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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 sklearn.cluster import KMeans\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\")\ndef normrows(a):\n    return a / np.maximum(la.norm(a,axis=1,keepdims=True),1e-12)\n\nwith threadpool_limits(limits=2):\n    g = np.asarray(W[\"ln1_w.0\"], dtype=float)\n    q = np.asarray(W[\"W_q.0\"][128:192],dtype=float)*g\n    k = np.asarray(W[\"W_k.0\"][128:192],dtype=float)*g\n    _,ps,pvt = svd(np.vstack([q,k]))\n    pos = pvt[:32].T\n    print(\"L0H2 stacked Q/K spectrum:\",ps[:48])\n    vv,oo,bb=[],[],[]\n    print(\"\\nL0 OV PRODUCTS\")\n    for j in range(6):\n        sl=slice(j*64,(j+1)*64)\n        b=(np.asarray(W[\"W_o.0\"][:,sl],dtype=float) @ np.asarray(W[\"W_v.0\"][sl],dtype=float))*g\n        u,s,vt=svd(b)\n        vv.append(vt[:4].T); oo.append(u[:4]); bb.append(b)\n        print(f\"H{j}: top_s={s[:8]}, top2_energy={sum(s[:2]**2)/sum(s*s):.4f}, \"\n              f\"top2_input_overlap_QK32={la.norm(pos.T@vt[:2].T)**2/2:.4f}\")\n        for side,vec in ((\"read\",vt[0]),(\"write\",u[:,0])):\n            ix=np.argsort(-abs(vec))[:8]\n            print(side, list(zip(ix.tolist(),np.round(vec[ix],4).tolist())))\n    print(\"Input top-2 subspace overlaps:\")\n    print(np.array([[la.norm(vv[i][:,:2].T@vv[j][:,:2])**2/2 for j in range(6)] for i in range(6)]))\n    print(\"Output top-2 subspace overlaps:\")\n    print(np.array([[la.norm(oo[i][:,:2].T@oo[j][:,:2])**2/2 for j in range(6)] for i in range(6)]))\n\n    print(\"\\nL0 MLP ROW GEOMETRY\")\n    f=np.asarray(W[\"W_fc.0\"],dtype=float)*W[\"ln2_w.0\"]\n    for name,a in ((\"F\",f),(\"F_times_OV_H2\",f@bb[2])):\n        a=normrows(a)\n        gram=a@a.T\n        np.fill_diagonal(gram,-2)\n        print(name,\"nearest cosine percentiles\",np.percentile(gram.max(axis=1),[0,10,25,50,75,90,99,100]))\n        for n in (16,24,28,40):\n            km=KMeans(n_clusters=n,n_init=3,random_state=0,max_iter=150).fit(a)\n            sizes=np.bincount(km.labels_,minlength=n)\n            print(f\"k={n}: inertia={km.inertia_:.3f}, sizes={np.sort(sizes)[::-1]}\")\n\n    print(\"\\nMLP READ/WRITE PRODUCTS: spectra and trace (no ReLU)\")\n    for l in range(4):\n        f=np.asarray(W[f\"W_fc.{l}\"],dtype=float)*W[f\"ln2_w.{l}\"]\n        p=np.asarray(W[f\"W_proj.{l}\"],dtype=float)\n        a=p@f\n        s=la.svdvals(a)\n        print(f\"L{l}: norm={la.norm(a):.3f}, trcos={np.trace(a)/(la.norm(a)*np.sqrt(384)):.4f}, top_s={s[:10]}\")\n```"}}
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