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{"type":"item.completed","item":{"id":"item_1","type":"agent_message","text":"```python\nimport numpy as np\nimport scipy.linalg as la\nfrom threadpoolctl import threadpool_limits\nthreadpool_limits(4)\n\nA, B = {}, {}\nfor l in range(4):\n    w = W[f\"ln1_w.{l}\"].astype(float)\n    bias = W[f\"ln1_b.{l}\"].astype(float)\n    print(\"\\nLAYER\", l, \"(gain-weighted matrices; no LayerNorm evaluation)\")\n    for j in range(6):\n        s = slice(64*j, 64*(j+1))\n        q0 = W[f\"W_q.{l}\"][s].astype(float)\n        k0 = W[f\"W_k.{l}\"][s].astype(float)\n        v0 = W[f\"W_v.{l}\"][s].astype(float)\n        o = W[f\"W_o.{l}\"][:,s].astype(float)\n        q, k, v = q0*w, k0*w, v0*w\n        a, b = q.T@k, o@v\n        A[l,j], B[l,j] = a, b\n        sv = la.svdvals(a)[:64]\n        qb, kb = q0@bias, k0@bias\n        key_linear = k.T@qb\n        query_linear = q.T@kb\n        print(f\"L{l}H{j}\",\n              \"QKnorm\", round(la.norm(a),4),\n              \"QKsv\", np.round(sv[:6],4),\n              \"QKtrace\", round(np.trace(a),4),\n              \"OVnorm\", round(la.norm(b),4),\n              \"bias_key/query_norm\", np.round([la.norm(key_linear),la.norm(query_linear)],4))\n\nprint(\"\\nNormalized trace(A_lh @ B_0j), columns L0H0..L0H5\")\nfor l in range(1,4):\n    for j in range(6):\n        a = A[l,j]\n        vals = [np.trace(a@B[0,k])/(la.norm(a)*la.norm(B[0,k])) for k in range(6)]\n        print(f\"L{l}H{j}\", np.round(vals,4))\n\nprint(\"\\nLargest earlier-head trace compositions (signed normalized trace)\")\nfor l in range(2,4):\n    for j in range(6):\n        a = A[l,j]\n        vals = []\n        for m in range(l):\n            for k in range(6):\n                b = B[m,k]\n                vals.append((float(np.trace(a@b)/(la.norm(a)*la.norm(b))), f\"L{m}H{k}\"))\n        print(f\"L{l}H{j}\", sorted(vals, reverse=True)[:5])\n\nprint(\"\\nL0H2 effective QK spectrum\")\na = A[0,2]\nu,s,vt = la.svd(a, full_matrices=False)\nprint(\"singular values\", np.round(s[:40],5))\nev = la.eigvals(a)\nix = np.argsort(abs(ev))[::-1][:24]\nprint(\"largest eigenvalues\", np.round(ev[ix],4))\nprint(\"left/right top-20 subspace overlap\", np.round(la.svdvals(u[:,:20].T@vt[:20].T),4))\n\nprint(\"\\nL0 query/key and value subspace overlap with L0H2 dominant QK subspace\")\np = la.orth(np.column_stack([u[:,:20],vt[:20].T]))\nfor j in range(6):\n    s0 = slice(64*j,64*(j+1))\n    vals=[]\n    for name in [\"W_q\",\"W_k\",\"W_v\"]:\n        m = W[f\"{name}.0\"][s0].astype(float)*W[\"ln1_w.0\"]\n        vals.append(la.norm(m@p)**2/la.norm(m)**2)\n    print(f\"L0H{j}\", np.round(vals,4))\n```\n"}}
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