1])]:\n        ix=np.argsort(-abs(z))[:8]\n        print(label,list(zip(ix.tolist(),np.round(z[ix],3).tolist())))\n    print(\"unscaled QK sv\",np.round(np.linalg.svd(q.T@k/8,compute_uv=False)[:12],3))\n\nprint(\"\\nKey-bias similarities within layers (weight-only affine coefficients)\")\nfor l in range(1,4):\n    g=W[f\"ln1_w.{l}\"].astype(float); b=W[f\"ln1_b.{l}\"].astype(float)\n    R=[]\n    for j in range(6):\n        s=slice(j*64,(j+1)*64)\n        r=(W[f\"W_q.{l}\"][s]@b)@(W[f\"W_k.{l}\"][s]*g)/8\n        R.append(r/np.linalg.norm(r))\n    print(\"L\",l,np.round(np.array(R)@np.array(R).T,2))\n    for j,r in enumerate(R):\n        ix=np.argsort(-abs(r))[:6]\n        print(\"H\",j,\"top coords\",list(zip(ix.tolist(),np.round(r[ix],3).tolist())),\n              \"OV0 output align\",np.round([r@np.linalg.svd(B,full_matrices=False)[0][:,0] for B in Bs],3))\n```\n"}}
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