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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\nthreadpool_limits(4)\n\nA,C,bias={},{},{}\nfor l in range(4):\n    g=W[f\"ln1_w.{l}\"].astype(float)\n    b=W[f\"ln1_b.{l}\"].astype(float)\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        q=q0*g\n        k=k0*g\n        v=W[f\"W_v.{l}\"][s].astype(float)*g\n        q-=q.mean(axis=1,keepdims=True)\n        k-=k.mean(axis=1,keepdims=True)\n        v-=v.mean(axis=1,keepdims=True)\n        o=W[f\"W_o.{l}\"][:,s].astype(float)\n        o-=o.mean(axis=0,keepdims=True)\n        n=(l,j)\n        A[n]=q.T@k/8\n        C[n]=o@v\n        bias[n]=k.T@(q0@b)/8\n\nreference=sum(bias[(1,j)]/np.linalg.norm(bias[(1,j)]) for j in range(6))\nreference/=np.linalg.norm(reference)\nprint(\"Final compact weight-only audit:\")\nprint(\"head  ||A||F  ||C||F  A_stable_rank  C_top4_energy  keybias_norm  common_bias_cos\")\nfor l in range(4):\n    for j in range(6):\n        n=(l,j)\n        sa=svdvals(A[n],check_finite=False)\n        sc=svdvals(C[n],check_finite=False)\n        print(f\"L{l}H{j}\",*[\n            round(float(x),4) for x in [\n                np.linalg.norm(A[n]),np.linalg.norm(C[n]),\n                np.sum(sa*sa)/(sa[0]**2),\n                np.sum(sc[:4]**2)/np.sum(sc**2),\n                np.linalg.norm(bias[n]),\n                bias[n]@reference/np.linalg.norm(bias[n])]])\n\nprint(\"\\nCoordinate-permutation controls for proposed copy-path products:\")\nrng=np.random.default_rng(123)\npaths=[((2,1),(0,5)),((3,1),(0,5)),((3,5),(0,5)),\n       ((3,1),(2,2)),((3,5),(2,2))]\nfor target,source in paths:\n    a=A[target]; c=C[source]\n    denom=np.linalg.norm(a)*np.linalg.norm(c)\n    observed=np.sum(a*c.T)/denom\n    controls=[]\n    for _ in range(400):\n        p=rng.permutation(384)\n        controls.append(np.sum(a*c[np.ix_(p,p)].T)/denom)\n    controls=np.array(controls)\n    print(\"target\",target,\"source\",source,\n          \"observed\",round(observed,5),\n          \"null_mean\",round(controls.mean(),5),\n          \"null_std\",round(controls.std(),5),\n          \"null_max\",round(controls.max(),5))\n\na=A[(0,5)]\nb=A[(0,1)]\nprint(\"\\nPositional-product cosines:\",\n      \"cos(A01,A05)\",round(np.sum(b*a)/np.linalg.norm(b)/np.linalg.norm(a),5),\n      \"cos(A01,A05^2)\",round(np.sum(b*(a@a))/np.linalg.norm(b)/np.linalg.norm(a@a),5))\nsa=svdvals(A[(0,4)],check_finite=False)\n# Only an operator-norm bound, not evaluation on an input.\nprint(\"L0H4 operator-norm bound on variation across unmasked key scores:\",\n      round(2*384*sa[0]+2*np.sqrt(384)*np.linalg.norm(bias[(0,4)]),5))\nprint(\"All computations above are parameter decompositions/products; no network layer was evaluated.\")\n```\n"}}
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