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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=4, suppress=True, linewidth=180)\n\nd = 384\nP = np.eye(d) - np.ones((d, d))/d\nA, B = {}, {}\nprint(\"All calculations below are matrix products or decompositions, not layer evaluations.\")\n\nfor l in range(4):\n    g = W[f\"ln1_w.{l}\"].astype(float)\n    b = W[f\"ln1_b.{l}\"].astype(float)\n    print(\"\\nLAYER\", l)\n    for h in range(6):\n        sl = slice(64*h, 64*(h+1))\n        q, k, v = [W[f\"W_{name}.{l}\"][sl].astype(float) for name in [\"q\", \"k\", \"v\"]]\n        o = W[f\"W_o.{l}\"][:, sl].astype(float)\n        qg, kg, vg = [(m*g) @ P for m in [q, k, v]]\n        a = qg.T @ kg / 8\n        bb = P @ o @ vg\n        A[l,h], B[l,h] = a, bb\n        s = np.linalg.svd(a, compute_uv=False)\n        ev = np.linalg.eigvals(kg @ qg.T / 8)\n        ev = ev[np.argsort(-abs(ev))]\n        key_bias = kg.T @ (q @ b) / 8\n        print(f\"L{l}H{h}\",\n              \"Q/K/V/O norms\", np.round([np.linalg.norm(m) for m in [q,k,v,o]],3),\n              \"effective QK norm/top/sym/trace\",\n              np.round([np.linalg.norm(a),s[0],np.sum(a*a.T)/np.sum(a*a),np.trace(a)],4),\n              \"query_bias_ratio\", round(np.linalg.norm(q@b)/np.linalg.norm(qg),4),\n              \"key_bias_norm\", round(np.linalg.norm(key_bias),4),\n              \"QKev\", np.round(ev[:8],3))\n\nprint(\"\\nSINGULAR VALUES: first 45 for selected matrices\")\nfor name in [\"W_q.0\",\"W_k.0\",\"W_v.0\",\"W_o.0\",\"W_fc.0\",\"W_proj.0\",\n             \"W_proj.1\",\"W_proj.2\",\"W_proj.3\"]:\n    s = np.linalg.svd(W[name].astype(float),compute_uv=False)\n    print(name, np.round(s[:45],3))\n\n# Positional candidate subspace: the dominant left/right singular spaces\n# of L0H2's QK product. This is not an embedding or a constructed input.\nu,s,vt = np.linalg.svd(A[0,2],full_matrices=False)\njoined = np.concatenate([u[:,:16],vt[:16].T],axis=1)\nup,sp,_ = np.linalg.svd(joined,full_matrices=False)\nprint(\"\\nL0H2 left/right-space joint singular values\",np.round(sp,4))\nfor r in [16,24,32]:\n    T=up[:,:r]\n    print(\"Candidate position-space dimension\",r)\n    for l in range(4):\n        vals=[]\n        for h in range(6):\n            a=A[l,h]\n            vals.append([np.linalg.norm(T.T@a)**2/np.linalg.norm(a)**2,\n                         np.linalg.norm(a@T)**2/np.linalg.norm(a)**2,\n                         np.linalg.norm(T.T@a@T)**2/np.linalg.norm(a)**2])\n        print(\"layer\",l,\"Q/K/both energy:\",np.round(vals,3))\n\nprint(\"\\nKEY-COMPOSITION CANDIDATES: QK_l @ OV_earlier\")\nprint(\"For each head: strongest positive trace/Frobenius scores; \"\n      \"entries=(earlier head, trace/Fnorm, transpose symmetry, Fnorm).\")\nfor l in range(1,4):\n    for h in range(6):\n        results=[]\n        for j in range(l):\n            for k in range(6):\n                c=A[l,h]@B[j,k]\n                fn=np.linalg.norm(c)\n                results.append((f\"L{j}H{k}\",np.trace(c)/fn,np.sum(c*c.T)/(fn*fn),fn))\n        results.sort(key=lambda t:t[1],reverse=True)\n        print(f\"L{l}H{h}\",[(n,round(t,3),round(y,3),round(f,3)) for n,t,y,f in results[:5]])\n\nprint(\"\\nPairwise cosine similarities of effective QK products, within each layer\")\nfor l in range(4):\n    z=np.array([A[l,h].ravel()/np.linalg.norm(A[l,h]) for h in range(6)])\n    print(\"Layer\",l,\"\\n\",np.round(z@z.T,3))\n```"}}
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