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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 sklearn.cluster import KMeans\nfrom threadpoolctl import threadpool_limits\nthreadpool_limits(limits=2)\nnp.set_printoptions(precision=3, suppress=True, linewidth=160)\n\ndef ov0(j):\n    sl=slice(64*j,64*(j+1))\n    v=W[\"W_v.0\"][sl].astype(float)*W[\"ln1_w.0\"][None,:]\n    v-=v.mean(axis=1,keepdims=True)\n    o=W[\"W_o.0\"][:,sl].astype(float)\n    o-=o.mean(axis=0,keepdims=True)\n    return o@v\n\nb=ov0(5)\nT=svd(b,full_matrices=False,check_finite=False)[2][:27].T\nf=W[\"W_fc.0\"].astype(float)*W[\"ln2_w.0\"][None,:]\nf-=f.mean(axis=1,keepdims=True)\nactive=np.linalg.norm(W[\"W_fc.0\"],axis=1)>1\nf=f[active]\ndirect=f@T\ntransported=f@b@T\ndn=np.linalg.norm(direct,axis=1)\npn=np.linalg.norm(transported,axis=1)\ndu=direct/dn[:,None]\npu=transported/pn[:,None]\n\n# Cluster the two sets of MLP weight covectors jointly, without evaluating\n# any neuron or feeding a representation into the model.\nz=np.concatenate([du,pu])\nkm=KMeans(n_clusters=28,n_init=20,max_iter=300,random_state=42).fit(z)\ncenters=km.cluster_centers_\ncenters/=np.linalg.norm(centers,axis=1,keepdims=True)\ndc=du@centers.T\npc=pu@centers.T\ndi=dc.argmax(axis=1); pi=pc.argmax(axis=1)\nds=dc.max(axis=1); ps=pc.max(axis=1)\nprint(\"Direct best-center cosine quantiles:\",np.quantile(ds,[0,.1,.25,.5,.75,.9,1]))\nprint(\"Transported best-center cosine quantiles:\",np.quantile(ps,[0,.1,.25,.5,.75,.9,1]))\nprint(\"Weight norm quantiles direct / transported:\",np.quantile(dn,[.1,.5,.9]),np.quantile(pn,[.1,.5,.9]))\nprint(\"Cluster: direct count, transported count, direct/transported mean best cosine\")\nfor c in range(28):\n    print(c,np.sum(di==c),np.sum(pi==c),\n          round(float(ds[di==c].mean()),3) if np.any(di==c) else None,\n          round(float(ps[pi==c].mean()),3) if np.any(pi==c) else None)\n\nfor threshold in [.60,.75]:\n    good=(ds>threshold)&(ps>threshold)\n    counts=np.zeros((28,28),dtype=int)\n    np.add.at(counts,(pi[good],di[good]),1)\n    print(\"\\nThreshold\",threshold,\"paired neurons\",good.sum(),\"nonzero directed pairs\",np.count_nonzero(counts),\n          \"diagonal count\",np.trace(counts))\n    for c in range(28):\n        targets=np.argsort(-counts[c])[:5]\n        print(c,[(int(t),int(counts[c,t])) for t in targets if counts[c,t]])\n\nprint(\"\\nDirect versus transported directions of the SAME neuron, cosine quantiles:\",\n      np.quantile(np.sum(du*pu,axis=1),[0,.1,.25,.5,.75,.9,1]))\nprint(\"Cluster-center cosine matrix, rounded:\")\nprint(np.round(centers@centers.T,1))\n```\n"}}
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