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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 threadpoolctl import threadpool_limits\nthreadpool_limits(limits=2)\nnp.set_printoptions(precision=3,suppress=True,linewidth=160)\n\nA=[]; B=[]\nfor j in range(6):\n    sl=slice(64*j,64*(j+1))\n    g=W[\"ln1_w.0\"].astype(float)\n    q=W[\"W_q.0\"][sl].astype(float)*g\n    k=W[\"W_k.0\"][sl].astype(float)*g\n    v=W[\"W_v.0\"][sl].astype(float)*g\n    for x in [q,k,v]: x-=x.mean(axis=1,keepdims=True)\n    o=W[\"W_o.0\"][:,sl].astype(float)\n    o-=o.mean(axis=0,keepdims=True)\n    A.append(q.T@k/8); B.append(o@v)\n\nP=svd(np.concatenate([A[1],A[1].T,A[5],A[5].T],axis=1),\n      full_matrices=False,check_finite=False)[0][:,:20]\nclean=B[5]-(B[5]@P)@P.T\n_,s,vt=svd(clean,full_matrices=False,check_finite=False)\nT=vt[:27].T\nprint(\"Position-orthogonalized H5 OV singular values:\",s[:40])\n\nf=W[\"W_fc.0\"].astype(float)*W[\"ln2_w.0\"][None,:]\nf-=f.mean(axis=1,keepdims=True)\nactive=np.linalg.norm(W[\"W_fc.0\"],axis=1)>1\noriginal_indices=np.where(active)[0]\nf=f[active]\ncov=[f@T,f@B[5]@T,f@B[1]@T]\nnorms=[np.linalg.norm(z,axis=1) for z in cov]\nunits=[z/n[:,None]for z,n in zip(cov,norms)]\n\n# Direct-read clusters provide an unlabeled dictionary of weight directions.\nkm=KMeans(n_clusters=28,n_init=20,max_iter=300,random_state=42).fit(units[0])\ncent=km.cluster_centers_\ncent/=np.linalg.norm(cent,axis=1,keepdims=True)\nscores=[z@cent.T for z in units]\nidx=[z.argmax(axis=1)for z in scores]\nbest=[z.max(axis=1)for z in scores]\nprint(\"Best cluster cosine quantiles, direct / H5-transported / H1-transported\")\nfor z in best: print(np.quantile(z,[.1,.25,.5,.75,.9]))\n\nprint(\"Cluster: direct size; repeated pair count; repeated triple count; \"\n      \"mean direct/H5/H1 covector norm for direct members\")\nfor c in range(28):\n    mask=idx[0]==c\n    pair=mask&(idx[1]==c)&(best[0]>.55)&(best[1]>.55)\n    triple=pair&(idx[2]==c)&(best[2]>.55)\n    print(c,int(mask.sum()),int(pair.sum()),int(triple.sum()),\n          [round(float(n[mask].mean()),3)for n in norms])\n\nsamecos=np.stack([np.sum(units[0]*units[1],axis=1),\n                  np.sum(units[0]*units[2],axis=1),\n                  np.sum(units[1]*units[2],axis=1)],axis=1)\ntriple_score=np.min(samecos,axis=1)\ntop=np.argsort(-triple_score)[:20]\nprint(\"\\nMost mutually aligned direct/H5/H1 MLP covectors:\")\nfor i in top:\n    print(\"neuron\",original_indices[i],\"cluster\",idx[0][i],\n          \"pairwise cosines\",samecos[i],\n          \"norms\",[round(float(n[i]),3)for n in norms],\n          \"center cosines\",[round(float(z[i]),3)for z in best])\n\n# Connections of content-sensitive L0 key-read singular covectors to these\n# learned MLP-row clusters. Both sides of every comparison are weights.\nfor j in [0,2,3]:\n    ak=A[j]@T\n    u,s,vh=svd(ak,full_matrices=False,check_finite=False)\n    print(\"\\nL0H%d token-restricted key singular values\"%j,s[:5])\n    for r in range(2):\n        align=cent@vh[r]\n        order=np.argsort(-np.abs(align))[:6]\n        print(\"key direction\",r,[(int(c),round(float(align[c]),3))for c in order])\n```\n"}}
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