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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    p=W[\"W_proj.3\"].astype(float)\n    u,s,vt=svd(p,full_matrices=False)\n    print(\"Final MLP projection-column clustering (weight vectors only)\")\n    for r in (20,24,28):\n        z=(u[:,:r].T@p).T\n        zn=np.linalg.norm(z,axis=1)\n        keep=zn>np.quantile(zn,.25)\n        z=z[keep]/zn[keep,None]\n        for k in (20,24,28):\n            km=KMeans(n_clusters=k,n_init=20,random_state=42).fit(z)\n            print(\"r\",r,\"k\",k,\"silhouette\",\n                  round(silhouette_score(z,km.labels_,sample_size=1000,random_state=42),4),\n                  \"sizes\",np.sort(np.bincount(km.labels_))[::-1])\n\n    print(\"\\nL3H3 induction composition versus other heads, with rotated-weight null controls\")\n    def qk(l,j):\n        g=W[f\"ln1_w.{l}\"].astype(float)\n        sl=slice(64*j,64*(j+1))\n        q=W[f\"W_q.{l}\"][sl].astype(float)*g\n        k=W[f\"W_k.{l}\"][sl].astype(float)*g\n        q-=q.mean(1,keepdims=True)\n        k-=k.mean(1,keepdims=True)\n        return q.T@k/8\n    def ov(l,j):\n        g=W[f\"ln1_w.{l}\"].astype(float)\n        sl=slice(64*j,64*(j+1))\n        v=W[f\"W_v.{l}\"][sl].astype(float)*g\n        v-=v.mean(1,keepdims=True)\n        return W[f\"W_o.{l}\"][:,sl].astype(float)@v\n    b=ov(0,3)\n    _,_,vb=svd(b,full_matrices=False)\n    bas=vb[:24].T\n    rng=np.random.default_rng(42)\n    for j in range(6):\n        a=qk(3,j)\n        t=bas.T@a@b@bas\n        sy=(t+t.T)/2\n        ev=np.linalg.eigvalsh(sy)\n        signed=np.trace(t)/np.linalg.norm(t)\n        c=bas.T@a\n        d=b@bas\n        null=[]\n        for _ in range(300):\n            perm=rng.permutation(384)\n            signs=rng.choice([-1.,1.],384)\n            tn=(c[:,perm]*signs)@d\n            null.append(np.trace(tn)/(np.linalg.norm(tn)+1e-30))\n        print(\"L3H\"+str(j),\"trace/norm\",round(signed,3),\n              \"symmetric positive/negative eigenvalue sums\",\n              np.round([ev[ev>0].sum(),ev[ev<0].sum()],4),\n              \"null mean/sd\",np.round([np.mean(null),np.std(null)],3),\n              \"null max\",round(max(null),3))\n```\n"}}
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