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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, eigvals\nfrom threadpoolctl import threadpool_limits\n\nwith threadpool_limits(limits=4):\n    g = W[\"ln1_w.0\"].astype(float)\n    A, B, decomps = [], [], []\n    for j in range(6):\n        sl = slice(64*j,64*(j+1))\n        q = W[\"W_q.0\"][sl].astype(float)*g\n        k = W[\"W_k.0\"][sl].astype(float)*g\n        v = W[\"W_v.0\"][sl].astype(float)*g\n        q -= q.mean(1,keepdims=True)\n        k -= k.mean(1,keepdims=True)\n        v -= v.mean(1,keepdims=True)\n        A.append(q.T@k/8)\n        B.append(W[\"W_o.0\"][:,sl].astype(float)@v)\n        decomps.append(svd(A[-1], full_matrices=False))\n    print(\"Layer 0 scaled QK: symmetric-energy fraction, positive/negative eigenvalue sums of symmetric part\")\n    for j,a in enumerate(A):\n        sym = (a+a.T)/2\n        ev = np.linalg.eigvalsh(sym)\n        z = eigvals(a)\n        z = z[np.argsort(abs(z))[::-1]][:24]\n        print(\"H\", j, np.round([np.linalg.norm(sym)**2/np.linalg.norm(a)**2,\n                               ev[ev>0].sum(),ev[ev<0].sum()],4))\n        print(\"eigenvalues:\", np.round(z,4))\n\n    print(\"\\nFraction of each OV's squared norm captured by QK H3 right/left subspaces\")\n    u,s,vt = decomps[3]\n    for r in (4,8,16,24,32,48):\n        print(\"rank\", r,\n              \"key\", np.round([np.linalg.norm(b@vt[:r].T)**2/np.linalg.norm(b)**2 for b in B],3),\n              \"query\", np.round([np.linalg.norm(b@u[:,:r])**2/np.linalg.norm(b)**2 for b in B],3))\n\n    print(\"\\nOwn-head QK/OV subspace overlaps (r=1,4,8,16,24):\")\n    for j in range(6):\n        u,s,vt=decomps[j]\n        _,sb,vb=svd(B[j],full_matrices=False)\n        vals=[]\n        for r in (1,4,8,16,24):\n            vals.append([np.linalg.norm(u[:,:r].T@vb[:r].T)**2/r,\n                         np.linalg.norm(vt[:r]@vb[:r].T)**2/r])\n        print(\"H\",j,np.round(vals,3))\n\n    print(\"\\nLayer 0 cross-head subspace overlap: top 8 query and key directions\")\n    for which in (\"query\",\"key\"):\n        bases=[z[0][:,:8] if which==\"query\" else z[2][:8].T for z in decomps]\n        print(which, np.round([[np.linalg.norm(a.T@b)**2/8 for b in bases] for a in bases],3))\n\n    print(\"\\nQK H3 singular-vector pair cosines:\")\n    u,s,vt=decomps[3]\n    print(np.round(np.diag(vt[:32]@u[:,:32]),3))\n    print(\"SV\",np.round(s[:40],4))\n    print(\"\\nL0 LN scale largest and smallest coordinates:\")\n    for ix in (np.argsort(g)[-24:][::-1],np.argsort(g)[:24]):\n        print(list(zip(ix.tolist(),np.round(g[ix],4).tolist())))\n```\n"}}
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