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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\nAs={};Bs={}\nfor l in range(4):\n    g=W[f\"ln1_w.{l}\"].astype(float)\n    for j in range(6):\n        s=slice(64*j,64*(j+1))\n        As[l,j]=(W[f\"W_q.{l}\"][s]*g).T@(W[f\"W_k.{l}\"][s]*g)/8\n        Bs[l,j]=W[f\"W_o.{l}\"][:,s].astype(float)@(W[f\"W_v.{l}\"][s]*g)\nprint(\"Trace(A_lh B_0j)/||A_lh B_0j||, for j=0..5 (positive matching composition)\")\nfor l in range(1,4):\n    for h in range(6):\n        vals=[]\n        for j in range(6):\n            C=As[l,h]@Bs[0,j]\n            vals.append(np.trace(C)/np.linalg.norm(C))\n        print(\"L%dH%d\"%(l,h),np.round(vals,3))\n\nprint(\"\\nStrongest matching compositions over ALL preceding heads\")\nfor l in range(1,4):\n    for h in range(6):\n        vals=[]\n        for p in range(l):\n            for j in range(6):\n                C=As[l,h]@Bs[p,j]\n                vals.append((np.trace(C)/np.linalg.norm(C),p,j))\n        print(\"L%dH%d\"%(l,h),[(round(x,3),p,j) for x,p,j in sorted(vals,reverse=True)[:4]])\n\nprint(\"\\nL0H3 Q,K,V singular spectra\")\nfor name in [\"W_q\",\"W_k\",\"W_v\"]:\n    a=W[f\"{name}.0\"][192:256].astype(float)\n    print(name,np.round(np.linalg.svd(a,compute_uv=False),3))\nprint(\"\\nMLP0 input spectrum\")\na=W[\"W_fc.0\"].astype(float)*W[\"ln2_w.0\"]\nprint(np.round(np.linalg.svd(a,compute_uv=False)[:100],3))\n\nprint(\"\\nPositional-like QK L0H3 versus value subspaces: squared overlap\")\n_,_,qv=np.linalg.svd(W[\"W_q.0\"][192:256],full_matrices=False)\n_,_,kv=np.linalg.svd(W[\"W_k.0\"][192:256],full_matrices=False)\n_,_,vv=np.linalg.svd(W[\"W_v.0\"][192:256],full_matrices=False)\nfor r in [16,24,28,32,40]:\n    print(r, \"Q/K\",np.linalg.norm(qv[:r]@kv[:r].T)**2/r,\n          \"Q/V\",np.linalg.norm(qv[:r]@vv[:r].T)**2/r,\n          \"K/V\",np.linalg.norm(kv[:r]@vv[:r].T)**2/r)\n```\n"}}
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