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{"type":"item.completed","item":{"id":"item_1","type":"agent_message","text":"```python\nimport numpy as np\nfrom scipy.linalg import svdvals\nfrom threadpoolctl import threadpool_limits\n\nwith threadpool_limits(limits=4):\n    print(\"LayerNorm parameters: mean, std, min, max, norm\")\n    for l in range(4):\n        for name in (\"ln1_w\", \"ln1_b\", \"ln2_w\", \"ln2_b\"):\n            a = W[f\"{name}.{l}\"].astype(np.float64)\n            print(f\"{name}.{l}\", np.round([a.mean(), a.std(), a.min(), a.max(), np.linalg.norm(a)], 4))\n    print(\"\\nMatrix summaries: Frobenius norm, top singular value, stable rank\")\n    for l in range(4):\n        for name in (\"W_q\", \"W_k\", \"W_v\", \"W_o\", \"W_fc\", \"W_proj\"):\n            a = W[f\"{name}.{l}\"].astype(np.float64)\n            s = svdvals(a)\n            print(f\"{name}.{l}\", np.round([np.linalg.norm(a), s[0], (s*s).sum()/s[0]**2], 4))\n    print(\"\\nHead algebra (no activations):\")\n    print(\"head | QK Frobenius, top SV, stable rank, trace, symmetric eig min/max\"\n          \" | OV Frobenius, top SV, stable rank, trace | ||Wq b||, ||Wk b||\")\n    for l in range(4):\n        b = W[f\"ln1_b.{l}\"].astype(np.float64)\n        for j in range(6):\n            s = slice(j*64, (j+1)*64)\n            q = W[f\"W_q.{l}\"][s].astype(np.float64)\n            k = W[f\"W_k.{l}\"][s].astype(np.float64)\n            v = W[f\"W_v.{l}\"][s].astype(np.float64)\n            o = W[f\"W_o.{l}\"][:, s].astype(np.float64)\n            qk = q.T @ k / 8\n            ov = o @ v\n            sq, so = svdvals(qk), svdvals(ov)\n            eq = np.linalg.eigvalsh((qk+qk.T)/2)\n            a = [np.linalg.norm(qk), sq[0], (sq*sq).sum()/sq[0]**2,\n                 np.trace(qk), eq[0], eq[-1]]\n            c = [np.linalg.norm(ov), so[0], (so*so).sum()/so[0]**2, np.trace(ov)]\n            print(f\"L{l}H{j}\", np.round(a, 3), \"|\", np.round(c, 3), \"|\",\n                  np.round([np.linalg.norm(q@b), np.linalg.norm(k@b)], 3))\n```\n"}}
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