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{"type":"item.completed","item":{"id":"item_2","type":"agent_message","text":"```python\nimport numpy as np\nfrom scipy.linalg import svd, svdvals\nfrom threadpoolctl import threadpool_limits\n\ndef cos(a,b):\n    return np.sum(a*b)/(np.linalg.norm(a)*np.linalg.norm(b)+1e-30)\n\nwith threadpool_limits(limits=2):\n    As, Bs, keybias, names = [], [], [], []\n    for l in range(4):\n        g = W[f\"ln1_w.{l}\"].astype(float)\n        b = W[f\"ln1_b.{l}\"].astype(float)\n        for j in range(6):\n            sl = slice(64*j,64*j+64)\n            q = W[f\"W_q.{l}\"][sl].astype(float)\n            k = W[f\"W_k.{l}\"][sl].astype(float)\n            v = W[f\"W_v.{l}\"][sl].astype(float)\n            o = W[f\"W_o.{l}\"][:,sl].astype(float)\n            qg,kg,vg = q*g,k*g,v*g\n            qg -= qg.mean(1,keepdims=True)\n            kg -= kg.mean(1,keepdims=True)\n            vg -= vg.mean(1,keepdims=True)\n            As.append(qg.T@kg/8)\n            Bs.append(o@vg)\n            keybias.append(kg.T@(q@b)/8)\n            names.append(f\"L{l}H{j}\")\n    for l in range(4):\n        ix = range(6*l,6*l+6)\n        print(\"\\nLAYER\",l,\"QK cosine matrix\")\n        print(np.round([[cos(As[i],As[j]) for j in ix] for i in ix],3))\n        print(\"OV cosine matrix\")\n        print(np.round([[cos(Bs[i],Bs[j]) for j in ix] for i in ix],3))\n        print(\"key-bias cosine matrix\")\n        print(np.round([[cos(keybias[i],keybias[j]) for j in ix] for i in ix],3))\n    print(\"\\nSPECTRA: first 12 singular values\")\n    for i in list(range(6))+list(range(18,24)):\n        sa=svdvals(As[i]); sb=svdvals(Bs[i])\n        print(names[i],\"QK\",np.round(sa[:12],3),\"OV\",np.round(sb[:12],3))\n    print(\"\\nCROSS-HEAD QK similarities: strongest other-layer matches\")\n    for i in range(24):\n        cs=[(cos(As[i],As[j]),names[j]) for j in range(24) if j//6!=i//6]\n        print(names[i],sorted(cs,reverse=True)[:3])\n    print(\"\\nMLP LINEAR-ALGEBRA STATISTICS (no nonlinearities applied)\")\n    for l in range(4):\n        f=W[f\"W_fc.{l}\"].astype(float)*W[f\"ln2_w.{l}\"]\n        f-=f.mean(1,keepdims=True)\n        p=W[f\"W_proj.{l}\"].astype(float)\n        sf=svdvals(f); sp=svdvals(p)\n        M=p@f\n        sm=svdvals(M)\n        rowcos=np.sum(f*p.T,axis=1)/(np.linalg.norm(f,axis=1)*np.linalg.norm(p,axis=0))\n        print(\"L\",l,\"FC spectrum\",np.round(sf[:20],2))\n        print(\"PROJ spectrum\",np.round(sp[:20],2))\n        print(\"PROJ@FC spectrum\",np.round(sm[:20],2),\n              \"trace/norm\",round(np.trace(M)/np.linalg.norm(M),3),\n              \"neuron input/output cos quantiles\",np.round(np.quantile(rowcos,[0,.1,.5,.9,1]),3))\n    print(\"\\nMost anisotropic coordinates\")\n    for l in range(4):\n        g=W[f\"ln1_w.{l}\"]\n        b=W[f\"ln1_b.{l}\"]\n        ids=np.argsort(np.abs(b))[-8:][::-1]\n        print(\"L\",l,\"largest ln1 biases\",[(int(i),round(float(b[i]),3),round(float(g[i]),3)) for i in ids])\n    ids=np.argsort(W[\"ln1_w.0\"])[-20:][::-1]\n    print(\"Largest L0 ln1 scales\",[(int(i),round(float(W[\"ln1_w.0\"][i]),3)) for i in ids])\n```\n"}}
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