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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, svdvals\nfrom threadpoolctl import threadpool_limits\n\nwith threadpool_limits(limits=2):\n    print(\"Last-layer output singular spectra (indices start at 1)\")\n    for name in [\"W_proj.3\",\"W_o.3\",\"W_proj.0\"]:\n        s=svdvals(W[name].astype(float))\n        print(name)\n        for start in range(0,80,20):\n            print(start+1, np.round(s[start:start+20],3))\n    T=np.concatenate([W[\"W_o.3\"],W[\"W_proj.3\"]],axis=1).astype(float)\n    u,s,vt=svd(T,full_matrices=False)\n    print(\"Combined final output spectrum\",np.round(s[:70],3))\n    print(\"Adjacent spectral ratios\",[(i+1,round(s[i]/s[i+1],3))\n          for i in np.argsort(s[:60]/s[1:61])[-12:][::-1]])\n    print(\"\\nL0 OV dominant input/output directions: largest coordinate loadings\")\n    for j in [0,1,2,3,4,5]:\n        sl=slice(64*j,64*j+64)\n        v=W[\"W_v.0\"][sl].astype(float)*W[\"ln1_w.0\"]\n        v-=v.mean(1,keepdims=True)\n        o=W[\"W_o.0\"][:,sl].astype(float)\n        uu,ss,vv=svd(o@v,full_matrices=False)\n        print(\"H\",j)\n        for r in range(2):\n            for tag,direction in [(\"in\",vv[r]),(\"out\",uu[:,r])]:\n                ix=np.argsort(np.abs(direction))[-6:][::-1]\n                print(r,tag,[(int(i),round(direction[i],3)) for i in ix],\n                      \"participation\",round(1/np.sum(direction**4),1))\n    print(\"\\nFinal output common-subspace concentration\")\n    for r in [20,22,24,26,27,28,32,40]:\n        U=u[:,:r]\n        vals=[]\n        for l in range(4):\n            p=W[f\"W_proj.{l}\"].astype(float)\n            vals.append(np.linalg.norm(U.T@p)**2/np.linalg.norm(p)**2)\n        print(\"rank\",r,\"MLP projection energy L0..L3\",np.round(vals,3))\n    print(\"\\nLayer0 FC input spectrum, additional indices\")\n    f=W[\"W_fc.0\"].astype(float)*W[\"ln2_w.0\"]\n    s=svdvals(f)\n    for start in range(0,100,20):\n        print(start+1,np.round(s[start:start+20],3))\n```\n"}}
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