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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\nfrom scipy.stats import skew\nfrom sklearn.decomposition import FastICA\nfrom threadpoolctl import threadpool_limits\nthreadpool_limits(limits=2)\n\nd=384\nP=np.eye(d)-np.ones((d,d))/d\nrs=[]\nfor h in [1,5]:\n    _,_,r=svd(np.asarray(W[\"W_v.0\"][64*h:64*(h+1)],float)@P,full_matrices=False)\n    rs.append(r[:28])\nee,U=np.linalg.eigh(sum(r.T@r for r in rs))\nU=U[:,np.argsort(ee)[::-1][:28]]\nF=np.asarray(W[\"W_fc.0\"],float)*W[\"ln2_w.0\"][None,:]\nica=FastICA(n_components=28,whiten=\"unit-variance\",random_state=17,max_iter=4000,tol=.001)\nZ=ica.fit_transform(F@U)\nZ*=np.where(skew(Z,axis=0)>=0,1.,-1.)[None,:]\n\n# A dictionary made entirely from existing MLP output-weight columns.\n# These are not inferred activations or a forward pass.\nO=np.asarray(W[\"W_proj.0\"],float)\nC=np.zeros((d,28))\nfor k in range(28):\n    ids=np.argsort(np.abs(Z[:,k]))[-3:]\n    coeff=Z[ids,k]\n    C[:,k]=O[:,ids]@coeff/np.linalg.norm(coeff)\nC/=np.linalg.norm(C,axis=0,keepdims=True)\n\nout_u,_,_=svd(np.asarray(W[\"W_proj.3\"],float),full_matrices=False)\nout_u=out_u[:,:28]\nJ=out_u.T@C\nBs={}\nfor l,h in [(2,1),(3,0),(3,1),(3,5)]:\n    s=slice(64*h,64*(h+1))\n    Bs[l,h]=np.asarray(W[f\"W_o.{l}\"][:,s],float)@(\n        np.asarray(W[f\"W_v.{l}\"][s],float)*W[f\"ln1_w.{l}\"][None,:])@P\nM={key:out_u.T@b@C for key,b in Bs.items()}\nprint(\"Alignment of copy-candidate output WEIGHT dictionaries\")\nkeys=list(M)\nfor key in keys:\n    print(key,[(key2,round(np.sum(M[key]*M[key2])/\n                          (np.linalg.norm(M[key])*np.linalg.norm(M[key2])),3))\n               for key2 in keys])\n\nprint(\"\\nDictionary singular values and output-subspace fractions\")\nprint(\"Initial dictionary:\",np.round(np.linalg.svd(C,compute_uv=False),3))\nfor key in keys:\n    print(key,\"output fraction\",round(np.linalg.norm(M[key])**2/np.linalg.norm(Bs[key]@C)**2,3),\n          \"singular values\",np.round(np.linalg.svd(M[key],compute_uv=False)[[0,4,9,14,19,23,26,27]],3))\n\n# A static coordinate comparison. This is NOT a table of model logits or\n# character-transition probabilities, and no linguistic labels are assigned.\nmaps={}\nfor key in [(2,1),(3,1),(3,5)]:\n    a=M[key]\n    uu,ss,vv=svd(a,full_matrices=False)\n    inverse=(vv.T*(ss/(ss*ss+(ss[0]*.15)**2))[None,:])@uu.T\n    maps[key]=inverse@J\nprint(\"\\nAgreement between static coordinate-comparison matrices\")\nfor key in maps:\n    print(key,[(k2,round(np.corrcoef(maps[key].ravel(),maps[k2].ravel())[0,1],3))\n               for k2 in maps])\n\nprint(\"\\nL3H5 static comparison: strongest off-diagonal coefficients for each column\")\ng=maps[3,5]\nfor k in range(28):\n    ix=np.argsort(g[:,k])[::-1]\n    ix=[int(i) for i in ix if i!=k][:4]\n    print(k,\"diag\",round(g[k,k],3),[(i,round(g[i,k],3)) for i in ix])\n```"}}
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