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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 scipy.stats import skew, kurtosis\nfrom sklearn.cluster import KMeans\nfrom sklearn.decomposition import FastICA\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\")\n\nwith threadpool_limits(limits=2):\n    print(\"MLP NEURON NORM QUANTILES: input row / output column\")\n    for l in range(4):\n        f=np.asarray(W[f\"W_fc.{l}\"],dtype=float)\n        p=np.asarray(W[f\"W_proj.{l}\"],dtype=float)\n        print(l,np.percentile(la.norm(f,axis=1),[0,5,25,50,75,95,100]),\n              np.percentile(la.norm(p,axis=0),[0,5,25,50,75,95,100]))\n\n    print(\"\\nLAST MLP OUTPUT-COLUMN GEOMETRY\")\n    P=np.asarray(W[\"W_proj.3\"],dtype=float).T\n    norms=la.norm(P,axis=1)\n    Z=P/norms[:,None]\n    gram=Z@Z.T\n    np.fill_diagonal(gram,-2)\n    print(\"nearest cosine percentiles:\",np.percentile(gram.max(axis=1),[0,10,25,50,75,90,99,100]))\n    for n in (20,24,28,32):\n        km=KMeans(n_clusters=n,n_init=5,random_state=0,max_iter=200).fit(Z)\n        sizes=np.bincount(km.labels_,minlength=n)\n        c_norm=la.norm(km.cluster_centers_,axis=1)\n        order=np.argsort(-sizes)\n        print(\"k\",n,\"inertia\",round(km.inertia_,3))\n        print(\"cluster sizes\",sizes[order])\n        print(\"centroid norms\",np.round(c_norm[order],3))\n\n    print(\"\\nINDEPENDENT-COMPONENT DECOMPOSITION OF OUTPUT WEIGHT COLUMNS\")\n    for nc in (24,28):\n        ica=FastICA(n_components=nc,whiten=\"unit-variance\",random_state=0,max_iter=1500,tol=1e-4)\n        S=ica.fit_transform(P)\n        kur=kurtosis(S,axis=0)\n        sk=skew(S,axis=0)\n        ix=np.argsort(-kur)\n        print(\"components\",nc,\"iterations\",ica.n_iter_)\n        print(\"excess kurtoses\",np.round(kur[ix],3))\n        print(\"absolute skewness\",np.round(abs(sk[ix]),3))\n\n    print(\"\\nINDUCTION-CANDIDATE MATRIX EIGENVALUES\")\n    g0=np.asarray(W[\"ln1_w.0\"],dtype=float)\n    b=(np.asarray(W[\"W_o.0\"][:,128:192],dtype=float)@np.asarray(W[\"W_v.0\"][128:192],dtype=float))*g0\n    g3=np.asarray(W[\"ln1_w.3\"],dtype=float)\n    q=np.asarray(W[\"W_q.3\"][64:128],dtype=float)*g3\n    k=np.asarray(W[\"W_k.3\"][64:128],dtype=float)*g3\n    a=q.T@k/8\n    _,_,vt=svd(b)\n    T=vt[:64].T\n    c=T.T@a@b@T\n    e=la.eigvals(c)\n    print(\"eigenvalues descending magnitude\",np.round(e[np.argsort(-abs(e))],4))\n    print(\"symmetric-part eigenvalues descending\",np.round(la.eigvalsh((c+c.T)/2)[::-1],4))\n```"}}
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