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{"type":"item.completed","item":{"id":"item_2","type":"agent_message","text":"```python\nimport numpy as np\nimport scipy.linalg as la\nfrom threadpoolctl import threadpool_limits\nnp.set_printoptions(precision=4,suppress=True,linewidth=180)\n\ndef svd(a):\n    return la.svd(a,full_matrices=False,lapack_driver=\"gesvd\")\ndef orth(a):\n    u,s,_=svd(a)\n    return u[:,s>s[0]*1e-8]\n\nwith threadpool_limits(limits=2):\n    F=np.asarray(W[\"W_fc.0\"],dtype=float)*W[\"ln2_w.0\"]\n    P=np.asarray(W[\"W_proj.0\"],dtype=float)\n    fn=la.norm(W[\"W_fc.0\"],axis=1)\n    pn=la.norm(P,axis=0)\n    active=(fn>0.7)&(pn>0.6)\n    print(\"L0 MLP substantial-weight neurons:\",int(active.sum()),\"of\",len(active))\n    print(\"Input-norm/output-norm correlation:\",np.corrcoef(fn,pn)[0,1])\n    g=np.asarray(W[\"ln1_w.0\"],dtype=float)\n    pos_weights=np.vstack([np.asarray(W[\"W_q.0\"][128:192],dtype=float)*g,\n                           np.asarray(W[\"W_k.0\"][128:192],dtype=float)*g])\n    _,_,vp=svd(pos_weights)\n    Bs=[]\n    for j in range(6):\n        sl=slice(j*64,j*64+64)\n        b=(np.asarray(W[\"W_o.0\"][:,sl],dtype=float)@np.asarray(W[\"W_v.0\"][sl],dtype=float))*g\n        Bs.append(b)\n    broad=svd(np.hstack([Bs[j] for j in (0,1,4,5)]))[0][:,:4]\n    other=svd(Bs[3])[0][:,:8]\n    prev=svd(Bs[2])[0]\n    V=np.asarray(W[\"W_v.0\"][128:192],dtype=float)*g\n\n    print(\"\\nRESIDUAL ROW SPECTRA AFTER REMOVING WEIGHT-DERIVED POSITION/WRITE DIRECTIONS\")\n    print(\"No token identities are assumed; these are orthogonal matrix projections.\")\n    for rp in (32,64,96):\n        for rv in (24,48):\n            N=orth(np.hstack([vp[:rp].T,broad,other,prev[:,:rv]]))\n            Fc=F[active]-(F[active]@N)@N.T\n            Vc=V-(V@N)@N.T\n            sf=svd(Fc)[1]\n            sv=svd(Vc)[1]\n            print(f\"posrank={rp}, prevrank={rv}, removedrank={N.shape[1]}\")\n            print(\"F spectrum\",sf[:45])\n            print(\"V spectrum\",sv[:40])\n            _,_,tf=svd(Fc)\n            _,_,tv=svd(Vc)\n            cc=la.svdvals(tf[:28]@tv[:28].T)\n            print(\"principal cosines between top-28 current/previous read spaces\",cc)\n\n    print(\"\\nACTIVE MLP ROW SIMILARITIES\")\n    A=F[active]/la.norm(F[active],axis=1)[:,None]\n    G=A@A.T\n    np.fill_diagonal(G,-2)\n    print(\"nearest cosine percentiles\",np.percentile(G.max(axis=1),[0,10,25,50,75,90,99,100]))\n```"}}
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