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{"type":"item.completed","item":{"id":"item_1","type":"agent_message","text":"```python\nimport numpy as np\nimport scipy.linalg as la\nfrom sklearn.cluster import KMeans\nfrom sklearn.metrics import silhouette_score\nfrom threadpoolctl import threadpool_limits\nthreadpool_limits(4)\n\nd=W[\"ln1_w.0\"].astype(float)\nv=W[\"W_v.0\"][128:192].astype(float)*d\no=W[\"W_o.0\"][:,128:192].astype(float)\nB=o@v\nF=W[\"W_fc.0\"].astype(float)*W[\"ln2_w.0\"]\nG=F@B\nu,s,vt=la.svd(G-G.mean(axis=0),full_matrices=False)\nprint(\"Singular values of centered W_fc.0 D_ln2.0 B_L0H2:\")\nprint(np.round(s[:50],4))\n\n# Clustering weight rows, not activations or model inputs.\nfor r in [20,24,27,32]:\n    X=(G-G.mean(axis=0))@vt[:r].T\n    X/=np.sqrt(s[:r])[None,:]\n    X/=np.maximum(la.norm(X,axis=1,keepdims=True),1e-12)\n    km=KMeans(n_clusters=r+1,n_init=10,random_state=0).fit(X)\n    sizes=np.bincount(km.labels_,minlength=r+1)\n    coh=np.array([la.norm(X[km.labels_==i].mean(axis=0)) for i in range(r+1)])\n    sil=silhouette_score(X,km.labels_,sample_size=1000,random_state=0)\n    print(\"rank\",r,\"clusters\",r+1,\"silhouette\",round(sil,4),\n          \"mean_cohesion\",round(np.average(coh,weights=sizes),4))\n    print(\"sizes descending\",np.sort(sizes)[::-1])\n\nprint(\"\\nEffective QK symmetric eigenvalue masses, no input evaluation:\")\nfor l in range(4):\n    d=W[f\"ln1_w.{l}\"].astype(float)\n    for j in range(6):\n        sl=slice(64*j,64*(j+1))\n        q=W[f\"W_q.{l}\"][sl].astype(float)*d\n        k=W[f\"W_k.{l}\"][sl].astype(float)*d\n        a=q.T@k\n        ev=la.eigvalsh((a+a.T)/2)\n        pos=ev[ev>0].sum()\n        neg=-ev[ev<0].sum()\n        print(f\"L{l}H{j}\", \"positive\",round(pos,3),\"negative\",round(neg,3),\n              \"signed_mass_fraction\",round((pos-neg)/(pos+neg),4))\n```\n"}}
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