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{"type":"item.completed","item":{"id":"item_2","type":"agent_message","text":"```python\nimport numpy as np\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\nA={}; B={}; kb={}\nfor l in range(4):\n    g=W[f\"ln1_w.{l}\"].astype(float)\n    b=W[f\"ln1_b.{l}\"].astype(float)\n    for h in range(6):\n        s=slice(64*h,64*(h+1))\n        q,k,v=[W[f\"W_{t}.{l}\"][s].astype(float) for t in [\"q\",\"k\",\"v\"]]\n        qg,kg,vg=[(m*g)@P for m in [q,k,v]]\n        A[l,h]=qg.T@kg/8\n        B[l,h]=P@W[f\"W_o.{l}\"][:,s].astype(float)@vg\n        kb[l,h]=kg.T@(q@b)/8\n\nr=sum(kb[1,h]/np.linalg.norm(kb[1,h]) for h in range(6))\nr/=np.linalg.norm(r)\nprint(\"Common L1 key-selector direction: each head's cosine and bias/QK norm ratio\")\nfor l in range(4):\n    print(l,np.round([[kb[l,h]@r/np.linalg.norm(kb[l,h]),\n                       np.linalg.norm(kb[l,h])/np.linalg.norm(A[l,h])]\n                      for h in range(6)],3))\n\nub,sb,_=np.linalg.svd(np.concatenate([B[0,h] for h in [0,1,4,5]],axis=1),full_matrices=False)\nTb=ub[:,:4]\nprint(\"Common selector fraction in top 2/4/8 broad-output dimensions\",\n      [round(np.linalg.norm(ub[:,:k].T@r)**2,4) for k in [2,4,8]])\nprint(\"Common selector composed with L0 OV heads: norms\",\n      [round(np.linalg.norm(r@B[0,h]),4) for h in range(6)])\n\nu0,s0,_=np.linalg.svd(P@W[\"W_proj.0\"].astype(float),full_matrices=False)\nu1,s1,_=np.linalg.svd(P@W[\"W_proj.1\"].astype(float),full_matrices=False)\n_,_,v0=np.linalg.svd((W[\"W_v.0\"][128:192].astype(float)*W[\"ln1_w.0\"])@P,full_matrices=False)\nspaces={\"V0H2-24\":v0[:24].T,\n        \"MLP0-32\":u0[:,:32],\n        \"MLP0-64\":u0[:,:64],\n        \"MLP1-64\":u1[:,:64]}\n\nprint(\"\\nProjected key-composition scores: strongest earlier heads\")\nprint(\"tuple = (earlier head, trace/F, symmetry, norm)\")\nfor name,T in spaces.items():\n    print(\"\\nSPACE\",name)\n    for l in [2,3]:\n        for h in range(6):\n            results=[]\n            for j in range(l):\n                for k in range(6):\n                    c=T.T@A[l,h]@B[j,k]@T\n                    fn=np.linalg.norm(c)\n                    results.append((f\"L{j}H{k}\",np.trace(c)/fn,\n                                    np.sum(c*c.T)/(fn*fn),fn))\n            results.sort(key=lambda x:x[1],reverse=True)\n            print(f\"L{l}H{h}\",[(n,round(t,3),round(y,3),round(f,3))\n                               for n,t,y,f in results[:2]])\n\nprint(\"\\nDirect-match versus predecessor-match on V0H2's 24-dimensional read space\")\nT=spaces[\"V0H2-24\"]\nfor l in [1,2,3]:\n    for h in range(6):\n        out=[]\n        for c in [T.T@A[l,h]@T,T.T@A[l,h]@B[0,2]@T,\n                  T.T@B[0,2].T@A[l,h]@T]:\n            fn=np.linalg.norm(c)\n            out.append([np.trace(c)/fn,np.sum(c*c.T)/(fn*fn),fn])\n        print(f\"L{l}H{h}\",np.round(out,3))\n\nprint(\"\\nMLP neuron weight-norm quantiles\")\nfor l in range(4):\n    a=np.linalg.norm(W[f\"W_fc.{l}\"],axis=1)\n    b=np.linalg.norm(W[f\"W_proj.{l}\"],axis=0)\n    print(l,\"read\",np.round(np.quantile(a,[.1,.25,.5,.75,.9]),3),\n          \"write\",np.round(np.quantile(b,[.1,.25,.5,.75,.9]),3),\n          \"small-write fraction\",round(float(np.mean(b<.4)),3))\n```"}}
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