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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=4, suppress=True, linewidth=180)\n\nd=384\nP=np.eye(d)-np.ones((d,d))/d\nA={}; B={}; QB={}; KB={}\nfor l in range(4):\n    g=W[f\"ln1_w.{l}\"].astype(float)\n    b=W[f\"ln1_b.{l}\"].astype(float)\n    for h in range(6):\n        s=slice(64*h,64*(h+1))\n        q,k,v=[W[f\"W_{t}.{l}\"][s].astype(float) for t in [\"q\",\"k\",\"v\"]]\n        o=P@W[f\"W_o.{l}\"][:,s].astype(float)\n        qg,kg,vg=[(m*g)@P for m in [q,k,v]]\n        A[l,h]=qg.T@kg/8\n        B[l,h]=o@vg\n        KB[l,h]=kg.T@(q@b)/8\n        QB[l,h]=qg.T@(k@b)/8\n\nprint(\"L0 OV spectra\")\nfor h in range(6):\n    s=np.linalg.svd(B[0,h],compute_uv=False)\n    print(h,np.round(s[:32],4))\n\nprint(\"\\nL0 OV pairwise cosines\")\nz=np.array([B[0,h].ravel()/np.linalg.norm(B[0,h]) for h in range(6)])\nprint(np.round(z@z.T,3))\n\nbroad=[0,1,4,5]\nub,sb,_=np.linalg.svd(np.concatenate([B[0,h] for h in broad],axis=1),full_matrices=False)\nprint(\"\\nJoint broad-head output spectrum\",np.round(sb[:35],4))\nfor r in [2,4,8,16]:\n    T=ub[:,:r]\n    print(\"Broad-output subspace dimension\",r)\n    for l in range(1,4):\n        print(\"layer\",l,\"Q/K/both energy\",np.round([\n            [np.linalg.norm(T.T@A[l,h])**2/np.linalg.norm(A[l,h])**2,\n             np.linalg.norm(A[l,h]@T)**2/np.linalg.norm(A[l,h])**2,\n             np.linalg.norm(T.T@A[l,h]@T)**2/np.linalg.norm(A[l,h])**2]\n            for h in range(6)],3))\n\nprint(\"\\nKey-bias vector cosines within layers\")\nfor l in range(4):\n    z=np.array([KB[l,h]/np.linalg.norm(KB[l,h]) for h in range(6)])\n    print(l,np.round(z@z.T,3))\n\nprint(\"\\nL0H2 nonzero effective QK eigenvalues, sorted by phase (positive imaginary part)\")\nev=np.linalg.eigvals(A[0,2])\nev=ev[(ev.imag>1e-5)&(abs(ev)>.03)]\nev=ev[np.argsort(np.angle(ev))]\nprint(\"magnitude, phase\",np.round(np.array([abs(ev),np.angle(ev)]).T,4))\n\n# Input directions read by L0H2's value matrix; no activations.\ng=W[\"ln1_w.0\"].astype(float)\nvg=(W[\"W_v.0\"][128:192].astype(float)*g)@P\n_,sv,tv=np.linalg.svd(vg,full_matrices=False)\nprint(\"\\nL0H2 effective V singular values\",np.round(sv,4))\nfor r in [16,24,28,40]:\n    T=tv[:r].T\n    print(\"V-input subspace dimension\",r)\n    for l in range(1,4):\n        out=[]\n        for h in range(6):\n            c=T.T@A[l,h]@B[0,2]@T\n            n=np.linalg.norm(c)\n            ev=np.linalg.eigvalsh((c+c.T)/2)\n            out.append([np.trace(c)/max(n,1e-12),\n                        np.sum(c*c.T)/max(n*n,1e-12),\n                        np.sum(ev[ev>0])/max(np.sum(abs(ev)),1e-12)])\n        print(\"layer\",l,\"composition trace/F, symmetry, positive-symmetric-mass\",np.round(out,3))\n\nprint(\"\\nMLP matrix-product spectra (not applying ReLU)\")\nfor l in range(4):\n    f=(W[f\"W_fc.{l}\"].astype(float)*W[f\"ln2_w.{l}\"])@P\n    o=P@W[f\"W_proj.{l}\"].astype(float)\n    m=o@f\n    s=np.linalg.svd(m,compute_uv=False)\n    print(l,\"norm\",round(np.linalg.norm(m),3),\"trace\",round(np.trace(m),3),\n          \"topSV\",np.round(s[:35],3))\n```"}}
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