{
  "execution_mode": "CPU algorithm with controlled inputs; any latency/capacity coefficients are assumptions",
  "equivalence_check": {
    "seq_len": 64,
    "head_dim": 16,
    "block_q": 16,
    "block_kv": 16,
    "max_abs_diff": 1.388e-16,
    "standard_materialized_elements": 4160,
    "flash_materialized_hbm_elements": 0,
    "flash_sram_tile_elements": 256,
    "flash_tiles_visited": 10,
    "sample_row0_first4": [
      -0.267257,
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      -0.775466,
      0.699456
    ],
    "sample_last_row_first4": [
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      0.059253,
      0.070964
    ]
  },
  "hbm_traffic_sweep": [
    {
      "seq_len": 1024,
      "num_heads": 32,
      "head_dim": 128,
      "standard_qkv_o_mb": 33.55,
      "standard_nxn_matrix_hbm_mb": 268.44,
      "standard_total_hbm_mb": 301.99,
      "tiled_logical_access_mb_no_cache_reuse": 92.27,
      "qkvo_compulsory_bytes_mb": 33.55,
      "num_q_blocks": 8,
      "accounting": "logical accesses, not measured HBM traffic; dense baseline and causal tiled loop differ in work"
    },
    {
      "seq_len": 4096,
      "num_heads": 32,
      "head_dim": 128,
      "standard_qkv_o_mb": 134.22,
      "standard_nxn_matrix_hbm_mb": 4294.97,
      "standard_total_hbm_mb": 4429.19,
      "tiled_logical_access_mb_no_cache_reuse": 1174.41,
      "qkvo_compulsory_bytes_mb": 134.22,
      "num_q_blocks": 32,
      "accounting": "logical accesses, not measured HBM traffic; dense baseline and causal tiled loop differ in work"
    },
    {
      "seq_len": 16384,
      "num_heads": 32,
      "head_dim": 128,
      "standard_qkv_o_mb": 536.87,
      "standard_nxn_matrix_hbm_mb": 68719.48,
      "standard_total_hbm_mb": 69256.35,
      "tiled_logical_access_mb_no_cache_reuse": 17582.52,
      "qkvo_compulsory_bytes_mb": 536.87,
      "num_q_blocks": 128,
      "accounting": "logical accesses, not measured HBM traffic; dense baseline and causal tiled loop differ in work"
    },
    {
      "seq_len": 32768,
      "num_heads": 32,
      "head_dim": 128,
      "standard_qkv_o_mb": 1073.74,
      "standard_nxn_matrix_hbm_mb": 274877.91,
      "standard_total_hbm_mb": 275951.65,
      "tiled_logical_access_mb_no_cache_reuse": 69524.78,
      "qkvo_compulsory_bytes_mb": 1073.74,
      "num_q_blocks": 256,
      "accounting": "logical accesses, not measured HBM traffic; dense baseline and causal tiled loop differ in work"
    }
  ]
}