{
  "schemaVersion": 1,
  "lessonId": "distributed-03",
  "contentHash": "8513af7c9ad7fd790134999a25b276112f6429a15cdbb2fd3f2528075d7372fa",
  "executedAt": "2026-10-20T10:47:48.161184+00:00",
  "environment": {
    "backend": "cpu",
    "deviceCount": 4,
    "python": "3.14.3",
    "jax": "0.9.2",
    "numpy": "2.4.4",
    "matplotlib": "3.10.8"
  },
  "stdout": "Gradient reference: [0.0029296851716935635, 0.00219726306386292, 0.0014648411888629198, 0.0007324193138629198, -2.6193447411060333e-09, -0.000732424552552402, -0.001464846427552402, -0.002197268418967724]\nLocal result shapes: replicated (8,), reduce-scatter (2,), gathered (8,)\nIdealized ring bytes per rank: 48.0 24.0\nCompleted CPU median microseconds: {'all_reduce': 99.08340871334076, 'reduce_scatter': 102.49996557831764, 'all_gather_only': 108.41712355613708}\nGradient reference: [0.0029296851716935635, 0.00219726306386292, 0.0014648411888629198, 0.0007324193138629198, -2.6193447411060333e-09, -0.000732424552552402, -0.001464846427552402, -0.002197268418967724]\nLocal result shapes: replicated (8,), reduce-scatter (2,), gathered (8,)\nIdealized ring bytes per rank: 48.0 24.0\nCompleted CPU median microseconds: {'all_reduce': 109.4592735171318, 'reduce_scatter': 109.74984616041183, 'all_gather_only': 86.12498641014099}\nSharded momentum matches the independent elementwise update.\nJoint permutation preserves the gradient; label-only reversal does not.\nIdealized payload/storage budget, not observed network traffic: [{'ranks': 2, 'all_reduce_bytes': 1048576, 'scatter_gather_bytes': 1048576, 'shard_storage_bytes': 524288}, {'ranks': 4, 'all_reduce_bytes': 1572864, 'scatter_gather_bytes': 1572864, 'shard_storage_bytes': 262144}, {'ranks': 8, 'all_reduce_bytes': 1835008, 'scatter_gather_bytes': 1835008, 'shard_storage_bytes': 131072}]\nPASS: distributed-03\n",
  "notebookCells": [
    {
      "sourceHash": "67aba87bf4a20f90de8316302ac4d3e338449254da63a04575b7fc9eb5fa699d",
      "outputs": []
    },
    {
      "sourceHash": "6916d6835951ec422c97e68dc564ec59277d8c09798da287c6fa7ff2b7233c5d",
      "outputs": []
    },
    {
      "sourceHash": "41dcbbbb08b88f0226c5115c61935588aaf57b481e464028bde39c3d42142cac",
      "outputs": []
    },
    {
      "sourceHash": "9519f6e31a19cd06547739f482dc8b799bb8eb1d653bf28cd63da15fc3d8c284",
      "outputs": []
    },
    {
      "sourceHash": "afc06023c22b4d1e9b13b4c2fb77a185170f9da06cc633daa8f1e325f6640119",
      "outputs": []
    },
    {
      "sourceHash": "f13c089ee72e6229c017ea023e42f940a4ce467e6db3499fc4f94e7974d39e97",
      "outputs": []
    },
    {
      "sourceHash": "885b67ce7e76d3dd913d01daf23523d23256de8a347bd1796098e1aae7c07e01",
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Gradient reference: [0.0029296851716935635, 0.00219726306386292, 0.0014648411888629198, 0.0007324193138629198, -2.6193447411060333e-09, -0.000732424552552402, -0.001464846427552402, -0.002197268418967724]\n",
            "Local result shapes: replicated (8,), reduce-scatter (2,), gathered (8,)\n",
            "Idealized ring bytes per rank: 48.0 24.0\n",
            "Completed CPU median microseconds: {'all_reduce': 98.45802560448647, 'reduce_scatter': 96.20841592550278, 'all_gather_only': 88.62512186169624}\n"
          ]
        }
      ]
    },
    {
      "sourceHash": "5b6e4990bc69ea4b684c4ecc439458d187a4068e0852a54ff6acecd0b952cb0e",
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Gradient reference: [0.0029296851716935635, 0.00219726306386292, 0.0014648411888629198, 0.0007324193138629198, -2.6193447411060333e-09, -0.000732424552552402, -0.001464846427552402, -0.002197268418967724]\n",
            "Local result shapes: replicated (8,), reduce-scatter (2,), gathered (8,)\n",
            "Idealized ring bytes per rank: 48.0 24.0\n",
            "Completed CPU median microseconds: {'all_reduce': 106.6247932612896, 'reduce_scatter': 93.00000965595245, 'all_gather_only': 106.29184544086456}\n"
          ]
        }
      ]
    },
    {
      "sourceHash": "76d2608f08a082da6d7d3db822c575d68fd53ed4b0c4795bd5dedafb6b8a74e8",
      "outputs": []
    },
    {
      "sourceHash": "25df6d662f9d3f0c4e984c6a201f79fa0cfd7a2633dc4b0773dfba6c2dd4ee6c",
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
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",
            "text/plain": [
              "Executed Matplotlib figure"
            ]
          }
        }
      ]
    },
    {
      "sourceHash": "6e8bcd2274514c2887e145852c26d3f045e53484e5f07a9a4f732acc59194a9b",
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Sharded momentum matches the independent elementwise update.\n"
          ]
        }
      ]
    },
    {
      "sourceHash": "253bf4555884ea703a6e86b4cc68f9751816c1078f972cda03eaf07b2efd5499",
      "outputs": []
    },
    {
      "sourceHash": "5fff598de2d505a8dcd4d82370486a248f4ee8000fcf9638a0cc6acf68dc35b5",
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Joint permutation preserves the gradient; label-only reversal does not.\n"
          ]
        }
      ]
    },
    {
      "sourceHash": "dea1c8e2869d4b4ec8c3d9ee33337cb4d5262aab084c70bbf3b4c7cb5a73c2cd",
      "outputs": []
    },
    {
      "sourceHash": "36722bc196794c59697566aa754d890e8aaeb663bf86d8f3ab9f088f298600d7",
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Idealized payload/storage budget, not observed network traffic: [{'ranks': 2, 'all_reduce_bytes': 1048576, 'scatter_gather_bytes': 1048576, 'shard_storage_bytes': 524288}, {'ranks': 4, 'all_reduce_bytes': 1572864, 'scatter_gather_bytes': 1572864, 'shard_storage_bytes': 262144}, {'ranks': 8, 'all_reduce_bytes': 1835008, 'scatter_gather_bytes': 1835008, 'shard_storage_bytes': 131072}]\n"
          ]
        }
      ]
    }
  ],
  "scope": "Recorded instructor reference run; all script assertions and notebook code cells passed. No accelerator performance claim."
}