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{"type":"item.completed","item":{"id":"item_2","type":"agent_message","text":"```python\nimport numpy as np\nfrom scipy.linalg import eigh\nfrom scipy.optimize import linear_sum_assignment\nfrom sklearn.cluster import KMeans\nfrom threadpoolctl import threadpool_limits\nthreadpool_limits(2)\nnp.set_printoptions(precision=3, suppress=True, linewidth=180)\n\ng1=W[\"ln1_w.0\"].astype(float)\ng2=W[\"ln2_w.0\"].astype(float)\nV=W[\"W_v.0\"][192:256].astype(float)*g1\nB=W[\"W_o.0\"][:,192:256].astype(float)@V\nF=W[\"W_fc.0\"].astype(float)*g2\n_,_,vt=np.linalg.svd(V,full_matrices=False)\n\nprint(\"MLP ROW-DIRECTION ASSOCIATION, NOT NEURON ACTIVATIONS\")\nfor rank in [18,22,24,27,32]:\n    T=vt[:rank].T\n    X=F@T\n    Y=F@B@T\n    mask=(np.linalg.norm(X,axis=1)>.4)&(np.linalg.norm(Y,axis=1)>.3)\n    X=X[mask];Y=Y[mask]\n    # Remove the average learned row direction.\n    X=X-X.mean(0)\n    Y=Y-Y.mean(0)\n    # Equalize the aggregate scales, without passing an input through the model.\n    Y=Y*np.linalg.norm(X)/np.linalg.norm(Y)\n    G=(X.T@X+Y.T@Y)/2\n    C=(X.T@Y+Y.T@X)/2\n    ev=eigh(C,G+np.eye(rank)*np.trace(G)/rank*.03,eigvals_only=True)\n    print(\"rank\",rank,\"rows\",mask.sum(),\"association eigenvalues\",ev)\n\nprint(\"\\nINDEPENDENT CLUSTERINGS OF CURRENT/OV-PATH ROW DIRECTIONS\")\nT=vt[:27].T\nX=F@T\nY=F@B@T\nmask=(np.linalg.norm(X,axis=1)>.4)&(np.linalg.norm(Y,axis=1)>.3)\nX=X[mask];Y=Y[mask]\nX-=X.mean(0);Y-=Y.mean(0)\nY*=np.linalg.norm(X)/np.linalg.norm(Y)\nG=(X.T@X+Y.T@Y)/2\nev,U=np.linalg.eigh(G)\nwh=U@np.diag(1/np.sqrt(np.maximum(ev,.08*ev.max())))@U.T\nX=X@wh;Y=Y@wh\nX/=np.linalg.norm(X,axis=1,keepdims=True)\nY/=np.linalg.norm(Y,axis=1,keepdims=True)\nfor nc in [18,22,24,28]:\n    kx=KMeans(n_clusters=nc,n_init=20,random_state=0).fit(X)\n    ky=KMeans(n_clusters=nc,n_init=20,random_state=0).fit(Y)\n    cx=kx.cluster_centers_;cy=ky.cluster_centers_\n    cx=cx/np.linalg.norm(cx,axis=1,keepdims=True)\n    cy=cy/np.linalg.norm(cy,axis=1,keepdims=True)\n    r,c=linear_sum_assignment(-(cx@cy.T))\n    remap=np.zeros(nc,dtype=int);remap[c]=r\n    tab=np.zeros((nc,nc))\n    np.add.at(tab,(kx.labels_,remap[ky.labels_]),1)\n    S=(tab+tab.T)/2\n    deg=S.sum(0)\n    norm=S/np.sqrt(np.maximum(deg[:,None]*deg[None,:],1))\n    spec=np.linalg.eigvalsh(norm)\n    print(\"clusters\",nc,\n          \"matched center cos quantiles\",np.percentile((cx@cy.T)[r,c],[0,25,50,75,100]),\n          \"graph eigenvalues\",spec)\n    print(\"cluster counts\",np.sort(np.bincount(kx.labels_,minlength=nc)))\n    if nc==24:\n        print(\"24-cluster association table (unlabelled weight directions):\")\n        print(tab.astype(int))\n\nprint(\"\\nL0H3 RAW QK COMPLEX MODES\")\nq=W[\"W_q.0\"][192:256].astype(float)\nk=W[\"W_k.0\"][192:256].astype(float)\nev=np.linalg.eigvals(k@q.T/8)\nsel=ev[(ev.imag>1e-6)&(abs(ev)>.10)]\nsel=sel[np.argsort(np.angle(sel))]\nprint(\"angle, magnitude:\",np.column_stack([np.angle(sel),abs(sel)]))\n```\n"}}
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