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{"type":"item.completed","item":{"id":"item_2","type":"agent_message","text":"```python\nimport numpy as np\nfrom sklearn.cluster import KMeans\nfrom sklearn.metrics import silhouette_score\nfrom threadpoolctl import threadpool_limits\nthreadpool_limits(2)\nnp.set_printoptions(precision=3,suppress=True,linewidth=180)\n\nd=384\nP=np.eye(d)-np.ones((d,d))/d\ndef products(l,h):\n    s=slice(64*h,64*(h+1))\n    g=W[f\"ln1_w.{l}\"].astype(float)\n    q,k,v=[(W[f\"W_{t}.{l}\"][s].astype(float)*g)@P for t in [\"q\",\"k\",\"v\"]]\n    return q.T@k/8, P@W[f\"W_o.{l}\"][:,s].astype(float)@v\na02,b02=products(0,2)\na31,b31=products(3,1)\nc=a31@b02\nev,u=np.linalg.eigh((c+c.T)/2)\nT=u[:,np.argsort(ev)[::-1][:24]]\n\nf=(W[\"W_fc.0\"].astype(float)*W[\"ln2_w.0\"])@P\no=P@W[\"W_proj.0\"].astype(float)\nX=f@T\nY=f@b02@T\nnx=np.linalg.norm(X,axis=1)\nny=np.linalg.norm(Y,axis=1)\non=np.linalg.norm(o,axis=0)\nprint(\"First-MLP output-column norm quantiles\",\n      np.quantile(on,[0,.1,.25,.5,.75,.9,.99,1]))\nprint(\"First-MLP current/previous/output norm correlations\",\n      np.corrcoef(np.stack([nx,ny,on])))\nprint(\"Number of neurons above current-read thresholds\",\n      [(t,int(np.sum(nx>t))) for t in [.1,.2,.3,.5,1]])\nprint(\"Number above previous-read thresholds\",\n      [(t,int(np.sum(ny>t))) for t in [.05,.1,.2,.3,.5]])\n\n# Cluster weight directions only. No nonlinear layer is evaluated.\nfor whiten in [False,True]:\n    C=np.concatenate([X[nx>.3],Y[ny>.15]],axis=0)\n    if whiten:\n        cov=C.T@C/len(C)\n        e,v=np.linalg.eigh(cov)\n        D=(v*(1/np.sqrt(np.maximum(e,.01*e.max()))))@v.T\n    else:\n        D=np.eye(24)\n    xx=X@D; yy=Y@D\n    xx=xx/np.maximum(np.linalg.norm(xx,axis=1,keepdims=True),1e-12)\n    yy=yy/np.maximum(np.linalg.norm(yy,axis=1,keepdims=True),1e-12)\n    Z=np.concatenate([xx[nx>.3],yy[ny>.15]],axis=0)\n    gram=Z@Z.T\n    np.fill_diagonal(gram,-1)\n    print(\"\\nWhiten\",whiten,\"samples\",len(Z),\n          \"nearest-other cosine quantiles\",np.quantile(gram.max(axis=1),[0,.1,.5,.9,1]))\n    for k in [16,20,24,28,32,40]:\n        km=KMeans(n_clusters=k,n_init=10,random_state=0).fit(Z)\n        centers=km.cluster_centers_\n        centers/=np.maximum(np.linalg.norm(centers,axis=1,keepdims=True),1e-12)\n        sim=Z@centers.T\n        print(\"K\",k,\"mean best cosine\",round(sim.max(axis=1).mean(),3),\n              \"silhouette\",round(silhouette_score(Z,km.labels_,metric=\"cosine\"),3),\n              \"sorted counts\",np.sort(np.bincount(km.labels_))[::-1])\n        if k==24:\n            sx=xx@centers.T; sy=yy@centers.T\n            ix=sx.argmax(axis=1); iy=sy.argmax(axis=1)\n            good=(nx>.3)&(ny>.15)&(sx.max(axis=1)>.65)&(sy.max(axis=1)>.65)\n            counts=np.zeros((k,k))\n            for i in np.where(good)[0]:\n                counts[iy[i],ix[i]]+=1\n            print(\"paired clear weight directions:\",int(good.sum()))\n            print(\"nonzero previous/current cluster pairs:\",\n                  [(int(i),int(j),int(counts[i,j])) for i,j in zip(*np.where(counts>=2))])\n            if counts.sum()>0:\n                adj=counts+counts.T\n                deg=adj.sum(axis=1)\n                norm=adj/np.sqrt(np.maximum(deg[:,None]*deg[None,:],1))\n                print(\"symmetric normalized graph eigenvalues\",\n                      np.linalg.eigvalsh(norm))\n```"}}
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