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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 threadpoolctl import threadpool_limits\nnp.set_printoptions(precision=4, suppress=True, linewidth=180)\n\ndef cosine(a, b):\n    return np.vdot(a, b).real / (la.norm(a) * la.norm(b) + 1e-30)\n\nwith threadpool_limits(limits=2):\n    QK, OV = {}, {}\n    for l in range(4):\n        g = np.asarray(W[f\"ln1_w.{l}\"], dtype=float)\n        for j in range(6):\n            s = slice(64*j, 64*j+64)\n            q = np.asarray(W[f\"W_q.{l}\"][s], dtype=float) * g\n            k = np.asarray(W[f\"W_k.{l}\"][s], dtype=float) * g\n            v = np.asarray(W[f\"W_v.{l}\"][s], dtype=float) * g\n            o = np.asarray(W[f\"W_o.{l}\"][:,s], dtype=float)\n            QK[l,j] = q.T @ k / 8\n            OV[l,j] = o @ v\n\n    print(\"GAIN-WEIGHTED PRODUCTS: A=diag(ln1_w) Q.T K diag(ln1_w)/8, B=O V diag(ln1_w)\")\n    print(\"These are matrix products only; no LayerNorm, attention, or MLP evaluations.\")\n    for l in range(4):\n        for j in range(6):\n            a, b = QK[l,j], OV[l,j]\n            s = la.svdvals(a)\n            ev = la.eigvals(a)\n            ev = ev[np.argsort(-abs(ev))][:12]\n            print(f\"L{l}H{j}: A_norm={la.norm(a):.4f}, sr={sum(s*s)/s[0]**2:.2f}, \"\n                  f\"symfrac={la.norm((a+a.T)/2)/la.norm(a):.3f}, B_norm={la.norm(b):.3f}, \"\n                  f\"top_s={np.round(s[:6],4)}, eig={np.round(ev[:8],4)}\")\n\n    print(\"\\nPAIRWISE QK COSINES WITHIN EACH LAYER\")\n    for l in range(4):\n        print(\"L\",l)\n        print(np.array([[cosine(QK[l,i], QK[l,j]) for j in range(6)] for i in range(6)]))\n\n    print(\"\\nL0H2 FULL NONZERO SINGULAR SPECTRUM\")\n    print(la.svdvals(QK[0,2])[:64])\n    print(\"\\nL0H2 TOP EIGENVALUES OF UNWEIGHTED Q.T K/8\")\n    q = np.asarray(W[\"W_q.0\"][128:192], dtype=float)\n    k = np.asarray(W[\"W_k.0\"][128:192], dtype=float)\n    ev = la.eigvals(k @ q.T / 8)\n    print(ev[np.argsort(-abs(ev))][:32])\n\n    print(\"\\nRESIDUAL COORDINATE CONCENTRATION\")\n    for l in range(4):\n        g = np.asarray(W[f\"ln1_w.{l}\"], dtype=float)\n        q = np.asarray(W[f\"W_q.{l}\"], dtype=float)\n        k = np.asarray(W[f\"W_k.{l}\"], dtype=float)\n        energy = np.sum((q*g)**2 + (k*g)**2, axis=0)\n        ix = np.argsort(-energy)[:16]\n        print(f\"L{l}: top_coordinates={ix}; fraction_top16={energy[ix].sum()/energy.sum():.4f}; gains={np.round(g[ix],4)}\")\n\n    print(\"\\nDIRECT OV ALIGNMENT WITH LATER QK (matrix composition only)\")\n    print(\"For each later head: strongest earlier B on key side; enrichment = ||A B||F/(||A||F||B||F/sqrt(384)).\")\n    for l in range(1,4):\n        for j in range(6):\n            a = QK[l,j]\n            scores = []\n            for m in range(l):\n                for h in range(6):\n                    b = OV[m,h]\n                    c = a @ b\n                    enrich = la.norm(c)*np.sqrt(384)/(la.norm(a)*la.norm(b))\n                    trace_ratio = np.trace(c)/(la.norm(c)*np.sqrt(384)+1e-30)\n                    scores.append((enrich, m, h, trace_ratio))\n            print(f\"L{l}H{j}:\", [(f\"L{m}H{h}\", round(e,3), round(t,4)) for e,m,h,t in sorted(scores, reverse=True)[:5]])\n```"}}
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