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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\ng0=W[\"ln1_w.0\"].astype(float)\nq=W[\"W_q.0\"][192:256].astype(float)\nk=W[\"W_k.0\"][192:256].astype(float)\nv=W[\"W_v.0\"][192:256].astype(float)\no=W[\"W_o.0\"][:,192:256].astype(float)\n_,_,qp=np.linalg.svd(q*g0,full_matrices=False)\n_,_,vp=np.linalg.svd(v*g0,full_matrices=False)\nP=qp[:20].T\nT=vp[:20].T\nB=o@(v*g0)\nU=np.linalg.svd(B,full_matrices=False)[0][:,:20]\nprint(\"QK energy captured by candidate position, token and previous-token subspaces\")\nprint(\"head | P-query P-key | T-query T-key | U-query U-key\")\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        A=(W[f\"W_q.{l}\"][s]*g).T@(W[f\"W_k.{l}\"][s]*g)/8\n        den=np.linalg.norm(A)**2\n        vals=[]\n        for Z in [P,T,U]:\n            vals += [np.linalg.norm(Z.T@A)**2/den,np.linalg.norm(A@Z)**2/den]\n        print(\"L%dH%d\"%(l,j),np.round(vals,3))\n\nprint(\"\\nL0H3 raw QK nonzero eigenvalues, descending magnitude\")\ne=np.linalg.eigvals(k@q.T/8)\ne=e[np.argsort(-abs(e))]\nprint(np.round(e[:40],4))\nprint(\"positive-imag phases\",np.round(np.sort(np.angle(e[(e.imag>0.01)&(abs(e)>.2)])),4))\n\nF=W[\"W_fc.0\"].astype(float)*W[\"ln2_w.0\"]\nprint(\"\\nMLP0 current/previous weight coupling (no activations)\")\nfor r in [16,20,24,28]:\n    T=vp[:r].T\n    X=F@T\n    Y=F@B@T\n    X-=X.mean(0)\n    Y-=Y.mean(0)\n    C=X.T@Y\n    ss=np.linalg.svd(C,compute_uv=False)\n    ev=np.linalg.eigvalsh((C+C.T)/2)\n    print(\"r\",r,\"sv\",np.round(ss[:10],2),\n          \"sym eig extremes\",np.round(np.r_[ev[:5],ev[-5:]],2),\n          \"trace/norm\",round(np.trace(C)/np.linalg.norm(C),3))\n```\n"}}
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