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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 sklearn.metrics import silhouette_score\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    ui,si,vi=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\n    # All rows below are weight directions or linear products of weights.\n    # No inputs, layer execution, activation functions, or attention distributions.\n    nuisance=np.concatenate([ui[:,:28],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=vi[:28].T\n    candidates-=N@(N.T@candidates)\n    X,_,_=svd(candidates,full_matrices=False)\n    X=X[:,:28]\n    C0=f@X\n    C1=f@B@X\n    C0-=C0.mean(0); C1-=C1.mean(0)\n    C0/=np.linalg.norm(C0)\n    C1/=np.linalg.norm(C1)\n    covariance=(C0.T@C0+C1.T@C1)/2\n    ev,U=eigh(covariance)\n    whitening=(U/np.sqrt(np.maximum(ev,ev[-1]*.015)))@U.T\n    D0=C0@whitening\n    D1=C1@whitening\n    cross=(D0.T@D1+D1.T@D0)/2\n    print(\"Symmetric, whitened FC/FC-OV direction covariance eigenvalues:\")\n    print(np.round(eigh(cross,eigvals_only=True),3))\n\n    Z=np.concatenate([unitrows(D0),unitrows(D1)])\n    print(\"\\nShared clustering of current/OV-composed FC weight directions\")\n    for nc in [20,24,28,32]:\n        km=KMeans(n_clusters=nc,n_init=10,random_state=42).fit(Z)\n        labels=km.labels_\n        cent=unitrows(km.cluster_centers_)\n        confidence=np.sum(Z*cent[labels],axis=1)\n        pairs=np.zeros((nc,nc))\n        for i in range(1536):\n            pairs[labels[i],labels[i+1536]]+=confidence[i]*confidence[i+1536]\n        pairs=(pairs+pairs.T)/2\n        degree=pairs.sum(1)\n        norm=pairs/np.sqrt(degree[:,None]*degree[None,:]+1e-12)\n        eig=eigh(norm,eigvals_only=True)\n        print(\"k\",nc,\"silhouette\",\n              round(silhouette_score(Z,labels,sample_size=1500,random_state=42),3),\n              \"confidence median\",round(float(np.median(confidence)),3),\n              \"pair-graph bottom eigenvalues\",np.round(eig[:5],3),\n              \"cluster counts\",sorted(np.bincount(labels).tolist(),reverse=True))\n\n    print(\"\\nFinal MLP output-weight clustering\")\n    p=W[\"W_proj.3\"].astype(float).T\n    _,s,vt=svd(p,full_matrices=False)\n    Z=unitrows(p@vt[:28].T)\n    for nc in [20,24,28,32]:\n        km=KMeans(n_clusters=nc,n_init=10,random_state=42).fit(Z)\n        print(\"k\",nc,\"silhouette\",\n              round(silhouette_score(Z,km.labels_,sample_size=1500,random_state=42),3),\n              \"counts\",sorted(np.bincount(km.labels_).tolist(),reverse=True))\n```\n"}}
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