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{"type":"item.completed","item":{"id":"item_1","type":"agent_message","text":"```python\nimport numpy as np\nimport torch\ntorch.set_num_threads(4)\ntorch.set_default_dtype(torch.float64)\nT=lambda a: torch.as_tensor(np.asarray(a),dtype=torch.float64)\nP=torch.eye(384)-torch.ones((384,384))/384\ng=T(W[\"ln1_w.0\"])\nv,b={},{}\nfor j in [1,5]:\n    sl=slice(64*j,64*(j+1))\n    v[j]=(T(W[\"W_v.0\"])[sl]*g)@P\n    b[j]=P@T(W[\"W_o.0\"])[:,sl]@v[j]\n_,u=torch.linalg.eigh(sum(x.T@x for x in v.values()))\nz=u.flip(1)[:,:28]\nf=(T(W[\"W_fc.0\"])*T(W[\"ln2_w.0\"]))@P\nactive=T(np.linalg.norm(W[\"W_fc.0\"],axis=1)>.8).bool()\na=[(x@z)[active] for x in [f,f@b[5],f@b[1]]]\na=[x/x.norm(dim=1,keepdim=True) for x in a]\nc=[]\nprint(\"Cross-covariance spectra of normalized MLP weight read-directions:\")\nfor i,j in [(0,1),(0,2),(1,2)]:\n    m=a[i].T@a[j]/len(a[i])\n    c.append(m)\n    se=torch.linalg.eigvalsh((m+m.T)/2)\n    sv=torch.linalg.svdvals(m)\n    print((i,j),\"trace\",round(float(torch.trace(m)),4),\n          \"SV\",np.round(sv[:12].numpy(),4),\n          \"sym eigenvalues\",np.round(se.numpy(),4))\nprint(\"\\nCosines between the three symmetric cross-covariance matrices:\")\ncs=[(x+x.T)/2 for x in c]\nprint(np.round([[float((x*y).sum()/(x.norm()*y.norm())) for y in cs] for x in cs],3))\nalt=cs[0]+cs[2]-cs[1]\ne,u=torch.linalg.eigh(alt)\nprint(\"Alternation-contrast eigenvalues\",np.round(e.numpy(),4))\nfor i in range(4):\n    d=u[:,i]\n    print(\"mode\",i,\"per-pair quadratic coefficients\",\n          np.round([float(d@m@d) for m in cs],4))\n```\n"}}
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