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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, eigvals\nfrom threadpoolctl import threadpool_limits\nthreadpool_limits(limits=2)\nnp.set_printoptions(precision=3, suppress=True, linewidth=160)\n\ndef scaled_read(name, l, sl=None):\n    a = W[f\"{name}.{l}\"].astype(float)\n    if sl is not None: a = a[sl]\n    a *= W[f\"ln1_w.{l}\"][None, :]\n    return a - a.mean(axis=1, keepdims=True)\n\nA, B, Vr = [], [], []\nfor l in range(4):\n    for j in range(6):\n        sl = slice(64*j,64*(j+1))\n        q,k,v = [scaled_read(n,l,sl) for n in [\"W_q\",\"W_k\",\"W_v\"]]\n        o = W[f\"W_o.{l}\"][:,sl].astype(float)\n        o -= o.mean(axis=0,keepdims=True)\n        A.append(q.T@k/8); B.append(o@v); Vr.append(v)\n\n_, s, vt = svd(Vr[5], full_matrices=False, check_finite=False)\nprint(\"L0H5 effective V singular values:\", s[:40])\nT = vt[:27].T\nprint(\"\\nL0 QK energy in L0H5 V-read top27; query / key\")\nfor j in range(6):\n    a = A[j]\n    print(j, np.linalg.norm(T.T@a)**2/np.linalg.norm(a)**2,\n          np.linalg.norm(a@T)**2/np.linalg.norm(a)**2)\n    raw = W[\"W_q.0\"][64*j:64*(j+1)].astype(float).T @ W[\"W_k.0\"][64*j:64*(j+1)].astype(float)/8\n    ev = eigvals(raw, check_finite=False)\n    print(\" raw QK largest eigenvalues:\", ev[np.argsort(-np.abs(ev))[:12]])\n\nprint(\"\\nProjected composition trace / Frobenius norm on the L0H5 value-read subspace\")\nprint(\"For each later head: best earlier OV head, trace/Frobenius, \"\n      \"positive-eigenvalue mass of symmetric part / total absolute mass\")\nfor l in range(1,4):\n    for j in range(6):\n        a = A[6*l+j]\n        rows = []\n        for m in range(6*l):\n            c = T.T @ a @ B[m] @ T\n            ratio = np.trace(c)/(np.linalg.norm(c)+1e-30)\n            ev = np.linalg.eigvalsh((c+c.T)/2)\n            pos = ev[ev>0].sum()/(np.abs(ev).sum()+1e-30)\n            rows.append((ratio, pos, m, np.linalg.norm(c)))\n        rows.sort(reverse=True)\n        print(\"L%dH%d:\"%(l,j),\n              [\"L%dH%d ratio %.3f pos %.3f norm %.3f\" %\n               (m//6,m%6,r,p,n) for r,p,m,n in rows[:3]])\n\n# Where each OV map reads and writes, measured as subspace energy.\nUout = svd(W[\"W_proj.3\"].astype(float), full_matrices=False, check_finite=False)[0][:,:28]\nprint(\"\\nOV energy fractions: read L0H5-value top27 / write final-MLP top28\")\nfor i,b in enumerate(B):\n    print(\"L%dH%d %.3f %.3f\"%(i//6,i%6,\n          np.linalg.norm(b@T)**2/np.linalg.norm(b)**2,\n          np.linalg.norm(Uout.T@b)**2/np.linalg.norm(b)**2))\n\n# Learned MLP-row counts versus small, nearly initialization-scale rows.\nfor l in range(4):\n    f = W[f\"W_fc.{l}\"].astype(float)\n    rn = np.linalg.norm(f,axis=1)\n    print(\"MLP\",l,\"row norm quantiles\",np.quantile(rn,[0,.1,.25,.5,.75,.9,1]),\n          \"rows norm>1:\",np.sum(rn>1),\"norm>2:\",np.sum(rn>2))\n```\n"}}
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