lecture_030/[GPU_MODE]_Quantized_training.ipynb

{
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  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "## Low-bit SGD\n",
        "\n",
        "https://pytorch.org/docs/stable/generated/torch.optim.SGD.html\n",
        "\n",
        "![image.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "rXikGHphH65g"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "from torch import Tensor\n",
        "\n",
        "def sgd(p: Tensor, grad: Tensor, momentum_buffer: Tensor, lr: float, momentum: float):\n",
        "    new_momentum_buffer = momentum_buffer * momentum + grad\n",
        "    new_p = p - lr * new_momentum_buffer\n",
        "\n",
        "    momentum_buffer.copy_(new_momentum_buffer)\n",
        "    p.copy_(new_p)\n",
        "\n",
        "lr = 1e-4\n",
        "momentum = 0.9\n",
        "\n",
        "torch.manual_seed(2024)\n",
        "p = torch.randn(4, 4)\n",
        "momentum_buffer = torch.randn(4, 4)\n",
        "\n",
        "for _ in range(5):\n",
        "    grad = torch.randn(4, 4)\n",
        "    sgd(p, grad, momentum_buffer, lr, momentum)\n",
        "p"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BVLM1WoTH6fp",
        "outputId": "9cc20573-1d3e-4d1b-f64c-4213a0f040fa"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[-1.2276, -0.0069,  1.5427, -0.4662],\n",
              "        [ 0.2781, -0.2610,  0.6238, -1.1576],\n",
              "        [ 0.1165, -1.8872,  2.1816, -0.1922],\n",
              "        [ 0.5355, -0.8906, -0.3107,  0.7731]])"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "SGD with BF16 optim state"
      ],
      "metadata": {
        "id": "cI-THA_U6BB7"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def sgd_bf16(p: Tensor, grad: Tensor, momentum_buffer: Tensor, lr: float, momentum: float):\n",
        "    # upcast to FP32 for accurate calculations\n",
        "    new_momentum_buffer = momentum_buffer.float() * momentum + grad\n",
        "    new_p = p - lr * new_momentum_buffer\n",
        "\n",
        "    momentum_buffer.copy_(new_momentum_buffer)  # implicit downcast to BF16\n",
        "    p.copy_(new_p)\n",
        "\n",
        "torch.manual_seed(2024)\n",
        "p = torch.randn(4, 4)\n",
        "grad = torch.randn(4, 4)\n",
        "momentum_buffer = torch.randn(4, 4).bfloat16()\n",
        "\n",
        "for _ in range(5):\n",
        "    grad = torch.randn(4, 4)\n",
        "    sgd_bf16(p, grad, momentum_buffer, lr, momentum)\n",
        "p"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nrqUQLlwJ2h_",
        "outputId": "69a9d138-213b-44b9-88d2-fd46a77ef177"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[-1.2275, -0.0075,  1.5428, -0.4662],\n",
              "        [ 0.2787, -0.2601,  0.6238, -1.1572],\n",
              "        [ 0.1170, -1.8873,  2.1821, -0.1927],\n",
              "        [ 0.5361, -0.8902, -0.3104,  0.7732]])"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "SGD with FP8 optim state"
      ],
      "metadata": {
        "id": "OMSy_Gng6FBM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def sgd_fp8(p: Tensor, grad: Tensor, momentum_buffer: Tensor, lr: float, momentum: float):\n",
        "    # upcast to FP32 for accurate calculations\n",
        "    new_momentum_buffer = momentum_buffer.float() * momentum + grad\n",
        "    new_p = p - lr * new_momentum_buffer\n",
        "\n",
        "    momentum_buffer.copy_(new_momentum_buffer)  # implicit downcast to FP8\n",
        "    p.copy_(new_p)\n",
        "\n",
        "torch.manual_seed(2024)\n",
        "p = torch.randn(4, 4)\n",
        "grad = torch.randn(4, 4)\n",
        "momentum_buffer = torch.randn(4, 4).to(torch.float8_e4m3fn)\n",
        "\n",
        "for _ in range(5):\n",
        "    grad = torch.randn(4, 4)\n",
        "    sgd_fp8(p, grad, momentum_buffer, lr, momentum)\n",
        "p"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6Bap5PWVLNEM",
        "outputId": "ef326148-7db1-475d-b64e-bbb153bff7f2"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[-1.2275, -0.0075,  1.5427, -0.4662],\n",
              "        [ 0.2787, -0.2601,  0.6238, -1.1572],\n",
              "        [ 0.1170, -1.8873,  2.1821, -0.1927],\n",
              "        [ 0.5361, -0.8902, -0.3104,  0.7732]])"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "SGD with scaled FP8 optim state (tensor-wise scaling)"
      ],
      "metadata": {
        "id": "W0l0MyQt6IOw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "DTYPE = torch.float8_e4m3fn\n",
        "\n",
        "def quantize_fp8(x: Tensor):\n",
        "    scale = x.abs().max() / torch.finfo(DTYPE).max\n",
        "    quantized_x = (x / scale.clip(1e-12)).to(DTYPE)\n",
        "    return quantized_x, scale\n",
        "\n",
        "def sgd_scaled_fp8(\n",
        "    p: Tensor,\n",
        "    grad: Tensor,\n",
        "    momentum_buffer: Tensor,\n",
        "    momentum_buffer_scale: Tensor,\n",
        "    lr: float,\n",
        "    momentum: float,\n",
        "):\n",
        "    # upcast to FP32 for accurate calculations\n",
        "    new_momentum_buffer = momentum_buffer.float() * momentum_buffer_scale * momentum + grad\n",
        "    new_p = p - lr * new_momentum_buffer\n",
        "\n",
        "    new_momentum_buffer_quantized, new_momentum_buffer_scale = quantize_fp8(new_momentum_buffer)\n",
        "    momentum_buffer.copy_(new_momentum_buffer_quantized)\n",
        "    momentum_buffer_scale.copy_(new_momentum_buffer_scale)\n",
        "    p.copy_(new_p)\n",
        "\n",
        "torch.manual_seed(2024)\n",
        "p = torch.randn(4, 4)\n",
        "grad = torch.randn(4, 4)\n",
        "momentum_buffer = torch.randn(4, 4)\n",
        "momentum_buffer, momentum_buffer_scale = quantize_fp8(momentum_buffer)\n",
        "\n",
        "for _ in range(5):\n",
        "    grad = torch.randn(4, 4)\n",
        "    sgd_scaled_fp8(p, grad, momentum_buffer, momentum_buffer_scale, lr, momentum)\n",
        "p"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cw6jLHdfLe9c",
        "outputId": "7fef759d-893b-4b80-cb99-0254879ed0a1"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[-1.2275, -0.0075,  1.5427, -0.4661],\n",
              "        [ 0.2787, -0.2602,  0.6238, -1.1573],\n",
              "        [ 0.1170, -1.8873,  2.1821, -0.1927],\n",
              "        [ 0.5361, -0.8902, -0.3104,  0.7731]])"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Stochastic rounding"
      ],
      "metadata": {
        "id": "J97oqmm95YOv"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Small changes in to a low-bit data won't change its value."
      ],
      "metadata": {
        "id": "1jvoopOW5z7d"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "\n",
        "# INT8 + small fraction\n",
        "\n",
        "x = torch.tensor(10, dtype=torch.int8)\n",
        "N = 100\n",
        "for _ in range(N):\n",
        "    x.copy_(x + 0.2)\n",
        "\n",
        "print(f\"Expected output: {10 + 0.2 * N}\")\n",
        "print(f\"Actual output: {x}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nYh3KpHq5X2B",
        "outputId": "8118c284-7378-47a8-ed94-5d87e91d84fa"
      },
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Expected output: 30.0\n",
            "Actual output: 10\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "$x$ will be rounded up to $\\lfloor x \\rfloor + 1$ with the probability of $(x - \\lfloor x \\rfloor)$, otherwise it is rounded down to $\\lfloor x \\rfloor + 1$."
      ],
      "metadata": {
        "id": "NsrMNXq-5zRc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def sr(x: torch.Tensor):\n",
        "    rand = torch.rand(x.shape, device=x.device)  # get a random number [0,1)\n",
        "    return torch.where(rand < x - x.floor(), x.floor() + 1, x.floor())\n",
        "\n",
        "x = torch.tensor(10, dtype=torch.int8)\n",
        "N = 100\n",
        "for _ in range(N):\n",
        "    x.copy_(sr(x.float() + 0.2))\n",
        "\n",
        "print(f\"Expected output: {10 + 0.2 * N}\")\n",
        "print(f\"Actual output: {x}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yLP3iyEV5yyg",
        "outputId": "973d23e8-c36c-4cbe-cdc5-98e3d841bb48"
      },
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Expected output: 30.0\n",
            "Actual output: 32\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Stochastic rounding for BF16\n",
        "\n",
        "<img src=\"https://i0.wp.com/semiengineering.com/wp-content/uploads/2019/10/Flex-Logix_BFloat16-fig1.png\" width=500>\n",
        "\n",
        "BF16 = FP32 with truncated mantissa bits. To do SR from FP32 -> BF16, we can do integer arithmetics on the mantissa bits"
      ],
      "metadata": {
        "id": "Lnf_23I27umq"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vikht-rm5Wav",
        "outputId": "7a900d28-26a7-439b-d171-cb3637796b78"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Expected output: 300\n",
            "Actual output: 256.0\n"
          ]
        }
      ],
      "source": [
        "x = torch.tensor(200, dtype=torch.bfloat16)\n",
        "N = 100\n",
        "for _ in range(N):\n",
        "    x.copy_(x + 1)\n",
        "\n",
        "print(f\"Expected output: {200 + N}\")\n",
        "print(f\"Actual output: {x}\")"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def bf16_sr(x: torch.Tensor):  # x is FP32\n",
        "    x_i32 = x.view(torch.int32)  # cast to INT32 to do bit manipulation\n",
        "    x_floor = x_i32 & 0xFFFF0000  # truncate the least significant 16 bits\n",
        "\n",
        "    # this will generate 31 random bits. we only need 16\n",
        "    rand = torch.empty(x.shape, dtype=torch.int32).random_()\n",
        "    rand = rand & 0xFFFF\n",
        "\n",
        "    out = torch.where(rand < (x_i32 & 0xFFFF), x_floor + 0x10000, x_floor)\n",
        "    return out.view(torch.float32).bfloat16()\n",
        "\n",
        "x = torch.tensor(200, dtype=torch.bfloat16)\n",
        "N = 100\n",
        "for _ in range(N):\n",
        "    x.copy_(bf16_sr(x.float() + 1))\n",
        "\n",
        "print(f\"Expected output: {200 + N}\")\n",
        "print(f\"Actual output: {x}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "m18zZZIw9MlO",
        "outputId": "685a9a3b-2b3f-4b54-e3c8-8dae5eaddf0b"
      },
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Expected output: 300\n",
            "Actual output: 300.0\n"
          ]
        }
      ]
    }
  ]
}