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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)\nD = 384\nA, B = {}, {}\nfor l in range(4):\n    g = W[f\"ln1_w.{l}\"].astype(float)\n    for j in range(6):\n        s = slice(64*j,64*j+64)\n        q = W[f\"W_q.{l}\"][s].astype(float)\n        k = W[f\"W_k.{l}\"][s].astype(float)\n        v = W[f\"W_v.{l}\"][s].astype(float)\n        o = W[f\"W_o.{l}\"][:,s].astype(float)\n        A[l,j] = (q*g).T @ (k*g) / 8\n        B[l,j] = o @ (v*g)\n\ndef cosine(x,y):\n    return np.sum(x*y)/(np.linalg.norm(x)*np.linalg.norm(y))\n\nprint(\"WITHIN-LAYER QK COSINES, THEN OV COSINES\")\nfor l in range(4):\n    print(\"L\",l,\"QK\")\n    print(np.array([[cosine(A[l,i],A[l,j]) for j in range(6)] for i in range(6)]))\n    print(\"OV\")\n    print(np.array([[cosine(B[l,i],B[l,j]) for j in range(6)] for i in range(6)]))\n\nprint(\"\\nL0 WEIGHT-ONLY EIGENSPECTRA AND ALIGNMENTS\")\nfor j in range(6):\n    s = slice(64*j,64*j+64)\n    q = W[\"W_q.0\"][s].astype(float)\n    k = W[\"W_k.0\"][s].astype(float)\n    g = W[\"ln1_w.0\"].astype(float)\n    for label,q1,k1 in [(\"raw\",q,k),(\"gain\",q*g,k*g)]:\n        ev = np.linalg.eigvals(k1 @ q1.T / 8)\n        ev = ev[np.argsort(abs(ev))[::-1]]\n        sv = np.linalg.svd(q1.T @ k1 / 8,compute_uv=False)\n        print(f\"H{j} {label}: eig_top12={ev[:12]}, sv_top8={sv[:8]}\")\n    u,sv,vt=np.linalg.svd(A[0,j],full_matrices=False)\n    print(\"top left/right cos\",np.round(np.diag(vt[:5]@u[:,:5]),3))\n    print(\"top left/right coordinate concentration\",\n          np.round(np.max(u[:,:5]**2,axis=0),3),\n          np.round(np.max(vt[:5]**2,axis=1),3))\n\nprint(\"\\nL0 QK TOP-DIRECTION COSINES (signed arbitrary; absolute values shown)\")\nus,vs=[],[]\nfor j in range(6):\n    u,s,vt=np.linalg.svd(A[0,j],full_matrices=False)\n    us.append(u[:,0]); vs.append(vt[0])\nprint(\"left\",np.abs(np.array(us)@np.array(us).T))\nprint(\"right\",np.abs(np.array(vs)@np.array(vs).T))\n\nprint(\"\\nATTENTION AFFINE PARAMETER NORMS (no activations)\")\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 j in range(6):\n        s=slice(64*j,64*j+64)\n        q=W[f\"W_q.{l}\"][s].astype(float)\n        k=W[f\"W_k.{l}\"][s].astype(float)\n        qb=q@b; kb=k@b\n        key_linear=(k*g).T@qb/8\n        query_linear=(q*g).T@kb/8\n        print(f\"L{l}H{j}: ||qD||={np.linalg.norm(q*g):.3f} ||kD||={np.linalg.norm(k*g):.3f}\",\n              f\"||qb||={np.linalg.norm(qb):.3f} ||kb||={np.linalg.norm(kb):.3f}\",\n              f\"||key_linear||={np.linalg.norm(key_linear):.3f} ||query_linear||={np.linalg.norm(query_linear):.3f}\")\n\nprint(\"\\nKEY-SIDE COMPOSITION: trace(A_l B_earlier)/||A_l B_earlier||_F\")\nprint(\"These are matrix-path diagnostics, not observed attention or induction.\")\nfor l in range(1,4):\n    for j in range(6):\n        vals=[]\n        for m in range(l):\n            for h in range(6):\n                c=A[l,j]@B[m,h]\n                vals.append((np.trace(c)/np.linalg.norm(c),m,h,np.linalg.norm(c)))\n        vals.sort(reverse=True)\n        print(f\"L{l}H{j}\",[(round(v,3),f\"L{m}H{h}\",round(n,3)) for v,m,h,n in vals[:5]])\n```\n"}}
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