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{"type":"item.completed","item":{"id":"item_1","type":"agent_message","text":"```python\nimport numpy as np\nimport torch\nfrom sklearn.cluster import KMeans\ntorch.set_num_threads(4)\ntorch.set_default_dtype(torch.float64)\nT=lambda a: torch.as_tensor(np.asarray(a), dtype=torch.float64)\nP=torch.eye(384)-torch.ones((384,384))/384\nM,B={},{}\n\nfor l in range(4):\n    g=T(W[f\"ln1_w.{l}\"])\n    for j in range(6):\n        s=slice(j*64,(j+1)*64)\n        q,k,v=[(T(W[f\"{n}.{l}\"])[s]*g)@P for n in [\"W_q\",\"W_k\",\"W_v\"]]\n        o=P@T(W[f\"W_o.{l}\"])[:,s]\n        M[l,j]=q.T@k/8\n        B[l,j]=o@v\n\nprint(\"L0 effective OV singular spectra (first 32):\")\nfor j in range(6):\n    print(j,np.round(torch.linalg.svdvals(B[0,j])[:32].numpy(),3))\nprint(\"\\nL0H5 symmetric-QK eigenvalues, descending:\")\ne=torch.linalg.eigvalsh((M[0,5]+M[0,5].T)/2).flip(0)\nprint(np.round(e[:45].numpy(),4))\nprint(\"Smallest:\",np.round(e[-15:].numpy(),4))\n\nprint(\"\\nQK energy reading leading 3 OUTPUT directions of each L0 OV:\")\nU={}\nfor j in range(6):\n    U[j]=torch.linalg.svd(B[0,j],full_matrices=False).U[:,:3]\nfor l in range(1,4):\n    for j in range(6):\n        a=M[l,j]\n        print(f\"L{l}H{j}\",\n              \"query\",np.round([float((u.T@a).norm().square()/a.norm().square())\n                                for u in U.values()],3),\n              \"key\",np.round([float((a@u).norm().square()/a.norm().square())\n                              for u in U.values()],3))\n\nprint(\"\\nSelected key-composition spectra, on weight products only:\")\nfor later,earlier in [((2,1),(0,5)),((3,1),(2,2)),((3,5),(2,2)),\n                      ((1,4),(0,4)),((2,2),(0,1)),((2,2),(1,2))]:\n    a=M[later]@B[earlier]\n    ev=torch.linalg.eigvals(a)\n    se=torch.linalg.eigvalsh((a+a.T)/2)\n    sv=torch.linalg.svdvals(a)\n    print(later,earlier,\"trace/Frob/nuclear\",\n          np.round([float(torch.trace(a)),float(a.norm()),float(sv.sum())],4),\n          \"sym_positive_fraction\",round(float(se.clamp(min=0).sum()/se.abs().sum()),4),\n          \"eig_top_real\",np.round(torch.sort(ev.real,descending=True).values[:12].numpy(),4))\n\nprint(\"\\nFirst MLP row-weight geometry:\")\nf=(T(W[\"W_fc.0\"])*T(W[\"ln2_w.0\"]))@P\nu,s,vh=torch.linalg.svd(f,full_matrices=False)\nprint(\"effective FC0 singular values (first 65)\",np.round(s[:65].numpy(),3))\n# Whitening and clustering weight rows, not evaluating neurons.\nfor r in [24,32,48]:\n    z=u[:,:r].numpy()\n    z=z/(np.linalg.norm(z,axis=1,keepdims=True)+1e-12)\n    for k in [20,24,28,32,40]:\n        km=KMeans(n_clusters=k,n_init=5,random_state=0).fit(z)\n        centers=km.cluster_centers_\n        norms=np.linalg.norm(centers,axis=1)\n        counts=np.bincount(km.labels_,minlength=k)\n        print(\"rank\",r,\"k\",k,\"mean within-cluster cosine\",\n              round(float(np.average(norms,weights=counts)),3),\n              \"coherent clusters (centroid norm > .65)\",\n              sorted([(int(counts[i]),round(float(norms[i]),3))\n                      for i in range(k) if norms[i]>.65],reverse=True))\n```\n"}}
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