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{"type":"item.completed","item":{"id":"item_1","type":"agent_message","text":"```python\nimport numpy as np\nfrom scipy.linalg import svd\nfrom sklearn.cluster import KMeans\nfrom sklearn.metrics import silhouette_score, adjusted_mutual_info_score\nfrom threadpoolctl import threadpool_limits\nthreadpool_limits(4)\n\ng1 = W[\"ln1_w.0\"].astype(float)\ng2 = W[\"ln2_w.0\"].astype(float)\nv1 = W[\"W_v.0\"][64:128].astype(float)\nv5 = W[\"W_v.0\"][320:384].astype(float)\no5 = W[\"W_o.0\"][:,320:384].astype(float)\nfc = W[\"W_fc.0\"].astype(float)*g2\n\nfor j in range(6):\n    s = np.linalg.svd(W[\"W_v.0\"][64*j:64*(j+1)].astype(float),compute_uv=False)\n    print(\"L0H%d raw V spectrum:\"%j,np.round(s[:40],3))\n\n# These are weight subspaces and products, not token representations or activations.\n_,s,vt = svd(np.concatenate([v1,v5]),full_matrices=False)\nprint(\"Joint raw V1,V5 spectrum:\",np.round(s[:50],3))\nB = vt[:28].T / g1[:,None]\nB -= B.mean(axis=0,keepdims=True)\nB,_ = np.linalg.qr(B)\nC5 = o5 @ (v5*g1)\nC5 -= C5.mean(axis=0,keepdims=True)\n\ncurrent = fc@B\npreceding = fc@C5@B\ndef whiten_columns(x, rank=27):\n    x=x-x.mean(axis=0,keepdims=True)\n    u,s,vt=svd(x,full_matrices=False)\n    return u[:,:rank]*np.sqrt(x.shape[0]),s\n\nlabels=[]\nfor title,x in [(\"current-weight coefficients\",current),(\"preceding-weight coefficients\",preceding)]:\n    z,s=whiten_columns(x)\n    print(\"\\n\",title,\"spectrum\",np.round(s,3))\n    zn=z/(np.linalg.norm(z,axis=1,keepdims=True)+1e-12)\n    for nc in [5,10,20,28,35,50]:\n        km=KMeans(n_clusters=nc,n_init=10,random_state=0).fit(zn)\n        sil=silhouette_score(zn,km.labels_,sample_size=1000,random_state=0)\n        centers=km.cluster_centers_\n        cos=np.sum(zn*centers[km.labels_],axis=1)/(np.linalg.norm(centers[km.labels_],axis=1)+1e-12)\n        print(\"K\",nc,\"silhouette\",round(sil,4),\"median member-center cosine\",round(np.median(cos),4),\n              \"sizes\",np.sort(np.bincount(km.labels_))[::-1])\n        if nc==28:\n            labels.append(km.labels_)\n            near=(centers/np.linalg.norm(centers,axis=1,keepdims=True))@(\n                centers/np.linalg.norm(centers,axis=1,keepdims=True)).T\n            pairs=sorted([(near[a,b],a,b) for a in range(nc) for b in range(a)],reverse=True)\n            print(\"closest cluster pairs:\",[(round(c,3),a,b) for c,a,b in pairs[:15]])\nprint(\"\\nMutual information between the two 28-way weight clusterings:\",\n      adjusted_mutual_info_score(labels[0],labels[1]))\nprint(\"Cross-cluster count matrix:\")\ntable=np.zeros((28,28),dtype=int)\nnp.add.at(table,(labels[0],labels[1]),1)\nfor row in table:\n    print(\" \".join(map(str,row)))\n```\n"}}
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