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{"type":"item.completed","item":{"id":"item_2","type":"agent_message","text":"```python\nimport numpy as np\nfrom threadpoolctl import threadpool_limits\nthreadpool_limits(2)\nnp.set_printoptions(precision=3, suppress=True, linewidth=180)\n\nprint(\"DETAILED SINGULAR VALUES\")\nfor l,name in [(0,\"W_q\"),(0,\"W_k\"),(0,\"W_v\"),(0,\"W_fc\"),\n               (0,\"W_proj\"),(1,\"W_fc\"),(3,\"W_proj\"),(3,\"W_fc\")]:\n    a=W[f\"{name}.{l}\"].astype(float)\n    sv=np.linalg.svd(a,compute_uv=False)\n    print(f\"{name}.{l} first 80:\",sv[:80])\n    print(\"at indices 96,128,192,256,320,383:\",sv[[95,127,191,255,319,382]])\n\nprint(\"\\nL0 HEAD Q/K/V SINGULAR VALUES\")\nfor j in range(6):\n    s=slice(64*j,64*j+64)\n    for name in [\"W_q\",\"W_k\",\"W_v\"]:\n        a=W[f\"{name}.0\"][s].astype(float)\n        sv=np.linalg.svd(a,compute_uv=False)\n        print(f\"H{j} {name}:\",sv[:12], \"tail8:\",sv[-8:])\n\nprint(\"\\nL0 SUBSPACE OVERLAPS\")\n_,_,Vv=np.linalg.svd(W[\"W_v.0\"].astype(float),full_matrices=False)\n_,_,Vf=np.linalg.svd(W[\"W_fc.0\"].astype(float),full_matrices=False)\ns=slice(192,256)\nqp=W[\"W_q.0\"][s].astype(float)\nkp=W[\"W_k.0\"][s].astype(float)\n_,_,Vp=np.linalg.svd(np.vstack([qp,kp]),full_matrices=False)\nfor j in range(6):\n    s=slice(64*j,64*j+64)\n    for name in [\"W_q\",\"W_k\",\"W_v\"]:\n        a=W[f\"{name}.0\"][s].astype(float)\n        n=np.linalg.norm(a)**2\n        print(f\"H{j} {name}\",\n              \"energy in V_all top27/top40=\",round(np.linalg.norm(a@Vv[:27].T)**2/n,3),round(np.linalg.norm(a@Vv[:40].T)**2/n,3),\n              \"FC top27/top40=\",round(np.linalg.norm(a@Vf[:27].T)**2/n,3),round(np.linalg.norm(a@Vf[:40].T)**2/n,3),\n              \"H3_QK top40=\",round(np.linalg.norm(a@Vp[:40].T)**2/n,3))\n\nprint(\"\\nRAW QK ROTATION COMPARISON WITH L0H3\")\n# Polar factors are obtained only from trained matrices. No inputs or activations.\nA0=W[\"W_q.0\"][192:256].astype(float).T@W[\"W_k.0\"][192:256].astype(float)/8\nu,s,vt=np.linalg.svd(A0,full_matrices=False)\nU=np.linalg.svd(np.hstack([u[:,:40],vt[:40].T]),full_matrices=False)[0][:,:50]\nbase=U.T@A0@U\nub,sb,vb=np.linalg.svd(base)\nrot=ub@vb\npowers={n:np.linalg.matrix_power(rot,n) for n in range(-8,9)}\nfor l in range(4):\n    for j in range(6):\n        ss=slice(64*j,64*j+64)\n        a=W[f\"W_q.{l}\"][ss].astype(float).T@W[f\"W_k.{l}\"][ss].astype(float)/8\n        ar=U.T@a@U\n        frac=np.linalg.norm(ar)**2/np.linalg.norm(a)**2\n        vals=[(np.sum(ar*p)/(np.linalg.norm(ar)*np.linalg.norm(p)),n) for n,p in powers.items()]\n        vals.sort(reverse=True)\n        print(f\"L{l}H{j} projected_fraction={frac:.3f} polar_correlations=\",\n              [(n,round(c,3)) for c,n in vals[:4]])\n\nprint(\"\\nLAYER-NORM EXTREME COORDINATES\")\nfor l in range(4):\n    for name in [\"ln1_w\",\"ln1_b\",\"ln2_w\",\"ln2_b\"]:\n        a=W[f\"{name}.{l}\"]\n        ii=np.argsort(abs(a-(1 if name.endswith(\"_w\") else 0)))[-8:][::-1]\n        print(f\"{name}.{l}\",[(int(i),round(float(a[i]),4)) for i in ii])\n```\n"}}
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