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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,eigh\nfrom sklearn.cluster import KMeans\nfrom threadpoolctl import threadpool_limits\n\ndef unitrows(x):\n    return x/(np.linalg.norm(x,axis=1,keepdims=True)+1e-12)\n\nwith threadpool_limits(limits=2):\n    g=W[\"ln1_w.0\"].astype(float)\n    q=W[\"W_q.0\"][192:256].astype(float)*g\n    k=W[\"W_k.0\"][192:256].astype(float)*g\n    v=W[\"W_v.0\"][192:256].astype(float)*g\n    for m in [q,k,v]:m-=m.mean(1,keepdims=True)\n    B=W[\"W_o.0\"][:,192:256].astype(float)@v\n    u,s,vt=svd(B,full_matrices=False)\n    uq,sq,vq=svd(q.T@k,full_matrices=False)\n    f=W[\"W_fc.0\"].astype(float)*W[\"ln2_w.0\"]\n    f-=f.mean(1,keepdims=True)\n    for mode in [\"plain\",\"remove_output\",\"remove_output_and_qk\"]:\n        candidates=vt[:28].T.copy()\n        if mode!=\"plain\":\n            nuisance=u[:,:28]\n            if mode==\"remove_output_and_qk\":\n                nuisance=np.concatenate([nuisance,uq[:,:24],vq[:24].T,\n                                          np.ones((384,1))/np.sqrt(384)],axis=1)\n            un,sn,_=svd(nuisance,full_matrices=False)\n            N=un[:,sn>1e-8]\n            candidates-=N@(N.T@candidates)\n        X,_,_=svd(candidates,full_matrices=False)\n        C0=f@X; C1=f@B@X\n        C0-=C0.mean(0); C1-=C1.mean(0)\n        C0/=np.linalg.norm(C0); C1/=np.linalg.norm(C1)\n        ev,U=eigh((C0.T@C0+C1.T@C1)/2)\n        whitening=(U/np.sqrt(np.maximum(ev,ev[-1]*.015)))@U.T\n        Z=np.concatenate([unitrows(C0@whitening),unitrows(C1@whitening)])\n        km=KMeans(n_clusters=24,n_init=15,random_state=42).fit(Z)\n        lab=km.labels_\n        n0=np.bincount(lab[:1536],minlength=24)\n        n1=np.bincount(lab[1536:],minlength=24)\n        pairs=np.zeros((24,24))\n        for i in range(1536):pairs[lab[i],lab[i+1536]]+=1\n        pairs=(pairs+pairs.T)/2\n        deg=pairs.sum(1)\n        norm=pairs/np.sqrt(deg[:,None]*deg[None,:]+1e-12)\n        ev,evec=eigh(norm)\n        origin=(n0-n1)/(n0+n1+1e-12)\n        graphaxis=evec[:,0]/np.sqrt(deg+1e-12)\n        print(\"\\nMode\",mode)\n        print(\"bottom graph eigenvalues\",np.round(ev[:5],3))\n        print(\"origin imbalance RMS\",round(float(np.sqrt(np.mean(origin**2))),3),\n              \"correlation of bipartition with sample origin\",\n              round(float(np.corrcoef(origin,graphaxis)[0,1]),3))\n        print(\"cluster: current-count, composed-count, graph-axis sign\")\n        print([(i,int(n0[i]),int(n1[i]),int(np.sign(graphaxis[i]))) for i in range(24)])\n```\n"}}
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