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{"type":"item.completed","item":{"id":"item_2","type":"agent_message","text":"```python\nimport numpy as np\nimport scipy.linalg as la\nfrom scipy.sparse import csr_matrix\nfrom scipy.sparse.csgraph import connected_components\nfrom threadpoolctl import threadpool_limits\nnp.set_printoptions(precision=4,suppress=True,linewidth=180)\n\ndef svd(a):\n    return la.svd(a,full_matrices=False,lapack_driver=\"gesvd\")\ndef unit(v):\n    return v/(la.norm(v)+1e-30)\n\nwith threadpool_limits(limits=2):\n    g=np.asarray(W[\"ln1_w.0\"],dtype=float)\n    q2=np.asarray(W[\"W_q.0\"][128:192],dtype=float)*g\n    k2=np.asarray(W[\"W_k.0\"][128:192],dtype=float)*g\n    P=svd(np.vstack([q2,k2]))[2][:32].T\n    left,right=[],[]\n    Bs=[]\n    print(\"L0 DOMINANT QK FACTORS\")\n    for j in range(6):\n        sl=slice(j*64,j*64+64)\n        q=np.asarray(W[\"W_q.0\"][sl],dtype=float)*g\n        k=np.asarray(W[\"W_k.0\"][sl],dtype=float)*g\n        a=q.T@k/8\n        u,s,vt=svd(a)\n        left.append(u[:,0]); right.append(vt[0])\n        b=(np.asarray(W[\"W_o.0\"][:,sl],dtype=float)@np.asarray(W[\"W_v.0\"][sl],dtype=float))*g\n        Bs.append(b)\n        print(f\"H{j}: top-mode energy={s[0]**2/sum(s*s):.4f}, \"\n              f\"query-pos32={la.norm(P.T@u[:,0])**2:.4f}, \"\n              f\"key-pos32={la.norm(P.T@vt[0])**2:.4f}\")\n    print(\"absolute cosines of leading query directions\")\n    print(abs(np.array(left)@np.array(left).T))\n    print(\"absolute cosines of leading key directions\")\n    print(abs(np.array(right)@np.array(right).T))\n\n    R=svd(np.hstack([Bs[j] for j in (0,1,4,5)]))[0][:,:3]\n    print(\"\\nPOSITION-SUBSPACE AND AFFINE WEIGHT COEFFICIENTS\")\n    print(\"query-pos32 fraction; key-linear norm / QK norm; key-linear fraction in common 3D writes\")\n    for l in range(1,4):\n        g1=np.asarray(W[f\"ln1_w.{l}\"],dtype=float)\n        b1=np.asarray(W[f\"ln1_b.{l}\"],dtype=float)\n        for j in range(6):\n            sl=slice(j*64,j*64+64)\n            raw=np.asarray(W[f\"W_q.{l}\"][sl],dtype=float).T@np.asarray(W[f\"W_k.{l}\"][sl],dtype=float)/8\n            a=g1[:,None]*raw*g1\n            c=(b1@raw)*g1\n            print(f\"L{l}H{j}\",\n                  np.round([la.norm(P.T@a)**2/la.norm(a)**2,\n                            la.norm(c)/la.norm(a),\n                            la.norm(c@R)**2/(la.norm(c)**2+1e-30)],4))\n\n    F=np.asarray(W[\"W_fc.0\"],dtype=float)*W[\"ln2_w.0\"]\n    proj=np.asarray(W[\"W_proj.0\"],dtype=float)\n    active=(la.norm(W[\"W_fc.0\"],axis=1)>0.7)&(la.norm(proj,axis=0)>0.6)\n    F=F[active]\n    Z=F/la.norm(F,axis=1)[:,None]\n    G=Z@Z.T\n    print(\"\\nACTIVE L0 MLP WEIGHT-ROW CLUSTERS\")\n    for threshold in (0.8,0.9,0.95,0.98):\n        n,labels=connected_components(csr_matrix(G>threshold),directed=False)\n        sizes=np.sort(np.bincount(labels))[::-1]\n        print(f\"cosine>{threshold}: components={n}, non-singleton neurons={sizes[sizes>1].sum()}, largest sizes={sizes[:30]}\")\n    U=svd(Bs[2])[0][:,:24]\n    fr_prev=la.norm(F@U,axis=1)**2/la.norm(F,axis=1)**2\n    fr_pos=la.norm(F@P,axis=1)**2/la.norm(F,axis=1)**2\n    print(\"Previous-write top24 read-energy fraction quantiles\",np.percentile(fr_prev,[0,10,25,50,75,90,100]))\n    print(\"Position top32 read-energy fraction quantiles\",np.percentile(fr_pos,[0,10,25,50,75,90,100]))\n```"}}
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