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{"type":"item.completed","item":{"id":"item_1","type":"agent_message","text":"```python\nimport numpy as np\nimport torch\nfrom sklearn.cluster import DBSCAN\ntorch.set_num_threads(4)\ntorch.set_default_dtype(torch.float64)\nT=lambda a: torch.as_tensor(np.asarray(a),dtype=torch.float64)\nP=torch.eye(384)-torch.ones((384,384))/384\ng=T(W[\"ln1_w.0\"])\nvs={}\nbs={}\nfor j in [1,5]:\n    sl=slice(64*j,64*(j+1))\n    vs[j]=(T(W[\"W_v.0\"])[sl]*g)@P\n    bs[j]=P@T(W[\"W_o.0\"])[:,sl]@vs[j]\n_,u=torch.linalg.eigh(sum(v.T@v for v in vs.values()))\nu=u.flip(1)\nf=(T(W[\"W_fc.0\"])*T(W[\"ln2_w.0\"]))@P\nactive=np.linalg.norm(W[\"W_fc.0\"],axis=1)>.8\nids=np.flatnonzero(active)\n\nprint(\"Static MLP read-direction alignments for current / H5-value / H1-value channels.\")\nprint(\"These are products of weight matrices, with no inputs or nonlinearities.\")\nfor r in [20,28,40]:\n    z=u[:,:r]\n    arr=[(a@z).numpy()[active] for a in [f,f@bs[5],f@bs[1]]]\n    norms=[np.linalg.norm(a,axis=1) for a in arr]\n    nn=[a/(n[:,None]+1e-12) for a,n in zip(arr,norms)]\n    cs=np.stack([(nn[0]*nn[1]).sum(1),(nn[0]*nn[2]).sum(1),\n                 (nn[1]*nn[2]).sum(1)],1)\n    print(\"\\nrank\",r)\n    print(\"Channel norm quantiles\",np.round([np.quantile(n,[.1,.5,.9]) for n in norms],3))\n    print(\"Pair cosine quantiles\",np.round(np.quantile(cs,[.01,.1,.5,.9,.99],axis=0),3))\n    for threshold in [.5,.65,.8]:\n        mask=cs.min(1)>threshold\n        print(\"all-three pair cosines >\",threshold,\"count\",int(mask.sum()))\n    order=np.argsort(cs.min(1))[::-1][:15]\n    print(\"best same-direction neurons (index, 3 cosines, 3 norms):\")\n    for i in order:\n        print(int(ids[i]),np.round(cs[i],3).tolist(),\n              np.round([n[i] for n in norms],3).tolist())\n    if r==28:\n        selected=np.flatnonzero(cs.min(1)>.5)\n        if len(selected):\n            sim=nn[0][selected]@nn[0][selected].T\n            print(\"Similarities among strongest repeated-direction candidates:\")\n            print(np.round(sim[:20,:20],2))\n        for a,b,label in [(0,1,\"current/H5\"),(0,2,\"current/H1\"),(1,2,\"H5/H1\")]:\n            # Permutation baseline for row correspondence.\n            rng=np.random.default_rng(0)\n            baseline=np.sum(nn[a]*nn[b][rng.permutation(len(ids))],axis=1)\n            actual=np.sum(nn[a]*nn[b],axis=1)\n            print(label,\"actual/random mean\",\n                  round(float(actual.mean()),4),round(float(baseline.mean()),4),\n                  \"actual/random fraction > .65\",\n                  round(float((actual>.65).mean()),4),round(float((baseline>.65).mean()),4))\n```\n"}}
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