ariG23498 · March 30, 2021 13:23
diff --git a/pos_enc.ipynb b/pos_enc.ipynb
 {
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "scratchpad",
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/ariG23498/85de26ade1b55876d67d65da097eb8f0/scratchpad.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lIYdn1woOS1n"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "C8O_OmysbG-V"
      },
      "source": [
        "# Building a binary representation\n",
        "# of 50 numbers with 10 binary units\n",
        "box = np.zeros(shape=(50,50))\n",
        "for n in range(50):\n",
        "    b = bin(n).replace(\"0b\", \"\")\n",
        "    size = len(b)\n",
        "    box[n,0:size]=[int(x) for x in b]"
      ],
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "id": "QrN4J7cvccKA",
        "outputId": "af8ba474-6dde-4242-d5ce-84618ffb0e29"
      },
      "source": [
        "plt.imshow(box)"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7f3bad722610>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FdByvOD0dW7W"
      },
      "source": [
        "def _sint(w,t):\n",
        "    return np.sin(w*t)\n",
        "def _cost(w,t):\n",
        "    return np.cos(w*t)"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9vIoL1atcea3"
      },
      "source": [
        "# Building a binary representation\n",
        "# of 50 numbers with positional embeddings\n",
        "box = np.zeros(shape=(50,50))\n",
        "d = 50\n",
        "for t in range(50):\n",
        "    for i in range(50):\n",
        "        if i%2 == 0:\n",
        "            # sin\n",
        "            k = i/2\n",
        "            w = 1/np.power(10_000,(2*k/d))\n",
        "            box[t,i]=_sint(w,t)\n",
        "        else:\n",
        "            # cos\n",
        "            k = i/2\n",
        "            w = 1/np.power(10_000,(2*k/d))\n",
        "            box[t,i]=_cost(w,t)"
      ],
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "id": "8VdcFP6NeQJm",
        "outputId": "ad31b396-c8df-4fe9-c9b0-449792542caf"
      },
      "source": [
        "plt.imshow(box)"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7f3bad76a2d0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
 }
	{
	"nbformat": 4,
	"nbformat_minor": 0,
	"metadata": {
	"colab": {
	"name": "scratchpad",
	"provenance": [],
	"include_colab_link": true
	},
	"kernelspec": {
	"display_name": "Python 3",
	"name": "python3"
	}
	},
	"cells": [
	{
	"cell_type": "markdown",
	"metadata": {
	"id": "view-in-github",
	"colab_type": "text"
	},
	"source": [
	"<a href=\"https://colab.research.google.com/gist/ariG23498/85de26ade1b55876d67d65da097eb8f0/scratchpad.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "lIYdn1woOS1n"
	},
	"source": [
	"import numpy as np\n",
	"import matplotlib.pyplot as plt"
	],
	"execution_count": 1,
	"outputs": []
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "C8O_OmysbG-V"
	},
	"source": [
	"# Building a binary representation\n",
	"# of 50 numbers with 10 binary units\n",
	"box = np.zeros(shape=(50,50))\n",
	"for n in range(50):\n",
	" b = bin(n).replace(\"0b\", \"\")\n",
	" size = len(b)\n",
	" box[n,0:size]=[int(x) for x in b]"
	],
	"execution_count": 20,
	"outputs": []
	},
	{
	"cell_type": "code",
	"metadata": {
	"colab": {
	"base_uri": "https://localhost:8080/",
	"height": 285
	},
	"id": "QrN4J7cvccKA",
	"outputId": "af8ba474-6dde-4242-d5ce-84618ffb0e29"
	},
	"source": [
	"plt.imshow(box)"
	],
	"execution_count": 21,
	"outputs": [
	{
	"output_type": "execute_result",
	"data": {
	"text/plain": [
	"<matplotlib.image.AxesImage at 0x7f3bad722610>"
	]
	},
	"metadata": {
	"tags": []
	},
	"execution_count": 21
	},
	{
	"output_type": "display_data",
	"data": {
	"image/png": "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\n",
	"text/plain": [
	"<Figure size 432x288 with 1 Axes>"
	]
	},
	"metadata": {
	"tags": [],
	"needs_background": "light"
	}
	}
	]
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "FdByvOD0dW7W"
	},
	"source": [
	"def _sint(w,t):\n",
	" return np.sin(w*t)\n",
	"def _cost(w,t):\n",
	" return np.cos(w*t)"
	],
	"execution_count": 11,
	"outputs": []
	},
	{
	"cell_type": "code",
	"metadata": {
	"id": "9vIoL1atcea3"
	},
	"source": [
	"# Building a binary representation\n",
	"# of 50 numbers with positional embeddings\n",
	"box = np.zeros(shape=(50,50))\n",
	"d = 50\n",
	"for t in range(50):\n",
	" for i in range(50):\n",
	" if i%2 == 0:\n",
	" # sin\n",
	" k = i/2\n",
	" w = 1/np.power(10_000,(2*k/d))\n",
	" box[t,i]=_sint(w,t)\n",
	" else:\n",
	" # cos\n",
	" k = i/2\n",
	" w = 1/np.power(10_000,(2*k/d))\n",
	" box[t,i]=_cost(w,t)"
	],
	"execution_count": 18,
	"outputs": []
	},
	{
	"cell_type": "code",
	"metadata": {
	"colab": {
	"base_uri": "https://localhost:8080/",
	"height": 285
	},
	"id": "8VdcFP6NeQJm",
	"outputId": "ad31b396-c8df-4fe9-c9b0-449792542caf"
	},
	"source": [
	"plt.imshow(box)"
	],
	"execution_count": 19,
	"outputs": [
	{
	"output_type": "execute_result",
	"data": {
	"text/plain": [
	"<matplotlib.image.AxesImage at 0x7f3bad76a2d0>"
	]
	},
	"metadata": {
	"tags": []
	},
	"execution_count": 19
	},
	{
	"output_type": "display_data",
	"data": {
	"image/png": "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\n",
	"text/plain": [
	"<Figure size 432x288 with 1 Axes>"
	]
	},
	"metadata": {
	"tags": [],
	"needs_background": "light"
	}
	}
	]
	}
	]
	}