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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\nfrom sklearn.cluster import KMeans\nfrom sklearn.metrics import silhouette_score\nfrom threadpoolctl import threadpool_limits\nthreadpool_limits(limits=2)\nnp.set_printoptions(precision=3, suppress=True, linewidth=160)\n\ng = W[\"ln1_w.0\"].astype(float)\nsl = slice(320,384)\nv = W[\"W_v.0\"][sl].astype(float)*g[None,:]\nv -= v.mean(axis=1,keepdims=True)\no = W[\"W_o.0\"][:,sl].astype(float)\no -= o.mean(axis=0,keepdims=True)\nu,s,vt = svd(o@v,full_matrices=False,check_finite=False)\nT = vt[:27].T\nprint(\"L0H5 effective OV first 40 singular values:\",s[:40])\n\nf = W[\"W_fc.0\"].astype(float)*W[\"ln2_w.0\"][None,:]\nf -= f.mean(axis=1,keepdims=True)\nft = f@T\nactive = np.linalg.norm(W[\"W_fc.0\"],axis=1)>1\nprint(\"MLP0 active row count:\",active.sum())\nprint(\"MLP0 active rows restricted to value-read subspace: singular values:\",\n      svd(ft[active],compute_uv=False,check_finite=False))\nprint(\"Fraction of each active MLP0 row's energy in that subspace, quantiles:\",\n      np.quantile(np.sum(ft[active]**2,axis=1)/np.sum(f[active]**2,axis=1),[0,.1,.25,.5,.75,.9,1]))\n\n# Cluster learned weight directions only.\ndatasets = {\n    \"MLP0 active token-read row directions\": ft[active],\n    \"MLP3 write-column directions\": W[\"W_proj.3\"].astype(float).T,\n}\nfor name,z in datasets.items():\n    z=z/np.linalg.norm(z,axis=1,keepdims=True)\n    print(\"\\n\",name)\n    for k in [8,16,20,24,28,32]:\n        km=KMeans(n_clusters=k,n_init=5,max_iter=150,random_state=0).fit(z)\n        labels=km.labels_\n        counts=np.bincount(labels,minlength=k)\n        centers=km.cluster_centers_\n        centers/=np.linalg.norm(centers,axis=1,keepdims=True)\n        cohesion=np.array([np.mean(z[labels==j]@centers[j]) for j in range(k)])\n        sil=silhouette_score(z,labels,metric=\"cosine\",sample_size=min(700,len(z)),random_state=0)\n        print(\"k\",k,\"silhouette\",round(sil,3),\"mean cohesion\",round(float(cohesion.mean()),3),\n              \"sizes\",np.sort(counts)[::-1])\n        if k==28:\n            idx=np.argsort(-counts)\n            print(\"cohesion by descending cluster size:\",np.round(cohesion[idx],3))\n            cc=centers@centers.T\n            np.fill_diagonal(cc,-1)\n            print(\"largest inter-center cosines:\",np.sort(cc.max(axis=1))[::-1])\n```\n"}}
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