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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, svdvals\nfrom sklearn.cluster import KMeans\nfrom threadpoolctl import threadpool_limits\nnp.set_printoptions(precision=3, suppress=True, linewidth=180)\n\nwith threadpool_limits(limits=4):\n    print(\"L0H2 FACTOR SPECTRA\")\n    for name, a in [\n        (\"Q\",W[\"W_q.0\"][128:192]),(\"K\",W[\"W_k.0\"][128:192]),\n        (\"V\",W[\"W_v.0\"][128:192]),(\"O\",W[\"W_o.0\"][:,128:192])\n    ]:\n        print(name,svdvals(a))\n    print(\"\\nLATE PROJECTION SPECTRA\")\n    for l in range(4):\n        a=W[f\"W_proj.{l}\"]\n        ss=svdvals(a)\n        print(\"layer\",l,\"top 50\",ss[:50],\n              \"energy top 16/24/28/32/64/128\",\n              np.array([np.sum(ss[:r]**2)/np.sum(ss**2) for r in [16,24,28,32,64,128]]))\n    print(\"\\nL0 EFFECTIVE MLP INPUT VS EARLY VALUE SUBSPACES\")\n    f=W[\"W_fc.0\"]*W[\"ln2_w.0\"]\n    f=f-f.mean(1,keepdims=True)\n    b=(W[\"W_o.0\"][:,128:192]@W[\"W_v.0\"][128:192])*W[\"ln1_w.0\"]\n    b=b-b.mean(0,keepdims=True)-b.mean(1,keepdims=True)+b.mean()\n    print(\"F spectrum\",svdvals(f)[:50])\n    print(\"F @ B02 spectrum\",svdvals(f@b)[:50])\n    print(\"\\nL0 MLP ROW COSINE CLUSTERING (weight directions, not activations)\")\n    for label, a in [(\"F\",f),(\"F_B02\",f@b)]:\n        u,ss,vh=svd(a,full_matrices=False)\n        z=u[:,:32]*ss[:32]\n        norms=np.linalg.norm(z,axis=1)\n        z=z/np.maximum(norms[:,None],1e-10)\n        sim=z@z.T\n        np.fill_diagonal(sim,-2)\n        print(label, \"nearest cosine quantiles\",np.quantile(sim.max(1),[0,.1,.25,.5,.75,.9,1]))\n        for n in [16,20,24,28,32]:\n            km=KMeans(n_clusters=n,n_init=5,random_state=0,max_iter=200).fit(z)\n            counts=np.bincount(km.labels_,minlength=n)\n            print(label,\"clusters\",n,\"inertia\",round(km.inertia_,2),\"counts\",np.sort(counts)[::-1])\n    print(\"\\nSHARED LOW-RANK L1 QK STRUCTURE\")\n    mats=[]\n    kb=[]\n    for j in range(6):\n        s=slice(64*j,64*(j+1))\n        q,k=W[\"W_q.1\"][s]*W[\"ln1_w.1\"],W[\"W_k.1\"][s]*W[\"ln1_w.1\"]\n        q=q-q.mean(1,keepdims=True)\n        k=k-k.mean(1,keepdims=True)\n        mats.append(q.T@k/8)\n        kb.append(k.T@(W[\"W_q.1\"][s]@W[\"ln1_b.1\"])/8)\n    def cos_table(a):\n        a=np.array([x.ravel() for x in a])\n        a=a/np.linalg.norm(a,axis=1,keepdims=True)\n        return a@a.T\n    print(\"QK cosines\\n\",cos_table(mats))\n    print(\"key-bias cosines\\n\",cos_table(kb))\n```\n"}}
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