nanogpt-experiments/scaling_laws.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reproducing some results from [Chinchilla](https://arxiv.org/pdf/2203.15556.pdf). I can't get the numbers to match exactly, please open an Issue if you understand why the results are off by a bit. Current running hypothesis is that this is because I am using the FLOPs = 6\\*N\\*D formula, instead of taking all the Gopher sizes and calculating their FLOPs individually, and using that to interpolate?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "gpt2 = dict(\n",
    "    seq_len = 1024,\n",
    "    vocab_size = 50257,\n",
    "    d_model = 768,\n",
    "    num_heads = 12,\n",
    "    num_layers = 12,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "123.653376"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def params(seq_len, vocab_size, d_model, num_heads, num_layers, ffw_size=4):\n",
    "    \"\"\" Given GPT config calculate total number of parameters\"\"\" \n",
    "    # token and position embeddings\n",
    "    embeddings = d_model * vocab_size + d_model * seq_len\n",
    "    # transformer blocks\n",
    "    attention = 3*d_model**2 + 3*d_model # weights and biases\n",
    "    attproj = d_model**2 + d_model\n",
    "    ffw = d_model*(ffw_size*d_model) + ffw_size*d_model\n",
    "    ffwproj = ffw_size*d_model*d_model + d_model\n",
    "    layernorms = 2*2*d_model\n",
    "    # dense\n",
    "    ln_f = 2*d_model\n",
    "    dense = d_model*vocab_size # note: no bias here\n",
    "    # note: embeddings are not included in the param count!\n",
    "    total_params = num_layers*(attention + attproj + ffw + ffwproj + layernorms) + ln_f + dense\n",
    "    return total_params\n",
    "\n",
    "params(**gpt2)/1e6 # OpenAI reports gpt2 (small) as having 124M params, good."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "766.006788096"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def flops(seq_len, vocab_size, d_model, num_heads, num_layers, ffw_size=4):\n",
    "    \"\"\" \n",
    "    Given GPT config calculate total number of FLOPs, see Chinchilla \n",
    "    paper Appendix F as reference: https://arxiv.org/pdf/2203.15556.pdf\n",
    "    \"\"\" \n",
    "    key_size = d_model // num_heads\n",
    "\n",
    "    # embeddings\n",
    "    embeddings = 2 * seq_len * vocab_size * d_model\n",
    "\n",
    "    # attention\n",
    "    # key, query, value projections\n",
    "    attention = 2 * 3 * seq_len * d_model * (key_size * num_heads)\n",
    "    # key @ query logits\n",
    "    attlogits = 2 * seq_len * seq_len * (key_size * num_heads)\n",
    "    # softmax\n",
    "    attsoftmax = 3 * num_heads * seq_len * seq_len # TODO why?\n",
    "    # softmax @ value reductions\n",
    "    attvalue = 2 * seq_len * seq_len * (key_size * num_heads)\n",
    "    # final linear\n",
    "    attlinear = 2 * seq_len * (key_size * num_heads) * d_model\n",
    "    att = attention + attlogits + attsoftmax + attvalue + attlinear\n",
    "    # feed forward\n",
    "    dense = 2 * seq_len * (d_model * ffw_size + d_model * ffw_size)\n",
    "\n",
    "    # logits\n",
    "    logits = 2 * seq_len * d_model * vocab_size\n",
    "\n",
    "    forward_flops = embeddings + num_layers * (att + dense) + logits\n",
    "    backward_flops = 2 * forward_flops # as in Kaplan et al. 2020\n",
    "    total_flops = forward_flops + backward_flops\n",
    "\n",
    "    return total_flops\n",
    "\n",
    "flops(**gpt2)/1e9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "params: 69.72M\n",
      "approx flops: 428.34B\n",
      "chinchilla flops: 434.11B\n",
      "ratio (chinchilla / approx): 1.01\n"
     ]
    }
   ],
   "source": [
    "# Reproduce Table A4 from Chinchilla paper Appendix, \n",
    "# comparing accurate flops above to approximate flops F = 6*N*D\n",
    "# note Chinchilla uses vocab_size = 32K\n",
    "\n",
    "chin_73M = dict(seq_len = 1024, vocab_size = 32000, d_model = 640, num_heads = 10, num_layers = 10)\n",
    "args = chin_73M\n",
    "\n",
    "D = 1024 # dataset size, cancels anyway\n",
    "N = params(**args) \n",
    "F = flops(**args)\n",
    "\n",
    "approx_flops = 6*D*N\n",
    "chinch_flops = F * (float(D) / args['seq_len'])\n",
    "\n",
    "print(f\"params: {N/1e6:.2f}M\")\n",
    "print(f\"approx flops: {approx_flops/1e9:.2f}B\")\n",
    "print(f\"chinchilla flops: {chinch_flops/1e9:.2f}B\")\n",
    "print(f\"ratio (chinchilla / approx): {chinch_flops / approx_flops:.2f}\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well this is awkward because Chinchilla paper claims that number of params for these args are 73M (we see only 70M), and the ratio is supposed to be 1.03 but we get 1.01. TODO stare at more..."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## scaling laws"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x7fd5bc48bb80>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def L(N, D):\n",
    "    \"\"\" \n",
    "    Approximates loss given N parameters and D dataset size (in tokens),\n",
    "    per Chinchilla paper.\n",
    "    \"\"\"\n",
    "    E = 1.69 # entropy of natural language, limit of infinite model on infinite data\n",
    "    A = 406.4\n",
    "    B = 410.7\n",
    "    alpha = 0.34\n",
    "    beta = 0.28\n",
    "    return A / (N ** alpha) + B / (D ** beta) + E\n",
    "\n",
    "ns = 10 ** np.arange(7, 11, step=2**-4) # model sizes from 10M to 100B\n",
    "ds = 10 ** np.arange(9, 12, step=2**-4) # dataset sizes from 1B to 1T\n",
    "plt.figure(figsize=(15, 5))\n",
    "# plot a heatmap of loss as a function of model size and dataset size\n",
    "plt.subplot(121)\n",
    "plt.imshow(np.array([[L(n, d) for d in ds] for n in ns]), extent=[9, 12, 7, 11], origin='lower')\n",
    "plt.xlabel('log10(dataset size)')\n",
    "plt.ylabel('log10(model size)')\n",
    "plt.title('loss')\n",
    "plt.colorbar()\n",
    "# plot the compute for each point, which is a deterministic function: flops = 6*N*D\n",
    "plt.subplot(122)\n",
    "plt.imshow(np.log10(np.array([[6*n*d for d in ds] for n in ns])), extent=[9, 12, 7, 11], origin='lower')\n",
    "plt.xlabel('log10(dataset size)')\n",
    "plt.ylabel('log10(model size)')\n",
    "plt.title('log10 flops')\n",
    "plt.colorbar()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok so given any N,D we can estimate both: 1) the loss, and 2) the total flops. Now we want to solve the following problem: Given a specific budget of flops C, find: N_opt, D_opt = argmin_{FLOPs(N,D) = C} L(N, D). i.e. how big of a model should we train and for how many tokens?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "best model size: 316.23M\n",
      "best dataset size: 10.12B\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'loss')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = 1.92e19 # target compute budget (usually know this because we know how many GPU for how long go brrr)\n",
    "# sweep model sizes from 10M to 100B\n",
    "ns = 10 ** np.arange(7, 11, step=2**-4)\n",
    "# using C = 6*N*D, solve for D that maintains the compute budget c\n",
    "ds = c / (6 * ns)\n",
    "# evaluate the loss in each case\n",
    "losses = L(ns, ds)\n",
    "# find the argmin\n",
    "best = np.argmin(losses)\n",
    "print(f\"best model size: {ns[best]/1e6:.2f}M\")\n",
    "print(f\"best dataset size: {ds[best]/1e9:.2f}B\")\n",
    "# plot the loss\n",
    "plt.figure(figsize=(3,3))\n",
    "plt.plot(ns, losses)\n",
    "plt.xscale('log')\n",
    "# plot a vertical bar at the best model size\n",
    "plt.axvline(ns[best], color='red')\n",
    "plt.xlabel('model size')\n",
    "plt.ylabel('loss')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the plot above, basically the models on the left of best are too small and trained for too long. The models on the right of best are way too large and trained for too little. The model at the red line is just right.\n",
    "\n",
    "Now, the Chinchilla paper says that best model size is 400M params and 8B tokens, so this disagrees and there is some calculations problem. TODO figure out and fix..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "compute budget 1.000000e+17: best model size: 29.43M, best dataset size: 0.57B\n",
      "compute budget 1.778279e+17: best model size: 36.52M, best dataset size: 0.81B\n",
      "compute budget 3.162278e+17: best model size: 48.70M, best dataset size: 1.08B\n",
      "compute budget 5.623413e+17: best model size: 60.43M, best dataset size: 1.55B\n",
      "compute budget 1.000000e+18: best model size: 80.58M, best dataset size: 2.07B\n",
      "compute budget 1.778279e+18: best model size: 107.46M, best dataset size: 2.76B\n",
      "compute budget 3.162278e+18: best model size: 133.35M, best dataset size: 3.95B\n",
      "compute budget 5.623413e+18: best model size: 177.83M, best dataset size: 5.27B\n",
      "compute budget 1.000000e+19: best model size: 220.67M, best dataset size: 7.55B\n",
      "compute budget 1.778279e+19: best model size: 294.27M, best dataset size: 10.07B\n",
      "compute budget 3.162278e+19: best model size: 392.42M, best dataset size: 13.43B\n",
      "compute budget 5.623413e+19: best model size: 486.97M, best dataset size: 19.25B\n",
      "compute budget 1.000000e+20: best model size: 649.38M, best dataset size: 25.67B\n",
      "compute budget 1.778279e+20: best model size: 865.96M, best dataset size: 34.23B\n",
      "compute budget 3.162278e+20: best model size: 1074.61M, best dataset size: 49.05B\n",
      "compute budget 5.623413e+20: best model size: 1433.01M, best dataset size: 65.40B\n",
      "compute budget 1.000000e+21: best model size: 1778.28M, best dataset size: 93.72B\n",
      "compute budget 1.778279e+21: best model size: 2371.37M, best dataset size: 124.98B\n",
      "compute budget 3.162278e+21: best model size: 3162.28M, best dataset size: 166.67B\n",
      "compute budget 5.623413e+21: best model size: 3924.19M, best dataset size: 238.84B\n",
      "compute budget 1.000000e+22: best model size: 5232.99M, best dataset size: 318.49B\n",
      "compute budget 1.778279e+22: best model size: 6493.82M, best dataset size: 456.40B\n",
      "compute budget 3.162278e+22: best model size: 8659.64M, best dataset size: 608.62B\n",
      "compute budget 5.623413e+22: best model size: 11547.82M, best dataset size: 811.61B\n",
      "compute budget 1.000000e+23: best model size: 14330.13M, best dataset size: 1163.05B\n",
      "compute budget 1.778279e+23: best model size: 19109.53M, best dataset size: 1550.95B\n",
      "compute budget 3.162278e+23: best model size: 23713.74M, best dataset size: 2222.54B\n",
      "compute budget 5.623413e+23: best model size: 31622.78M, best dataset size: 2963.80B\n",
      "compute budget 1.000000e+24: best model size: 42169.65M, best dataset size: 3952.29B\n",
      "compute budget 1.778279e+24: best model size: 52329.91M, best dataset size: 5663.68B\n",
      "compute budget 3.162278e+24: best model size: 69783.06M, best dataset size: 7552.64B\n",
      "compute budget 5.623413e+24: best model size: 93057.20M, best dataset size: 10071.61B\n",
      "compute budget 1.000000e+25: best model size: 115478.20M, best dataset size: 14432.74B\n",
      "compute budget 1.778279e+25: best model size: 153992.65M, best dataset size: 19246.37B\n",
      "compute budget 3.162278e+25: best model size: 191095.30M, best dataset size: 27580.28B\n",
      "compute budget 5.623413e+25: best model size: 254829.67M, best dataset size: 36778.90B\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd5bc240070>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# sweep over compute budgets from 1e17 to 1e26\n",
    "cs = 10 ** np.arange(17, 26, step=2**-2)\n",
    "best_ns = []\n",
    "best_ds = []\n",
    "for c in cs:\n",
    "    ns = 10 ** np.arange(7, 14, step=2**-5)\n",
    "    ds = c / (6 * ns)\n",
    "    losses = L(ns, ds)\n",
    "    best = np.argmin(losses)\n",
    "    best_ns.append(ns[best])\n",
    "    best_ds.append(ds[best])\n",
    "    print(f\"compute budget {c:e}: best model size: {ns[best]/1e6:.2f}M, best dataset size: {ds[best]/1e9:.2f}B\")\n",
    "\n",
    "# plot both the model size and dataset size as a function of compute budget, on one plot\n",
    "plt.figure(figsize=(10,3))\n",
    "plt.plot(cs, best_ns, label='model size')\n",
    "plt.plot(cs, best_ds, label='dataset size')\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.xlabel('compute budget')\n",
    "plt.ylabel('model size / dataset size')\n",
    "plt.grid(True, which=\"both\", ls=\"-\", color='k', alpha=0.2)\n",
    "plt.legend()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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