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{"type":"item.completed","item":{"id":"item_1","type":"agent_message","text":"```python\nimport numpy as np\nimport scipy.linalg as la\nfrom threadpoolctl import threadpool_limits\nthreadpool_limits(4)\n\nfor l in range(4):\n    print(\"\\nLAYER\",l)\n    for name in [\"W_fc\",\"W_proj\"]:\n        m = W[f\"{name}.{l}\"].astype(float)\n        s = la.svdvals(m)\n        print(name,\"first 40 SV:\",np.round(s[:40],3))\n        print(\"SV indices 40,60,80,100,150,200,300,383:\",\n              np.round(s[[40,60,80,100,150,200,300,383]],3))\n\ndef head(l,j):\n    sl=slice(j*64,(j+1)*64)\n    w=W[f\"ln1_w.{l}\"].astype(float)\n    q=W[f\"W_q.{l}\"][sl].astype(float)*w\n    k=W[f\"W_k.{l}\"][sl].astype(float)*w\n    v=W[f\"W_v.{l}\"][sl].astype(float)*w\n    o=W[f\"W_o.{l}\"][:,sl].astype(float)\n    return q.T@k,o@v\n\naa=[head(0,j)[0] for j in range(6)]\nbb=[head(0,j)[1] for j in range(6)]\nprint(\"\\nL0 OV matrix cosine similarities:\")\nprint(np.round([[np.sum(x*y)/(la.norm(x)*la.norm(y)) for y in bb] for x in bb],3))\nprint(\"L0 QK matrix cosine similarities:\")\nprint(np.round([[np.sum(x*y)/(la.norm(x)*la.norm(y)) for y in aa] for x in aa],3))\n\nprint(\"\\nL0H2 unweighted QK singular values:\")\nq=W[\"W_q.0\"][128:192].astype(float)\nk=W[\"W_k.0\"][128:192].astype(float)\nu,s,vt=la.svd(q.T@k,full_matrices=False)\nprint(np.round(s[:48],3))\np=la.orth(np.column_stack((u[:,:20],vt[:20].T)))\nprint(\"L0 raw Q/K/V energy in this subspace:\")\nfor j in range(6):\n    print(j, np.round([la.norm(W[f\"{name}.0\"][64*j:64*(j+1)]@p)**2/\n                       la.norm(W[f\"{name}.0\"][64*j:64*(j+1)])**2\n                       for name in [\"W_q\",\"W_k\",\"W_v\"]],4))\n\nprint(\"\\nL1 key-bias weight directions and L0 OV outputs\")\nfor j in range(6):\n    sl=slice(j*64,(j+1)*64)\n    q=W[\"W_q.1\"][sl].astype(float)\n    k=W[\"W_k.1\"][sl].astype(float)\n    r=(k*W[\"ln1_w.1\"]).T@(q@W[\"ln1_b.1\"])\n    vals=[]\n    for b in bb:\n        vals.append(la.norm(r@b)/(la.norm(r)*la.norm(b)))\n    print(j,np.round(vals,4))\n\nprint(\"\\nLinear-algebra-only MLP products: normalized trace with later QK\")\n# These are matrix products, not MLP evaluations: there is no ReLU or input.\nmats={}\nfor l in range(3):\n    f=W[f\"W_fc.{l}\"].astype(float)*W[f\"ln2_w.{l}\"]\n    mats[l]=W[f\"W_proj.{l}\"].astype(float)@f\nfor l in range(1,4):\n    for j in range(6):\n        a,b=head(l,j)\n        print(f\"L{l}H{j}\",\n              np.round([np.trace(a@mats[m])/(la.norm(a)*la.norm(mats[m]))\n                        for m in range(l)],4))\n```\n"}}
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