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{"type":"item.completed","item":{"id":"item_1","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\n\nwith threadpool_limits(limits=4):\n    print(\"Final-layer projection spectrum\")\n    up,sp,vp=svd(W[\"W_proj.3\"].astype(float),full_matrices=False)\n    print(np.round(sp[:40],3))\n    print(\"Leading output directions: participation ratio, max absolute coordinate, mean-direction cosine\")\n    for j in range(6):\n        u=up[:,j]\n        ix=np.argsort(abs(u))[-8:][::-1]\n        print(j,np.round([1/(u**4).sum(),abs(u).max(),u.sum()/np.sqrt(384)],4),\n              list(zip(ix.tolist(),np.round(u[ix],3).tolist())))\n    print(\"\\nFinal-layer output-column cosine quantiles with leading output direction\")\n    p=W[\"W_proj.3\"].astype(float)\n    for j in range(3):\n        c=(up[:,j]@p)/np.linalg.norm(p,axis=0)\n        print(j,np.round(np.quantile(c,[0,.01,.1,.25,.5,.75,.9,.99,1]),3))\n\n    print(\"\\nFirst-layer MLP coefficient clustering in H3's leading input-weight subspace\")\n    g=W[\"ln1_w.0\"].astype(float)\n    v=W[\"W_v.0\"][192:256].astype(float)*g\n    v-=v.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    f=W[\"W_fc.0\"].astype(float)*W[\"ln2_w.0\"].astype(float)\n    f-=f.mean(1,keepdims=True)\n    x=f@vt[:20].T\n    x-=x.mean(0)\n    ux,sx,vx=svd(x,full_matrices=False)\n    x=ux*np.sqrt(len(x))\n    x/=np.linalg.norm(x,axis=1,keepdims=True)\n    for k in (8,12,16,20,24,28,32):\n        fit=KMeans(n_clusters=k,n_init=10,random_state=42).fit(x)\n        sizes=np.bincount(fit.labels_,minlength=k)\n        sil=silhouette_score(x,fit.labels_,sample_size=1000,random_state=42)\n        print(\"k\",k,\"silhouette\",round(sil,4),\"sizes\",np.sort(sizes)[::-1])\n    print(\"\\nFirst-layer MLP coefficient row-norm quantiles in current/prior subspaces\")\n    for r in (16,20,24):\n        basis=vt[:r].T\n        cur=f@basis\n        prev=f@b@basis\n        for name,z in ((\"current\",cur),(\"prior\",prev)):\n            print(r,name,np.round(np.quantile(np.linalg.norm(z,axis=1),[0,.1,.5,.9,1]),3))\n\n    print(\"\\nL0 output-row norms for low-rank heads and MLP0\")\n    for j in (1,2,4,5):\n        o=W[\"W_o.0\"][:,64*j:64*(j+1)].astype(float)\n        rn=np.linalg.norm(o,axis=1)\n        ix=np.argsort(rn)[-10:][::-1]\n        print(\"H\",j,list(zip(ix.tolist(),np.round(rn[ix],3).tolist())))\n    p=W[\"W_proj.0\"].astype(float)\n    rn=np.linalg.norm(p,axis=1)\n    ix=np.argsort(rn)[-10:][::-1]\n    print(\"MLP0\",list(zip(ix.tolist(),np.round(rn[ix],3).tolist())))\n```\n"}}
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