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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, kurtosis\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,:]\nO=np.asarray(W[\"W_proj.0\"],float)\nX=F@u\nica=FastICA(n_components=28,whiten=\"unit-variance\",random_state=17,\n            max_iter=4000,tol=.001)\nZ=ica.fit_transform(X)\nsg=np.where(skew(Z,axis=0)>=0,1.,-1.)\nZ*=sg\nmix=ica.mixing_*sg[None,:]\nprint(\"ICA component: kurtosis, dominant row and its coefficient, top-five row indices, output-column norm\")\nfor k in range(28):\n    ix=np.argsort(np.abs(Z[:,k]))[-5:][::-1]\n    print(k,round(kurtosis(Z[:,k]),1),int(ix[0]),round(Z[ix[0],k],2),\n          ix.tolist(),round(np.linalg.norm(O[:,ix[0]]),3))\n\nprint(\"\\nLargest initial MLP input row norms: row, full norm, content-projection norm, output-column norm\")\nix=np.argsort(np.linalg.norm(F,axis=1))[-40:][::-1]\nfor i in ix:\n    print(int(i),round(np.linalg.norm(F[i]),3),round(np.linalg.norm(X[i]),3),\n          round(np.linalg.norm(O[:,i]),3))\n\nprint(\"\\nCharacter-direction candidate geometry\")\ndirs=u@mix\ndirs/=np.linalg.norm(dirs,axis=0,keepdims=True)\ngram=dirs.T@dirs\nprint(\"Pairwise cosine quantiles:\",np.round(np.quantile(gram[np.triu_indices(28,1)],[0,.1,.25,.5,.75,.9,1]),3))\nfor k in range(28):\n    ix=np.argsort(gram[k])[-4:][::-1]\n    print(k,[(int(i),round(gram[k,i],3)) for i in ix if i!=k])\n\nprint(\"\\nContent-key geometry of L0H2, in the candidate direction basis\")\ns=slice(128,192)\na=np.asarray(W[\"W_q.0\"][s],float).T@np.asarray(W[\"W_k.0\"][s],float)\ng=dirs.T@a@dirs\ng/=np.linalg.norm(g)\nfor k in range(28):\n    ix=np.argsort(g[k])[-3:][::-1]\n    print(k,[(int(i),round(g[k,i],3)) for i in ix])\n```"}}
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