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algal/Shuffling in torch vs numpy-public.ipynb

Created December 20, 2024 06:46
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Shuffling in torch vs numpy-public.ipynb
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Shuffling in torch vs numpy-public.ipynb
{
"cells": [
{
"metadata": {},
"id": "3631be3b",
"cell_type": "markdown",
"source": "# Torch vs Numpy shuffling\n\nThe purpose of this notebook is\n\n1. to confirm Oskar's analysis of problems with `torch.randperm`.\n\n2. to show that it can be fixed by using numpy's default random number generator or the PCG64DXSM generator specifically.\n\n\nOskar's analysis implied that `torch.randperm` was not shuffling elements uniformly when the number of elements became very large, e.g., a billion or more ([discord link](https://discord.com/channels/1200111522916094103/1276053252571533313/1278328850803064865)). We confirmed this in the notebook below.\n\nSpecifically, this notebook confirms the following: If you start with 3 billion elements, tag them as belonging to ten \"deciles\" representing the first 10% of elements, the second 10% of elements, and so on, then shuffle all the elements, and then look at the first 10,000 elements, you do not find that the ten deciles are approximately uniformly distributed among the first 10,000 elements. Instead, `torch.randperm` is more likely to put the earlier elements (the lower deciles) into the first 10,000 elements of the shuffled collection. This corresponds to the bottom-left figure in Oskar's original post.\n\nWe then found that switching to numpy's random number generator, or to numpy's PCG64DXSM generator, resolves this issue, and seems to produces an approximately uniform distribution of deciles within the first 10,000 elements of the shuffled collection..\n\nWe noticed that OLMo encountered a similar issue and resolved it by using a specific numpy generator ([OLMo link](https://discord.com/channels/1200111522916094103/1276053252571533313/1278402521391562752) ).\n"
},
{
"metadata": {},
"id": "48ff4441",
"cell_type": "markdown",
"source": "## How uniform is torch's shuffling with randperm?"
},
{
"metadata": {
"trusted": false
},
"id": "816fad78",
"cell_type": "markdown",
"source": "Let's generate an array representing a shuffling of the integers from 0 to (3 * 10^9 - 1)"
},
{
"metadata": {
"trusted": true
},
"id": "cd483264",
"cell_type": "code",
"source": "import torch\n\nshuffled = torch.randperm(3 * 10**9)",
"execution_count": null,
"outputs": []
},
{
"metadata": {
"trusted": false
},
"id": "76553ee0",
"cell_type": "code",
"source": "shuffled_interval = shuffled[:10_000]",
"execution_count": 2,
"outputs": []
},
{
"metadata": {
"trusted": false
},
"id": "f7042107",
"cell_type": "code",
"source": "shuffled_interval[:50]",
"execution_count": 3,
"outputs": [
{
"data": {
"text/plain": "tensor([1994940797, 2347954103, 1691579500, 262720464, 2748298413, 2222743612,\n 1653995, 2342555504, 1440586107, 1077345365, 668539175, 2788525165,\n 117518658, 699722858, 1290958150, 2665873790, 2552246067, 2283160201,\n 177004620, 31564517, 2704208229, 1047164862, 25139448, 2216018010,\n 1004277474, 2440298876, 1240531966, 326584590, 943397255, 34365751,\n 150611451, 129402432, 2867900352, 1395077156, 256310869, 1292414480,\n 209935101, 440610241, 848544906, 407409817, 2578392564, 1809067203,\n 1297671095, 1108743574, 1086617589, 1632128034, 681494780, 1207082789,\n 1001392368, 879276196])"
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
]
},
{
"metadata": {
"trusted": false
},
"id": "e776543d",
"cell_type": "code",
"source": "[x.item() for x in shuffled_interval[:10]]",
"execution_count": 4,
"outputs": [
{
"data": {
"text/plain": "[1994940797,\n 2347954103,\n 1691579500,\n 262720464,\n 2748298413,\n 2222743612,\n 1653995,\n 2342555504,\n 1440586107,\n 1077345365]"
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
]
},
{
"metadata": {
"trusted": false
},
"id": "c97d3956",
"cell_type": "code",
"source": "shuffled.shape[0]",
"execution_count": 5,
"outputs": [
{
"data": {
"text/plain": "3000000000"
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
]
},
{
"metadata": {},
"id": "82671979",
"cell_type": "markdown",
"source": "Define a decile function, which tells us which of the ten \"decile\" bins an element belonged to. That is, in the original unshuffled collection, was it in the first 10%, the second 10%, ... and so on."
},
{
"metadata": {
"trusted": false
},
"id": "d8528af6",
"cell_type": "code",
"source": "def decile(index, collection_size):\n \"Returns 1 to 10, for the decile of `index` within `collection_size`\"\n return 1 + int(index // (collection_size / 10))",
"execution_count": 6,
"outputs": []
},
{
"metadata": {},
"id": "525e11ae",
"cell_type": "markdown",
"source": "Verify the above function works as expected:"
},
{
"metadata": {
"trusted": false
},
"id": "6e6ec9cd",
"cell_type": "code",
"source": "n = 20\n[decile(x,n) for x in range(n)]",
"execution_count": 7,
"outputs": [
{
"data": {
"text/plain": "[1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10]"
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
]
},
{
"metadata": {
"trusted": false
},
"id": "bde78acd",
"cell_type": "code",
"source": "del n",
"execution_count": 8,
"outputs": []
},
{
"metadata": {},
"id": "de916fa2",
"cell_type": "markdown",
"source": "Compute the deciles for the first 10,000 shuffled values"
},
{
"metadata": {
"trusted": false
},
"id": "ba80ed86",
"cell_type": "code",
"source": "deciles = [decile(x.item(),shuffled.shape[0]) for x in shuffled_interval]",
"execution_count": 9,
"outputs": []
},
{
"metadata": {
"trusted": false
},
"id": "4845849e",
"cell_type": "markdown",
"source": "Let's graph a histogram of the values in deciles."
},
{
"metadata": {
"trusted": false
},
"id": "d983a9eb",
"cell_type": "code",
"source": "%matplotlib inline\nimport matplotlib.pyplot as plt\n\nplt.figure(figsize=(10, 6))\nplt.hist(deciles, bins=range(1, 12), align='left', rwidth=0.8)\nplt.xlabel('Decile')\nplt.ylabel('Frequency')\nplt.title('Histogram of Deciles, with torch.randperm')\nplt.xticks(range(1, 11))\nplt.show()",
"execution_count": 11,
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": "<Figure size 1000x600 with 1 Axes>"
},
"metadata": {},
"output_type": "display_data"
}
]
},
{
"metadata": {},
"id": "cd811ebd",
"cell_type": "markdown",
"source": "The above shows that torch's shuffler is not producing a uniform shuffle over a collection of 3 B elements."
},
{
"metadata": {},
"id": "ac04d4fe",
"cell_type": "markdown",
"source": "## Now let's try numpy with the PCG64DXSM generator."
},
{
"metadata": {
"trusted": false
},
"id": "da392490",
"cell_type": "markdown",
"source": "Let's generate an array representing a shuffling of the integers from 0 to (3 * 10^9 - 1), but using this random number generator from numpy: numpy.random.PCG64DXSM"
},
{
"metadata": {
"trusted": false
},
"id": "359b2270",
"cell_type": "code",
"source": "import numpy as np\n\nrng = np.random.Generator(np.random.PCG64DXSM())\nshuffled = rng.permutation(3 * 10**9)\nshuffled = torch.from_numpy(shuffled)\nshuffled_interval = shuffled[:10_000]",
"execution_count": 12,
"outputs": []
},
{
"metadata": {
"trusted": false
},
"id": "12e73269",
"cell_type": "code",
"source": "deciles = [decile(x.item(),shuffled.shape[0]) for x in shuffled_interval]",
"execution_count": 13,
"outputs": []
},
{
"metadata": {
"trusted": false
},
"id": "c1e19f7c",
"cell_type": "code",
"source": "%matplotlib inline\nimport matplotlib.pyplot as plt\n\nplt.figure(figsize=(10, 6))\nplt.hist(deciles, bins=range(1, 12), align='left', rwidth=0.8)\nplt.xlabel('Decile')\nplt.ylabel('Frequency')\nplt.title('Histogram of Deciles with PCG64DXSM randomization')\nplt.xticks(range(1, 11))\nplt.show()",
"execution_count": 14,
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": "<Figure size 1000x600 with 1 Axes>"
},
"metadata": {},
"output_type": "display_data"
}
]
},
{
"metadata": {},
"id": "6c6ad989",
"cell_type": "markdown",
"source": "This is much closer to a uniform distribution."
},
{
"metadata": {},
"id": "3df62049",
"cell_type": "markdown",
"source": "## Now let's try with numpy's default randperm."
},
{
"metadata": {
"trusted": false
},
"id": "85f9db59",
"cell_type": "code",
"source": "import numpy as np\n\nrng = np.random.default_rng()\nshuffled = rng.permutation(3 * 10**9)\nshuffled = torch.from_numpy(shuffled)\nshuffled_interval = shuffled[:10_000]",
"execution_count": 15,
"outputs": []
},
{
"metadata": {
"trusted": false
},
"id": "02839455",
"cell_type": "code",
"source": "deciles = [decile(x.item(),shuffled.shape[0]) for x in shuffled_interval]",
"execution_count": 16,
"outputs": []
},
{
"metadata": {
"trusted": false
},
"id": "52b2a6b4",
"cell_type": "code",
"source": "%matplotlib inline\nimport matplotlib.pyplot as plt\n\nplt.figure(figsize=(10, 6))\nplt.hist(deciles, bins=range(1, 12), align='left', rwidth=0.8)\nplt.xlabel('Decile')\nplt.ylabel('Frequency')\nplt.title('Histogram of Deciles with numpy default rng')\nplt.xticks(range(1, 11))\nplt.show()",
"execution_count": 17,
"outputs": [
{
"data": {
"image/png": 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/rsuXL2vz5s2qW7euQkND7+h4/P397ZatVqsk3VYw9PLyKnC5ndVqveX9Tr92m+7u7gVep/nthe0rKCio0LZfXr7ZvHlzPfzww7Z7+z766COdPn36lhNU5G+jqH380vfff69Lly7J3d29wGslJSXF9jopynfffaeHH35Y58+f19tvv61PP/1USUlJtppvN7ybwcvLq8hLgm9+TUk/vy7y601LS5NhGL/qPRBAyXDPFgCn4urqqrFjx2rs2LG6dOmSNm/erBdffFGdO3fW2bNni51tK/8DRnJycoEP9RcuXLDdr5Xfr7B7E1JSUgr9Vr2we3KWLVumyMhIzZkzx649MzOz+IMsBb881ptduHBBFSpUUJUqVUp9v1988YVSUlI0dOhQSVKVKlXk4uKiAQMGaOTIkYWukx9GqlWrVmCikpLI/ztOnDhRMTExhfapX7++JMnb21tTpkzRlClT9P3339tGubp37243KcfN3N3d1aZNG23evFk1atRQUFCQmjRpYrvfZdu2bdqyZYuio6Pv+HjMlh+cfjlphqRbBo07kZKSUmjbvffea9c2evRoPf7449q/f79mz56tevXqqWPHjsVuO/+1X9Q+fil/0pENGzYUuq1fjv4UZu3atbpy5YpWr16t2rVr29oL+506Dw+PAudY+vk8579mS9OdTGJRpUoVWSyWIt8DAZQeRrYAOK3KlSvrD3/4g0aOHKmLFy/q9OnTkor+5r99+/aSfg5Bv5SUlKRjx47ZZutq1aqVrFarVq1aZddvz549v+ryK4vFYqsl35dffmk3G6BZ6tevr+rVq2v58uV2l/VduXJFH3zwgW2GwtJ08eJFPf3003Jzc9Ozzz4r6edv19u1a6cDBw6oadOmhY5o5n847tKli06cOHFbEz8Up379+goLC9OhQ4cK3V94eHihH6IDAwM1ePBg/fGPf9Tx48dveZllhw4dtG/fPn3wwQe2SwW9vb31u9/9TomJibpw4cJtXUL4yxEFR8j/8uDLL7+0a7/VBCx34ubfYtu1a5fOnDlTYNKYXr16qVatWho3bpw2b96sESNG3DJE1K9fX8HBwVqxYoXda//MmTO2yz7zRUdH66efflJubm6hr5P8UF6U/Fp++e/cMAy98847BfrWqVOnwDk+ceKE7ZLW4vya0czS4O3trfDwcK1du1bZ2dm29suXLxc6ayGAkmNkC4BT6d69uxo3bqzw8HBVq1ZNZ86c0axZs1S7dm2FhYVJku33nd5++20NGjRIbm5uql+/vurXr6+nnnpKiYmJqlChgrp06WKbjbBmzZq2gODn56exY8dq+vTpqlKlinr16qVz585pypQpCg4OtrsHqjjR0dF65ZVXNHnyZLVt21bHjx/X1KlTFRoaWuhsjKWpQoUKSkhIUL9+/RQdHa3hw4crKytLM2bM0KVLl2xTdZfU119/rT179igvL08//fSTPv/8cy1YsEAZGRlasmSJGjVqZOv79ttvq02bNnr44Yf15z//WXXq1FFmZqZOnjypf//737ZwFRsbq1WrVqlnz56aMGGCHnzwQV27dk3bt29XdHS02rVrd9v1zZs3T126dFHnzp01ePBgVa9eXRcvXtSxY8e0f/9+231ArVq1UnR0tJo2baoqVaro2LFjWrp06W2F0aioKOXm5mrLli12U5x36NBBkydPlsVisQX84jRp0kTbtm3Tv//9bwUHB8vHx+eWH/JLU1BQkDp06GB7vdeuXVtbtmzR6tWrTdvn3r17NWzYMD3++OM6e/asJk2apOrVq9su88zn4uKikSNH6oUXXpC3t3ehU6ffrEKFCnrllVc0bNgw9erVS3/605906dIlxcXFFbiM8IknntA//vEPde3aVWPGjNGDDz4oNzc3nTt3Tlu3blXPnj3Vq1evIvfVsWNHubu7649//KOef/55Xb9+XXPmzCn0Et0BAwaof//+GjFihH7/+9/rzJkzSkhIULVq1W55TEW9p91q5O1OTJ06Vd26dVPnzp01ZswY5ebmasaMGapYsaIuXrxo2n6Bcseh03MAuKvkz0SWlJRU6PPdunW75WyEb775phEREWFUrVrVcHd3N2rVqmUMHTrUOH36tN16EydONEJCQowKFSrYzbSWm5trvP7660a9evUMNzc3o2rVqkb//v2Ns2fP2q2fl5dnTJs2zahRo4bh7u5uNG3a1Pjoo4+MZs2a2c2kVtzsfFlZWcb48eON6tWrGx4eHkaLFi2MtWvXFpiRLn/2sRkzZtitX9S2b3Uef2nt2rVGq1atDA8PD8Pb29uIiooyPvvss9vaT2Hy++Y/XF1dDX9/f6N169bGiy++WODv8MtjHDJkiFG9enXDzc3NqFatmhEREWE3+5xhGEZaWpoxZswYo1atWoabm5sREBBgdOvWzfjqq69sfXQbsxEahmEcOnTI6N27txEQEGC4ubkZQUFBRvv27Y25c+fa+kyYMMEIDw83qlSpYlitVqNu3brGs88+a/z444+3PBd5eXlG1apVDUnG+fPnbe35M+u1aNGiwDqFzUZ48OBB46GHHjK8vLzsZrss6u9c1PEWtq/CZs+bPHlygdnkkpOTjT/84Q+Gn5+f4evra/Tv39/Yu3dvobMRFrbNtm3bGo0aNSrQXrt2baNbt2625fxj2rhxozFgwACjcuXKhqenp9G1a1fj66+/LvQ4Tp8+bUgynn766WKP92bvvvuuERYWZri7uxv16tUz3nvvvULPf05OjvHGG28YzZo1Mzw8PIyKFSsaDRo0MIYPH25XU1HH/u9//9u2bvXq1Y3nnnvOWL9+fYG/UV5enpGQkGDUrVvX8PDwMMLDw41PPvnktmYjNIyi39MKU9zMiZKMkSNHFmgvbLbENWvWGE2aNLG917722mvG6NGjjSpVqhS5bwC/jsUwbuOHbwCgHDh16pQaNGigyZMn68UXX3R0OUCZk//7V0lJSQoPD7+tdRITEzV69GgdOXLEbsQUv72cnBzdf//9ql69ujZu3OjocoC7ApcRAiiXDh06pBUrVigiIkKVKlXS8ePHlZCQoEqVKtkmfwBgngMHDujUqVOaOnWqevbsSdBygPwfnw4ODlZKSormzp2rY8eO6e2333Z0acBdg7AFoFzy9vbW3r17tWDBAl26dEm+vr6KjIzUq6++ytTHwG+gV69eSklJ0cMPP6y5c+c6upxyKTMzU+PHj9cPP/wgNzc3tWjRQv/973/v+LfjAPwfLiMEAAAAABMw9TsAAAAAmICwBQAAAAAmIGwBAAAAgAmYIOM25eXl6cKFC/Lx8bnlr9sDAAAAuHsZhqHMzEyFhISoQoWix68IW7fpwoULqlmzpqPLAAAAAOAkzp49qxo1ahT5PGHrNvn4+Ej6+YRWqlTJwdUAAAAAcJSMjAzVrFnTlhGKQti6TfmXDlaqVImwBQAAAOCWtxcxQQYAAAAAmICwBQAAAAAmIGwBAAAAgAkIWwAAAABgAsIWAAAAAJiAsAUAAAAAJiBsAQAAAIAJCFsAAAAAYALCFgAAAACYgLAFAAAAACYgbAEAAACACQhbAAAAAGACwhYAAAAAmICwBQAAAAAmIGwBAAAAgAkIWwAAAABgAsIWAAAAAJiAsAUAAAAAJiBsAQAAAIAJXB1dAAA4mzoT/uPoEkx3+rVuji4BAIC7HiNbAAAAAGACwhYAAAAAmICwBQAAAAAmIGwBAAAAgAkIWwAAAABgAsIWAAAAAJiAsAUAAAAAJiBsAQAAAIAJCFsAAAAAYALCFgAAAACYwNXRBQD47dWZ8B9Hl2C60691c3QJAACgnCNsAQAAAGVcefgiVSp7X6ZyGSEAAAAAmICwBQAAAAAm4DJCAABKCZfxAAB+iZEtAAAAADABYQsAAAAATODQsLVjxw51795dISEhslgsWrt2rd3zhmEoLi5OISEh8vT0VGRkpI4ePWrXJysrS88884yqVq0qb29v9ejRQ+fOnbPrk5aWpgEDBsjX11e+vr4aMGCALl26ZPLRAQAAACjPHBq2rly5ombNmmn27NmFPp+QkKCZM2dq9uzZSkpKUlBQkDp27KjMzExbn9jYWK1Zs0YrV67Uzp07dfnyZUVHRys3N9fWp2/fvjp48KA2bNigDRs26ODBgxowYIDpxwcAAACg/HLoBBldunRRly5dCn3OMAzNmjVLkyZNUkxMjCRp8eLFCgwM1PLlyzV8+HClp6drwYIFWrp0qTp06CBJWrZsmWrWrKnNmzerc+fOOnbsmDZs2KA9e/aoVatWkqR33nlHrVu31vHjx1W/fv1C95+VlaWsrCzbckZGRmkeOgAAAIC7nNPORnjq1CmlpKSoU6dOtjar1aq2bdtq165dGj58uPbt26ecnBy7PiEhIWrcuLF27dqlzp07a/fu3fL19bUFLUn63e9+J19fX+3atavIsDV9+nRNmTLFvAOEqcrDjGDMBgYAAODcnHaCjJSUFElSYGCgXXtgYKDtuZSUFLm7u6tKlSrF9gkICCiw/YCAAFufwkycOFHp6em2x9mzZ+/oeAAAAACUL047spXPYrHYLRuGUaDtZjf3Kaz/rbZjtVpltVp/ZbUAAKAo5eGqA4krDwD8H6cd2QoKCpKkAqNPqampttGuoKAgZWdnKy0trdg+33//fYHt//DDDwVGzQAAAACgtDht2AoNDVVQUJA2bdpka8vOztb27dsVEREhSWrZsqXc3Nzs+iQnJ+vIkSO2Pq1bt1Z6erq++OILW5/PP/9c6enptj4AAAAAUNocehnh5cuXdfLkSdvyqVOndPDgQfn5+alWrVqKjY1VfHy8wsLCFBYWpvj4eHl5ealv376SJF9fXw0dOlTjxo2Tv7+//Pz8NH78eDVp0sQ2O2HDhg316KOP6k9/+pPmzZsnSXrqqacUHR1d5OQYAAAAAHCnHBq29u7dq3bt2tmWx44dK0kaNGiQFi1apOeff17Xrl3TiBEjlJaWplatWmnjxo3y8fGxrfPWW2/J1dVVvXv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",
"text/plain": "<Figure size 1000x600 with 1 Axes>"
},
"metadata": {},
"output_type": "display_data"
}
]
},
{
"metadata": {},
"id": "feb5266b",
"cell_type": "markdown",
"source": "## Version check"
},
{
"metadata": {
"trusted": false
},
"id": "cced2ac8",
"cell_type": "code",
"source": "%%aip 0\nGenerate code to report my version of torch",
"execution_count": null,
"outputs": []
},
{
"metadata": {
"trusted": false
},
"id": "8ed42c35",
"cell_type": "code",
"source": "import torch\nprint(f\"PyTorch version: {torch.__version__}\")",
"execution_count": 18,
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": "PyTorch version: 2.4.0\n"
}
]
},
{
"metadata": {
"trusted": false
},
"id": "34b45e3e",
"cell_type": "code",
"source": "print(f\"Numpy version: {np.__version__}\")",
"execution_count": 20,
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": "Numpy version: 2.0.1\n"
}
]
},
{
"metadata": {
"trusted": false
},
"id": "5d26a2d8",
"cell_type": "code",
"source": "import os\ncpu_count = os.cpu_count()\ntry:\n with open(\"/proc/meminfo\",'r') as mem:\n meminfo = next(mem)\nexcept:\n meminfo ='unknown'\nprint(f\"CPU: {cpu_count} logical cores\")\nprint(meminfo)",
"execution_count": 26,
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": "CPU: 16 logical cores\nMemTotal: 131177156 kB\n\n"
}
]
}
],
"metadata": {
"kernelspec": {
"name": "python3",
"display_name": "Python 3 (ipykernel)",
"language": "python"
},
"language_info": {
"name": "python",
"version": "3.12.0",
"mimetype": "text/x-python",
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"pygments_lexer": "ipython3",
"nbconvert_exporter": "python",
"file_extension": ".py"
},
"gist": {
"id": "",
"data": {
"description": "Shuffling in torch vs numpy-public.ipynb",
"public": true
}
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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