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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 sklearn.cluster import KMeans\nfrom threadpoolctl import threadpool_limits\nnp.set_printoptions(precision=4, suppress=True, linewidth=180)\n\nwith threadpool_limits(limits=2):\n    print(\"SPECTRAL DETAIL: first 64 singular values\")\n    for name in (\"W_v.0\", \"W_o.0\", \"W_fc.0\", \"W_proj.0\", \"W_proj.3\"):\n        a = np.asarray(W[name], dtype=float)\n        print(name, la.svdvals(a)[:64])\n    print(\"\\nGAIN-WEIGHTED MLP INPUT SPECTRA\")\n    for l in range(4):\n        a = np.asarray(W[f\"W_fc.{l}\"], dtype=float) * W[f\"ln2_w.{l}\"]\n        print(f\"L{l}\", la.svdvals(a)[:40])\n\n    print(\"\\nL0 COORDINATES WITH LARGEST ln1_w\")\n    ix = np.argsort(-W[\"ln1_w.0\"])[:35]\n    print(\"coordinate, ln1_w, ln2_w, ln1_b, ln2_b\")\n    for i in ix:\n        print(i, *[round(float(W[f\"{n}.0\"][i]),5) for n in (\"ln1_w\",\"ln2_w\",\"ln1_b\",\"ln2_b\")])\n\n    print(\"\\nL0 VALUE-PATH SPECTRA AND PRINCIPAL INPUT DIRECTIONS\")\n    vv, oo = [], []\n    for j in range(6):\n        sl = slice(j*64,(j+1)*64)\n        a = (np.asarray(W[\"W_o.0\"][:,sl],dtype=float)\n             @ np.asarray(W[\"W_v.0\"][sl],dtype=float)) * W[\"ln1_w.0\"]\n        u,s,vt = la.svd(a, full_matrices=False)\n        vv.append(vt[:4].T)\n        oo.append(u[:4])\n        print(f\"H{j}: singular={s[:32]}; energy_first2={sum(s[:2]**2)/sum(s*s):.4f}\")\n    print(\"L0 value-input top-2 subspace overlaps (sum squared principal cosines / 2)\")\n    print(np.array([[la.norm(vv[i][:,:2].T@vv[j][:,:2])**2/2 for j in range(6)] for i in range(6)]))\n    print(\"L0 value-output top-2 subspace overlaps\")\n    print(np.array([[la.norm(oo[i][:,:2].T@oo[j][:,:2])**2/2 for j in range(6)] for i in range(6)]))\n\n    print(\"\\nL0 MLP INPUT ROW GEOMETRY (no activations)\")\n    a = np.asarray(W[\"W_fc.0\"],dtype=float)*W[\"ln2_w.0\"]\n    a /= la.norm(a,axis=1)[:,None]\n    gram = a @ a.T\n    np.fill_diagonal(gram,-2)\n    print(\"nearest-row cosine percentiles\",np.percentile(gram.max(axis=1),[0,10,25,50,75,90,99,100]))\n    for n in (16,20,24,28,32,48):\n        km = KMeans(n_clusters=n,n_init=5,random_state=0,max_iter=200).fit(a)\n        sizes=np.bincount(km.labels_,minlength=n)\n        print(f\"k={n}: inertia={km.inertia_:.3f}, sizes={np.sort(sizes)[::-1]}\")\n```"}}
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