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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 threadpoolctl import threadpool_limits\n\nwith threadpool_limits(limits=2):\n    A=[]; B=[]; bases=[]\n    for l in range(4):\n        g=W[f\"ln1_w.{l}\"].astype(float)\n        for j in range(6):\n            sl=slice(64*j,64*j+64)\n            q=W[f\"W_q.{l}\"][sl].astype(float)*g\n            k=W[f\"W_k.{l}\"][sl].astype(float)*g\n            v=W[f\"W_v.{l}\"][sl].astype(float)*g\n            for m in [q,k,v]:m-=m.mean(1,keepdims=True)\n            A.append(q.T@k/8)\n            B.append(W[f\"W_o.{l}\"][:,sl].astype(float)@v)\n            bases.append(svd(v,full_matrices=False)[2][:20].T)\n\n    print(\"Weight-only matching diagnostic:\")\n    print(\"trace(P.T @ QK_lh @ OV_source @ P) / Frobenius norm;\")\n    print(\"P = top 20 right singular directions of source V.\")\n    for i in range(6,24):\n        scores=[]\n        syms=[]\n        for j in range((i//6)*6):\n            P=bases[j]\n            C=P.T@A[i]@B[j]@P\n            n=np.linalg.norm(C)\n            scores.append(np.trace(C)/n)\n            syms.append(np.sum(C*C.T)/(n*n))\n        best=np.argsort(scores)[::-1][:3]\n        print(\"L%dH%d\"%(i//6,i%6),\n              \"L0-source scores\",np.round(scores[:6],3),\n              \"best\",[\n                  (\"L%dH%d\"%(j//6,j%6),round(scores[j],3),round(syms[j],3))\n                  for j in best])\n\n    rng=np.random.default_rng(874)\n    P=bases[3]\n    left=P.T@A[21]\n    right=B[3]@P\n    C=left@right\n    observed=np.trace(C)/np.linalg.norm(C)\n    null=[]\n    for _ in range(1000):\n        signs=rng.choice([-1.,1.],size=384)\n        D=(left*signs)@right\n        null.append(np.trace(D)/np.linalg.norm(D))\n    print(\"\\nL3H3 <- L0H3 matching score:\",round(observed,4))\n    print(\"Coordinate-sign scrambling of the weight connection, null quantiles:\",\n          np.round(np.quantile(null,[0,.01,.5,.99,1]),4))\n\n    print(\"\\nSelected literal LayerNorm weights\")\n    for name,inds in [\n        (\"ln1_b.1\",[39,58,99,21]),\n        (\"ln1_b.2\",[39,58,99,21]),\n        (\"ln1_w.0\",[180,184,162,99,211])]:\n        print(name,[(i,float(W[name][i])) for i in inds])\n```\n"}}
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