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{"type":"item.completed","item":{"id":"item_1","type":"agent_message","text":"```python\nimport numpy as np\nfrom scipy.linalg import svd, svdvals, eigvalsh\nfrom threadpoolctl import threadpool_limits\nnp.set_printoptions(precision=4, suppress=True, linewidth=180)\n\ndef cent(a):\n    return a-a.mean(0,keepdims=True)-a.mean(1,keepdims=True)+a.mean()\n\nwith threadpool_limits(limits=4):\n    print(\"DIRECT POSITION-REGISTER WEIGHTS\")\n    for name in [\"ln1_w.0\",\"ln2_w.0\",\"ln1_w.1\",\"ln1_b.1\",\"ln1_w.2\",\"ln1_b.2\",\"ln1_w.3\",\"ln1_b.3\"]:\n        print(name, {i:round(float(W[name][i]),5) for i in [72,78,103,222,360]})\n\n    print(\"\\nCOPY-CIRCUIT ROBUSTNESS TO ALGEBRAIC CONVENTIONS\")\n    for gains in [False,True]:\n        g0=W[\"ln1_w.0\"] if gains else np.ones(384)\n        g3=W[\"ln1_w.3\"] if gains else np.ones(384)\n        b=cent((W[\"W_o.0\"][:,128:192]@W[\"W_v.0\"][128:192])*g0)\n        value_read=W[\"W_v.0\"][128:192]*g0\n        value_read-=value_read.mean(1,keepdims=True)\n        basis=svd(value_read,full_matrices=False)[2].T\n        for j in [0,1,2,3,4,5]:\n            s=slice(64*j,64*(j+1))\n            a=cent((W[\"W_q.3\"][s]*g3).T@(W[\"W_k.3\"][s]*g3)/8)\n            c=a@b\n            vals=[]\n            for rank in [16,20,24,28,32]:\n                u=basis[:,:rank]\n                cr=u.T@c@u\n                vals.append(float(np.trace(cr)/svdvals(cr).sum()))\n            print(\"gains\",gains,f\"L3H{j}\",\"restricted trace/nuclear at ranks16,20,24,28,32\",np.round(vals,4))\n\n    print(\"\\nLATE CONTENT-SPACE DIMENSION CHECK\")\n    for name,mat in [\n        (\"W_proj.3\",W[\"W_proj.3\"]),\n        (\"L3H1 W_o\",W[\"W_o.3\"][:,64:128]),\n        (\"L3H5 W_o\",W[\"W_o.3\"][:,320:384])\n    ]:\n        ss=svdvals(mat)\n        print(name,\"singular values 19..36\",ss[18:36])\n\n    print(\"\\nHEAD READ/WRITE ALIGNMENT WITH THREE SHARED REGISTERS\")\n    for l in range(4):\n        g=W[f\"ln1_w.{l}\"]\n        for j in range(6):\n            s=slice(64*j,64*(j+1))\n            q=W[f\"W_q.{l}\"][s]*g\n            k=W[f\"W_k.{l}\"][s]*g\n            a=cent(q.T@k/8)\n            qb=W[f\"W_q.{l}\"][s]@W[f\"ln1_b.{l}\"]\n            kb=k.T@qb/8\n            kb-=kb.mean()\n            reg=[72,78,222]\n            print(f\"L{l}H{j}\",\n                  \"QK key-register fraction\",round(float(np.sum(a[:,reg]**2)/np.sum(a*a)),3),\n                  \"bias key-register fraction\",round(float(np.sum(kb[reg]**2)/np.sum(kb*kb)),3),\n                  \"key bias norm\",round(float(np.linalg.norm(kb)),3))\n```\n"}}
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