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{"type":"item.completed","item":{"id":"item_2","type":"agent_message","text":"```python\nimport numpy as np\nfrom threadpoolctl import threadpool_limits\nthreadpool_limits(2)\nnp.set_printoptions(precision=3, suppress=True, linewidth=180)\nrng=np.random.default_rng(1729)\n\n# C = I - 11^T/d is used only as a linear-algebra projector on weights.\n# No normalization, attention, activation function, or network evaluation is performed.\ndef centered_reader(name,l,j):\n    a=W[f\"{name}.{l}\"][64*j:64*j+64].astype(float)*W[f\"ln1_w.{l}\"]\n    return a-a.mean(axis=1,keepdims=True)\n\nA={};B={};Kbias={}\nfor l in range(4):\n    bias=W[f\"ln1_b.{l}\"].astype(float)\n    for j in range(6):\n        q=centered_reader(\"W_q\",l,j)\n        k=centered_reader(\"W_k\",l,j)\n        v=centered_reader(\"W_v\",l,j)\n        o=W[f\"W_o.{l}\"][:,64*j:64*j+64].astype(float)\n        A[l,j]=q.T@k/8\n        B[l,j]=o@v\n        Kbias[l,j]=k.T@(W[f\"W_q.{l}\"][64*j:64*j+64].astype(float)@bias)/8\n\nprint(\"CENTERED WEIGHT DIAGNOSTICS\")\nprint(\"QKnorm; QK effective rank; trace/F; key-affine norm; fraction of key-affine energy at coordinate 21\")\nfor l in range(4):\n    for j in range(6):\n        a=A[l,j]\n        s=np.linalg.svd(a,compute_uv=False)[:64]\n        z=Kbias[l,j]\n        print(f\"L{l}H{j}\",np.round([\n            np.linalg.norm(a),(s@s)**2/np.sum(s**4),\n            np.trace(a)/np.linalg.norm(a),np.linalg.norm(z),\n            z[21]**2/(z@z)],4))\n\nv=centered_reader(\"W_v\",0,3)\no=W[\"W_o.0\"][:,192:256].astype(float)\n_,_,vt=np.linalg.svd(v,full_matrices=False)\nperms=[rng.permutation(64) for _ in range(300)]\n\nprint(\"\\nKEY-SIDE MATCHING, WITH BROKEN-OV-PAIRING CONTROLS\")\nfor r in [16,20,24,28,32]:\n    T=vt[:r].T\n    right=v@T\n    print(\"subspace rank\",r)\n    for l,j in [(1,1),(1,2),(1,5),(2,4),(3,0),(3,3),(3,4)]:\n        left=T.T@A[l,j]@o\n        c=left@right\n        actual=np.trace(c)/np.linalg.norm(c)\n        null=np.array([np.trace(left[:,p]@right)/np.linalg.norm(left[:,p]@right) for p in perms])\n        print(f\"L{l}H{j}: actual={actual:.3f} null_mean={null.mean():.3f}\",\n              f\"null_sd={null.std():.3f} null_max={null.max():.3f}\")\n\nprint(\"\\nL0H0 RELATIVE ROTATION CHECK: ROBUSTNESS TO SUBSPACE SIZE\")\nq=W[\"W_q.0\"][192:256].astype(float)\nk=W[\"W_k.0\"][192:256].astype(float)\nref=q.T@k/8\nu,s,vt=np.linalg.svd(ref,full_matrices=False)\na0=W[\"W_q.0\"][:64].astype(float).T@W[\"W_k.0\"][:64].astype(float)/8\nfor rank in [24,32,40,48,56]:\n    U=np.linalg.svd(np.hstack([u[:,:rank],vt[:rank].T]),full_matrices=False)[0][:,:rank]\n    base=U.T@ref@U\n    uu,ss,vv=np.linalg.svd(base)\n    rotation=uu@vv\n    target=U.T@a0@U\n    correlations=[]\n    for n in range(-8,9):\n        p=np.linalg.matrix_power(rotation,n)\n        correlations.append((n,float(np.sum(target*p)/(np.linalg.norm(target)*np.linalg.norm(p)))))\n    print(\"rank\",rank,\"best\",sorted(correlations,key=lambda x:-x[1])[:5])\n```\n"}}
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