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{"type":"item.completed","item":{"id":"item_2","type":"agent_message","text":"```python\nimport numpy as np\nfrom scipy.linalg import svd, eig\nfrom threadpoolctl import threadpool_limits\nthreadpool_limits(limits=2)\nnp.set_printoptions(precision=3,suppress=True,linewidth=160)\n\nA=[]\nfor j in range(6):\n    sl=slice(64*j,64*(j+1))\n    A.append(W[\"W_q.0\"][sl].astype(float).T @ W[\"W_k.0\"][sl].astype(float)/8)\nu=svd(np.concatenate([A[1],A[1].T,A[5],A[5].T],axis=1),\n      full_matrices=False,check_finite=False)[0]\n\nfor r in [16,24]:\n    p=u[:,:r]\n    mats=[p.T@a@p for a in A]\n    vals,vecs=eig(mats[5],mats[5].T,check_finite=False)\n    zs=[]\n    for n,lam in enumerate(vals):\n        if not np.isfinite(lam) or np.imag(lam)<=1e-5 or abs(np.log(abs(lam)))>.1:\n            continue\n        z=vecs[:,n]\n        c=np.vdot(z,mats[5]@z)\n        if abs(c)<.02: continue\n        if np.angle(c)<0: z=z.conj()\n        zs.append(z)\n    zs.sort(key=lambda z: np.angle(np.vdot(z,mats[5]@z)))\n    coeff=np.array([[np.vdot(z,m@z) for z in zs]for m in mats])\n    theta=np.angle(coeff[5])\n    print(\"\\nrank\",r,\"reference H5 mode phases:\",theta)\n    for j in range(6):\n        mag=np.abs(coeff[j])\n        phase=np.angle(coeff[j])\n        print(\"H%d magnitudes\"%j,mag)\n        print(\"H%d phases\"%j,phase)\n        ks=np.arange(0,13)\n        scores=np.array([np.average(np.cos(phase-k*theta),weights=mag+1e-20)for k in ks])\n        print(\"phase agreement for multipliers 0..12:\",np.round(scores,3))\n\n# Signed agreement of the strongest induction candidates, across several\n# independently defined first-layer read subspaces and ranks.\ndef products(l,j):\n    sl=slice(j*64,(j+1)*64)\n    g=W[f\"ln1_w.{l}\"].astype(float)\n    q=W[f\"W_q.{l}\"][sl].astype(float)*g\n    k=W[f\"W_k.{l}\"][sl].astype(float)*g\n    v=W[f\"W_v.{l}\"][sl].astype(float)*g\n    q-=q.mean(axis=1,keepdims=True)\n    k-=k.mean(axis=1,keepdims=True)\n    v-=v.mean(axis=1,keepdims=True)\n    o=W[f\"W_o.{l}\"][:,sl].astype(float)\n    o-=o.mean(axis=0,keepdims=True)\n    return q.T@k/8,o@v\npairs=[products(l,j)for l in range(4)for j in range(6)]\nfor source in [1,5]:\n    _,_,vt=svd(pairs[source][1],full_matrices=False,check_finite=False)\n    for rank in [16,24,32]:\n        t=vt[:rank].T\n        print(\"\\nRead basis from L0H%d OV, rank%d\"%(source,rank))\n        for target,earlier in [(13,5),(19,5),(23,5),(19,14),(23,14),(12,5),(18,5)]:\n            c=t.T@pairs[target][0]@pairs[earlier][1]@t\n            print(\"L%dH%d <- L%dH%d: trace/norm %.3f\"%(target//6,target%6,\n                  earlier//6,earlier%6,np.trace(c)/(np.linalg.norm(c)+1e-30)))\n```\n"}}
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