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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\nfor l in range(4):\n    print(\"\\nLAYER\",l)\n    for name in [\"W_q\",\"W_k\",\"W_v\",\"W_o\",\"W_fc\",\"W_proj\"]:\n        a=W[f\"{name}.{l}\"].astype(float)\n        sv=np.linalg.svd(a,compute_uv=False)\n        print(name,\"sv12\",np.round(sv[:12],3),\n              \"energy ranks 1,5,10,28,64\",np.round([np.sum(sv[:r]**2)/np.sum(sv**2) for r in [1,5,10,28,64]],3))\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        v=W[f\"W_v.{l}\"][s].astype(float)\n        o=W[f\"W_o.{l}\"][:,s].astype(float)\n        e=np.linalg.eigvals((k*g)@(q*g).T/8)\n        e=e[np.argsort(-abs(e))]\n        A=(q*g).T@(k*g)/8\n        keybias=(q@b)@(k*g)/8\n        u,sv,vt=np.linalg.svd(A,full_matrices=False)\n        print(\"L%dH%d\"%(l,j),\"QK eig12\",np.round(e[:12],3),\n              \"keybias_norm=%.3f\"%np.linalg.norm(keybias),\n              \"keybias_topright=%.3f\"%(keybias@vt[0]/(np.linalg.norm(keybias)+1e-12)))\n    print(\"LN1 largest bias coords\", sorted(enumerate(b),key=lambda z:-abs(z[1]))[:8])\n\nprint(\"\\nFIRST-LAYER HEAD QK AND OV COSINES\")\nAs=[];Bs=[]\nfor j in range(6):\n    s=slice(64*j,64*(j+1)); g=W[\"ln1_w.0\"]\n    As.append((W[\"W_q.0\"][s]*g).T@(W[\"W_k.0\"][s]*g)/8)\n    Bs.append(W[\"W_o.0\"][:,s]@(W[\"W_v.0\"][s]*g))\nfor label,mat in [(\"QK\",As),(\"OV\",Bs)]:\n    print(label)\n    print(np.round([[np.sum(a*b)/(np.linalg.norm(a)*np.linalg.norm(b)) for b in mat] for a in mat],3))\n```\n"}}
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