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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 threadpoolctl import threadpool_limits\nnp.set_printoptions(precision=4, suppress=True, linewidth=160)\n\nwith threadpool_limits(limits=4):\n    print(\"EARLY READ-SUBSPACE SEPARATION\")\n    for gained in [False,True]:\n        g=W[\"ln1_w.0\"] if gained else np.ones(384)\n        posmat=np.vstack([W[\"W_q.0\"][128:192]*g,W[\"W_k.0\"][128:192]*g])\n        valmat=W[\"W_v.0\"][128:192]*g\n        posmat-=posmat.mean(1,keepdims=True)\n        valmat-=valmat.mean(1,keepdims=True)\n        p=svd(posmat,full_matrices=False)[2][:32].T\n        t=svd(valmat,full_matrices=False)[2][:24].T\n        print(\"gains\",gained,\"position/value overlap\",np.linalg.norm(p.T@t)**2/24)\n        for j in range(6):\n            s=slice(j*64,(j+1)*64)\n            b=(W[\"W_o.0\"][:,s]@W[\"W_v.0\"][s])*g\n            b=b-b.mean(1,keepdims=True)\n            q=W[\"W_q.0\"][s]*g\n            k=W[\"W_k.0\"][s]*g\n            q=q-q.mean(1,keepdims=True)\n            k=k-k.mean(1,keepdims=True)\n            u,ss,vh=svd(q.T@k/8,full_matrices=False)\n            dirs={\"QK_left1\":u[:,0],\"QK_right1\":vh[0],\n                  \"OV_row222\":b[222],\"OV_row78\":b[78],\"OV_row72\":b[72]}\n            vals=[]\n            for name,z in dirs.items():\n                z=z/np.linalg.norm(z)\n                vals.append((name,round(float(np.linalg.norm(p.T@z)**2),3),\n                             round(float(np.linalg.norm(t.T@z)**2),3)))\n            print(f\"L0H{j}\",\"direction, pos-overlap, value-overlap:\",vals)\n    print(\"\\nL0 SHARED-REGISTER READ-DIRECTION SIMILARITY\")\n    for coord in [72,78,222]:\n        reads=[]\n        for j in [0,1,3,4,5]:\n            s=slice(j*64,(j+1)*64)\n            row=W[\"W_o.0\"][coord,s]@W[\"W_v.0\"][s]\n            reads.append(row/np.linalg.norm(row))\n        z=np.stack(reads)\n        print(\"coord\",coord,\"heads [0,1,3,4,5]\\n\",z@z.T)\n```\n"}}
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