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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\nfrom scipy.stats import skew\nfrom sklearn.decomposition import FastICA\nfrom threadpoolctl import threadpool_limits\nthreadpool_limits(limits=2)\n\nd=384\nP=np.eye(d)-np.ones((d,d))/d\nrs=[]\nfor h in [1,5]:\n    _,_,r=svd(np.asarray(W[\"W_v.0\"][64*h:64*(h+1)],float)@P,full_matrices=False)\n    rs.append(r[:28])\nG=sum(r.T@r for r in rs)\ne,u=np.linalg.eigh(G)\nu=u[:,np.argsort(e)[::-1][:28]]\nF=np.asarray(W[\"W_fc.0\"],float)*W[\"ln2_w.0\"][None,:]\nica=FastICA(n_components=28,whiten=\"unit-variance\",random_state=17,max_iter=4000,tol=.001)\nZ=ica.fit_transform(F@u)\nsg=np.where(skew(Z,axis=0)>=0,1.,-1.)\nmix=ica.mixing_*sg[None,:]\nT=u@np.linalg.pinv(mix.T)\n\n# These are coefficients of MLP WEIGHT rows in weight-derived bases.\n# No LayerNorm, attention distribution, or nonlinear MLP is evaluated.\nC=F@T\nC-=C.mean(0)\nprev=[]\nfor h in [1,5]:\n    s=slice(64*h,64*(h+1))\n    b=np.asarray(W[\"W_o.0\"][:,s],float)@(\n        np.asarray(W[\"W_v.0\"][s],float)*W[\"ln1_w.0\"][None,:])@P\n    R=F@b@T\n    R-=R.mean(0)\n    R/=np.std(R,axis=0,keepdims=True)\n    prev.append(R)\nC/=np.std(C,axis=0,keepdims=True)\n\nfor name,R in [(\"current\",C),(\"H1 route\",prev[0]),(\"H5 route\",prev[1])]:\n    strength=np.abs(R)\n    ids=np.argmax(strength,axis=1)\n    top=np.max(strength,axis=1)\n    counts=np.bincount(ids[top>1.5],minlength=28)\n    print(name,\"dominant-axis counts (>1.5 SD):\",counts.tolist())\n\nprint(\"\\nWeight-row co-specialization: current axis versus H5-route axis\")\nprint(\"Rows count neurons with both dominant coefficients >1.5 SD; positive coefficient fraction is also shown.\")\nci=np.argmax(np.abs(C),axis=1)\nri=np.argmax(np.abs(prev[1]),axis=1)\ncm=np.max(np.abs(C),axis=1)\nrm=np.max(np.abs(prev[1]),axis=1)\nsel=(cm>1.5)&(rm>1.5)\ncounts=np.zeros((28,28),dtype=int)\nfor n in np.where(sel)[0]:\n    counts[ci[n],ri[n]]+=1\nprint(\"Selected neurons\",int(sel.sum()),\"positive current/route fractions\",\n      round(np.mean(C[np.where(sel)[0],ci[sel]]>0),3),\n      round(np.mean(prev[1][np.where(sel)[0],ri[sel]]>0),3))\nfor k in range(28):\n    ix=np.argsort(counts[k])[::-1][:6]\n    print(k,\"rowtotal\",int(counts[k].sum()),\n          [(int(j),int(counts[k,j])) for j in ix if counts[k,j]])\n\n# Shared low-dimensional attention-weight structure, independent of the ICA.\nA={};B={}\nfor l in range(4):\n    scale=np.asarray(W[f\"ln1_w.{l}\"],float)\n    for h in range(6):\n        s=slice(64*h,64*(h+1))\n        q,k,v=[np.asarray(W[f\"W_{n}.{l}\"][s],float) for n in [\"q\",\"k\",\"v\"]]\n        A[l,h]=P@(scale[:,None]*(q.T@k)*scale[None,:])@P\n        B[l,h]=np.asarray(W[f\"W_o.{l}\"][:,s],float)@(v*scale[None,:])@P\nub,sb,vb=svd(B[0,4],full_matrices=False)\nprint(\"\\nL0H4 effective OV singular values:\",np.round(sb[:12],3))\nfor rank in [2,3,6]:\n    U=ub[:,:rank]\n    print(\"Rank\",rank,\"L0H4 output subspace: later QK query/key energy fractions\")\n    for l in range(1,4):\n        print(\"layer\",l,[\n            (h,round(np.linalg.norm(U.T@A[l,h])**2/np.linalg.norm(A[l,h])**2,3),\n             round(np.linalg.norm(A[l,h]@U)**2/np.linalg.norm(A[l,h])**2,3))\n            for h in range(6)])\n```"}}
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