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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, svdvals, eigvals\nfrom threadpoolctl import threadpool_limits\nthreadpool_limits(limits=2)\n\nD = 384\nP = np.eye(D) - np.ones((D, D))/D\n\ndef eff(name, l, norm=\"ln1\"):\n    # Linear weight geometry only: absorb learned coordinate scaling and\n    # project away the all-ones direction. No normalization or network evaluation.\n    return (np.asarray(W[f\"{name}.{l}\"], dtype=float)\n            * np.asarray(W[f\"{norm}_w.{l}\"], dtype=float)[None, :]) @ P\n\nQK, OV = {}, {}\nfor l in range(4):\n    q, k, v = [eff(\"W_\"+n, l) for n in [\"q\",\"k\",\"v\"]]\n    for j in range(6):\n        s = slice(64*j,64*(j+1))\n        QK[l,j] = q[s].T @ k[s]\n        OV[l,j] = np.asarray(W[f\"W_o.{l}\"][:,s],dtype=float) @ v[s]\n\nprint(\"L0 ln1_w: largest 45 coordinates\")\na = W[\"ln1_w.0\"]\nix = np.argsort(a)[-45:][::-1]\nprint([(int(i), round(float(a[i]),4)) for i in ix])\n\nprint(\"\\nEffective QK spectra and largest-magnitude eigenvalues\")\nfor l in range(4):\n    for j in range(6):\n        a = QK[l,j]\n        s = svdvals(a)\n        ev = eigvals(a)\n        ev = ev[np.argsort(np.abs(ev))[::-1]][:8]\n        print(f\"L{l}H{j}\", \"norm\", round(np.linalg.norm(a),3),\n              \"SV\", np.round(s[:8],3), \"eig\", np.round(ev,3),\n              \"symfrac\", round(np.linalg.norm((a+a.T)/2)**2/np.linalg.norm(a)**2,3))\n\nprint(\"\\nFull singular spectra at selected quantiles\")\nfor l in [0,3]:\n    for name in [\"W_fc\",\"W_proj\"]:\n        a = np.asarray(W[f\"{name}.{l}\"],dtype=float)\n        s = svdvals(a)\n        idx = [0,1,2,3,4,5,9,14,19,24,25,26,27,28,29,31,39,49,63,79,99,127,191,255,319,383]\n        print(name,l,[(i+1,round(s[i],3)) for i in idx])\n\nprint(\"\\nL0 QK pairwise Frobenius cosine\")\nprint(np.round([[np.sum(QK[0,j]*QK[0,k])/\n                 (np.linalg.norm(QK[0,j])*np.linalg.norm(QK[0,k]))\n                 for k in range(6)] for j in range(6)],3))\n\nprint(\"\\nWeight-only key-composition enrichment\")\nprint(\"For later head B and earlier head A: ||QK_B OV_A||_F / (||QK_B||_F ||OV_A||_F/sqrt(384)).\")\nfor l in range(1,4):\n    for j in range(6):\n        vals = []\n        a = QK[l,j]\n        for m in range(l):\n            for k in range(6):\n                b = OV[m,k]\n                c = np.linalg.norm(a @ b)*np.sqrt(D)/(np.linalg.norm(a)*np.linalg.norm(b))\n                vals.append((c, f\"L{m}H{k}\"))\n        vals.sort(reverse=True)\n        print(f\"L{l}H{j}\", [(h,round(c,3)) for c,h in vals[:6]])\n```"}}
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