jax_opti.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "jax_opti.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "sXNntKuSEFOw",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import jax\n",
        "import jax.numpy as np\n",
        "import numpy as onp\n",
        "from jax.api import jit, grad\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "\n",
        "from sklearn.datasets import make_moons\n",
        "onp.random.seed(42)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gC_XQ8zoI6sF",
        "colab_type": "code",
        "outputId": "6cdbd6dd-afeb-4c45-f0dd-ad6623781369",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "X, y = make_moons(1000, noise = 0.5)\n",
        "\n",
        "axes = [-1.5, 2.5, -1, 1.5]\n",
        "def plot_data(X, y, axes):\n",
        "  plt.plot(X[:,0][y==0], X[:,1][y==0], \"bs\")\n",
        "  plt.plot(X[:,0][y==1], X[:,1][y==1], \"g^\")\n",
        "\n",
        "plot_data(X, y, axes)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ImJ424gOWOEbfcH6Vb92JOKWOTk8DCx+Wj8VakMZ3W8mM1Hg+8MwLju/vebem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\nrkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CIfVVQwvG3Fr",
        "colab_type": "code",
        "outputId": "db438277-edf4-4c6b-f551-e3ac5f16ac23",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "X.shape"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1000, 2)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GAY89kvsJFeE",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def sigmoid(x):\n",
        "  return 1/(1+np.exp(x))\n",
        "\n",
        "def init_params():\n",
        "  onp.random.seed(2)\n",
        "  return [onp.random.randn(2, 4), #w1\n",
        "  onp.zeros(4), #b1\n",
        "  onp.random.randn(4, 1),#w2\n",
        "  onp.random.randn(1)]\n",
        "\n",
        "def predict(X, params):\n",
        "  W1 = params[0]\n",
        "  b1 = params[1]\n",
        "  W2 = params[2]\n",
        "  b2 = params[3]\n",
        "  Z1 = np.dot(X, W1) + b1\n",
        "  A1 = sigmoid(Z1)\n",
        "  Z2 = np.dot(A1, W2) + b2\n",
        "  A2 = sigmoid(Z2)\n",
        "\n",
        "  return A2\n",
        "\n",
        "def loss(params, X, y):\n",
        "  A2 = predict(X, params)\n",
        "  m = 1000*1000\n",
        "  loss = -(1/m)*np.sum(y*np.log(A2) + (1-y)*np.log(1-A2))\n",
        "  return loss"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dsVNAxo7OWzt",
        "colab_type": "code",
        "outputId": "065ab234-a0ce-4414-9bb8-80f56dbb1dca",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 381
        }
      },
      "source": [
        "X1 = np.asarray(X)\n",
        "lr = 0.01\n",
        "num_epochs = 5000\n",
        "loss_grads = jax.jit(jax.grad(loss))\n",
        "params = init_params()\n",
        "costs = []\n",
        "for i in range(num_epochs):\n",
        "  #print(\"epoch-> \" + str(i+1))\n",
        "  A2 = predict(X, params)\n",
        "  cost = loss(params, X, y)\n",
        "  costs.append(cost)\n",
        "  #print(\"cost ->\" + str(cost))\n",
        "  grads = (loss_grads(params, X, y))\n",
        "  params = [param - lr*grad for param, grad in zip(params, grads)]\n",
        "  if i%500 == 0:\n",
        "    print(\"epoch ->\" + str(i))\n",
        "    print(\"cost ->\" + str(cost))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "epoch ->0\n",
            "cost ->0.73080736\n",
            "epoch ->500\n",
            "cost ->0.7121929\n",
            "epoch ->1000\n",
            "cost ->0.7046052\n",
            "epoch ->1500\n",
            "cost ->0.7007019\n",
            "epoch ->2000\n",
            "cost ->0.6985697\n",
            "epoch ->2500\n",
            "cost ->0.6973104\n",
            "epoch ->3000\n",
            "cost ->0.6965039\n",
            "epoch ->3500\n",
            "cost ->0.69594675\n",
            "epoch ->4000\n",
            "cost ->0.6955439\n",
            "epoch ->4500\n",
            "cost ->0.6952377\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "56UVa4kAP9dG",
        "colab_type": "code",
        "outputId": "dd91e567-d62c-4a06-edb8-8e805b32fb6d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "plt.plot(costs)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f204c176fd0>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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KgG52+1XjaG515r+qsQAR6dsUAN1sdH46M0uH89jynToKEJE+TQHQA+64WkcBItL3KQB6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\ngg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gMFxUcD_RdbB",
        "colab_type": "code",
        "outputId": "0f2e9679-9bfc-4b11-d82a-2f25f7f6c244",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 381
        }
      },
      "source": [
        "#stochastic gd with learning rate decay\n",
        "params = init_params()\n",
        "costs_2 = []\n",
        "lrl = 0.01\n",
        "lrT = 0.01*lrl\n",
        "T = 3500\n",
        "num_epochs = 5000\n",
        "for i in range(num_epochs):\n",
        "  A2 = predict(X, params)\n",
        "  cost = loss(params, X, y)\n",
        "  costs_2.append(cost)\n",
        "  #print(\"cost ->\" + str(cost))\n",
        "  if lrl>lrT:\n",
        "    lrl = lrl*(1-i/T) + lrT\n",
        "  else:\n",
        "    lrl = lrT\n",
        "  grads = (loss_grads(params, X, y))\n",
        "  params = [param - lrl*grad for param, grad in zip(params, grads)]\n",
        "  if i%500 == 0:\n",
        "    print(\"epoch ->\" + str(i))\n",
        "    print(\"cost ->\" + str(cost))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "epoch ->0\n",
            "cost ->0.7308064\n",
            "epoch ->500\n",
            "cost ->0.7213865\n",
            "epoch ->1000\n",
            "cost ->0.72047585\n",
            "epoch ->1500\n",
            "cost ->0.7199732\n",
            "epoch ->2000\n",
            "cost ->0.71962583\n",
            "epoch ->2500\n",
            "cost ->0.71936333\n",
            "epoch ->3000\n",
            "cost ->0.7191511\n",
            "epoch ->3500\n",
            "cost ->0.71897525\n",
            "epoch ->4000\n",
            "cost ->0.718812\n",
            "epoch ->4500\n",
            "cost ->0.71865344\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GF2f-SJCY6Po",
        "colab_type": "code",
        "outputId": "b7a40f55-19c5-48a1-bc7f-1e18a607bfa8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "plt.plot(costs_2)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f1cb1f1a390>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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F1efN5JV3mjjcqncEi8jUpwBI8fELa3CHJ9/I6isKREQmhAIgxYKqYpbUlLLm9QPZboqI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\nQEQkohQAIiIRpQAQEYmo/w/rvKV45DArGwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YCkESk17ax5n",
        "colab_type": "code",
        "outputId": "5f9c8204-9745-4607-ed6d-923584d608fe",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "#sgd with weight updates starts converging before the 1000th epoch\n",
        "plt.plot(costs_2[0:1000]) "
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f206e9559e8>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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BzQ8kIpOPAmCCmBl/vGwWu9uP6cYwEZmUFAAT6NpFM1hQlss//3IrvX0D8S5HRGQYBcAE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\nASAiElIKABGRkFIAiIiElAJARCSk/j9/MlF1ZeMgtAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Vh-90Zt2a65W",
        "colab_type": "code",
        "outputId": "76b6a0d4-df9f-4177-cc5f-7e79ae02ac58",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 381
        }
      },
      "source": [
        "#momentum\n",
        "def init_vel():\n",
        "  return [onp.zeros((2, 4)),\n",
        "          onp.zeros((4)),\n",
        "          onp.zeros((4,1)),\n",
        "          onp.zeros((1))]\n",
        "\n",
        "vel = init_vel()\n",
        "alpha = 0.9\n",
        "params = init_params()\n",
        "num_epochs = 5000\n",
        "lr = 0.01\n",
        "costs_3 = []\n",
        "for i in range(num_epochs):\n",
        "  A2 = predict(X, params)\n",
        "  cost = loss(params, X, y)\n",
        "  costs_3.append(cost)\n",
        "  #print(\"cost ->\" + str(cost))\n",
        "  grads = (loss_grads(params, X, y))\n",
        "  vel = [alpha*v - lr*grad for v, grad in zip(vel, grads)]\n",
        "  params = [param + v for v, param in zip(vel, params)]\n",
        "  if i%500 == 0:\n",
        "    print(\"epoch ->\" + str(i))\n",
        "    print(\"cost ->\" + str(cost))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "epoch ->0\n",
            "cost ->0.73080677\n",
            "epoch ->500\n",
            "cost ->0.6949923\n",
            "epoch ->1000\n",
            "cost ->0.6941223\n",
            "epoch ->1500\n",
            "cost ->0.69392157\n",
            "epoch ->2000\n",
            "cost ->0.69380355\n",
            "epoch ->2500\n",
            "cost ->0.6937118\n",
            "epoch ->3000\n",
            "cost ->0.6936388\n",
            "epoch ->3500\n",
            "cost ->0.69357693\n",
            "epoch ->4000\n",
            "cost ->0.69352573\n",
            "epoch ->4500\n",
            "cost ->0.693483\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fJgUekVeeSID",
        "colab_type": "code",
        "outputId": "f24f471d-d282-43ad-e5f6-bc92b8b1a2f8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "plt.plot(costs_3)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f1cb1d79c88>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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pEUlbJG2W9F9T+aTtt6RWST+U9JPU5z9J5YslPZb69iVJlVTektY70/aLcsf6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\n0mN6ma8AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yK3IcUlRPo8x",
        "colab_type": "code",
        "outputId": "3caed26e-a3dd-422e-f804-9efcd4cf6b6e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "#this also starts converging before the 1000th epoch\n",
        "plt.plot(costs_3[0:1000])"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f1cb1c7df60>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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EonoBn0wsmQTATKA9bboDuGJInfMBzOwXpA4TfcndnwZ+DdxjZn8LlALv4cTg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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3yQatXBFhbTo",
        "colab_type": "code",
        "outputId": "cc4fdb6e-d356-4ca5-f980-2f96ac82b6e2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 381
        }
      },
      "source": [
        "#nestero momentum\n",
        "vel = init_vel()\n",
        "params = init_params()\n",
        "params1 = init_params() #not required to init the same way\n",
        "alpha = 0.9\n",
        "lr = 0.01\n",
        "num_epochs = 5000\n",
        "costs_4 = []\n",
        "for i in range(num_epochs):\n",
        "  A2 = predict(X, params)\n",
        "  cost = loss(params, X, y)\n",
        "  costs_4.append(cost)\n",
        "  param1 = [param + alpha*v for param, v in zip(params, vel)]\n",
        "  grads = loss_grads(param1, X, y)\n",
        "  vel = [alpha*v - lr*grad for v, grad in zip(vel, grads)]\n",
        "  params = [param + v for param, v in zip(params, vel)]\n",
        "  if i%500 ==0:\n",
        "    print(\"epoch ->\" + str(i))\n",
        "    print(\"cost ->\" + str(cost))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "epoch ->0\n",
            "cost ->0.73080724\n",
            "epoch ->500\n",
            "cost ->0.6949979\n",
            "epoch ->1000\n",
            "cost ->0.6941221\n",
            "epoch ->1500\n",
            "cost ->0.6939217\n",
            "epoch ->2000\n",
            "cost ->0.69380367\n",
            "epoch ->2500\n",
            "cost ->0.69371253\n",
            "epoch ->3000\n",
            "cost ->0.69363886\n",
            "epoch ->3500\n",
            "cost ->0.69357705\n",
            "epoch ->4000\n",
            "cost ->0.69352627\n",
            "epoch ->4500\n",
            "cost ->0.6934829\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_A-zCsHJuVyW",
        "colab_type": "code",
        "outputId": "474ce8e6-0129-4a66-c041-0ce078a3758b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "plt.plot(costs_4)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f1cb1b149e8>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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pbw9Iqqby5rTcldZfntvXJ1P5NknvbEyP6iepLOmfJH0vLU/pPkv6iaQnJW2W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\nKAeAmVlBOQDMzArKAWBmVlAOADOzgvr/oR3D9eNdsFcAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YJiZO703P3tW",
        "colab_type": "code",
        "outputId": "fde0087c-9390-4cdd-b728-04a2b7ec5ff4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "#starts converging before the 1000th epoch as well\n",
        "plt.plot(costs_4[0:1000])"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f1cb19866a0>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 33
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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edrbvPcz2vYfZtvfwUfNrt+2j9WAHhztTfW4DYFhhgsrSJJUlR4dDVUmSitIk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\nAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3gqx8FEhumDx",
        "colab_type": "code",
        "outputId": "ac679789-2ef2-4306-e675-7ff87001f1e2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 381
        }
      },
      "source": [
        "#adagrad\n",
        "def init_r():\n",
        "  return [np.zeros((2,4)),\n",
        "          np.zeros((4)),\n",
        "          np.zeros((4,1)),\n",
        "          np.zeros((1))]\n",
        "\n",
        "r = init_r()\n",
        "delta_params = init_r() #same fn can be used\n",
        "costs_5 = []\n",
        "delta = 1e-7\n",
        "params = init_params()\n",
        "num_epochs = 5000\n",
        "lr = 0.01\n",
        "for i in range(num_epochs):\n",
        "  A2 = predict(X, params)\n",
        "  cost = loss(params, X, y)\n",
        "  costs_5.append(cost)\n",
        "  grads = loss_grads(params, X, y)\n",
        "  r = [r1 + grad*grad for r1, grad in zip(r, grads)]\n",
        "  delta_params = [-(lr/(delta+np.sqrt(r1)))*grad for r1, grad in zip(r, grads)]\n",
        "  params = [param + delta_param for param, delta_param in zip(params, delta_params)]\n",
        "  if i%500==0:\n",
        "    print(\"epoch ->\" + str(i))\n",
        "    print(\"cost ->\" + str(cost))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "epoch ->0\n",
            "cost ->0.7308077\n",
            "epoch ->500\n",
            "cost ->0.6953798\n",
            "epoch ->1000\n",
            "cost ->0.6941752\n",
            "epoch ->1500\n",
            "cost ->0.6938345\n",
            "epoch ->2000\n",
            "cost ->0.69364655\n",
            "epoch ->2500\n",
            "cost ->0.69352406\n",
            "epoch ->3000\n",
            "cost ->0.69343996\n",
            "epoch ->3500\n",
            "cost ->0.6933802\n",
            "epoch ->4000\n",
            "cost ->0.6933365\n",
            "epoch ->4500\n",
            "cost ->0.69330364\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dJMdH3Ciypjk",
        "colab_type": "code",
        "outputId": "2a78fd32-00c8-4cb9-e357-88c6dc31ce68",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "plt.plot(costs_5)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f1cb18aafd0>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 36
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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zAJiZFZQDwMysoBwAZmYF5QAwMysoB4CZWUE5AMzMCsoBYGZWUOPq20AldQC/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\nTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eJA_bPR37pa-",
        "colab_type": "code",
        "outputId": "b0c16618-6f7c-469b-9404-9414efeed4e7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "#starts converging before the 1000th epoch as well\n",
        "plt.plot(costs_5[0:1000])"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f1cb149e2e8>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 37
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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IBZ4zs9+5+95g01vdfX5GeySSJjOjtCBOaUH8sHMMHdydhoOtbN7TyOaGJjY3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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GmBh3NLPz2O9",
        "colab_type": "code",
        "outputId": "6c18dca4-7850-4735-fd3e-c5aa3a50d422",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 381
        }
      },
      "source": [
        "#rmsprop\n",
        "r = init_r()\n",
        "vel = init_vel()\n",
        "lr = 0.01\n",
        "rho = 0.1\n",
        "alpha = 0.9\n",
        "costs_6 = []\n",
        "delta = 1e-7\n",
        "params = init_params()\n",
        "params1 = init_params()\n",
        "num_epochs = 5000\n",
        "for i in range(num_epochs):\n",
        "  A2 = predict(X, params)\n",
        "  cost = loss(params, X, y)\n",
        "  costs_6.append(cost)\n",
        "  params1 = [param + alpha*v for param, v in zip(params, vel)]\n",
        "  grads = loss_grads(params1, X, y)\n",
        "  r = [r1*rho + (1-rho)*grad*grad for r1, grad in zip(r, grads)]\n",
        "  vel = [alpha*v - grad*lr/(delta + np.sqrt(r1)) for v, r1, grad in zip(vel, r, grads)]\n",
        "  params = [param + v for param, v in zip(params, vel)]\n",
        "  if i%500==0:\n",
        "    print(\"epoch ->\" + str(i))\n",
        "    print(\"cost ->\" + str(cost))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "epoch ->0\n",
            "cost ->0.730807\n",
            "epoch ->500\n",
            "cost ->0.6931673\n",
            "epoch ->1000\n",
            "cost ->0.69316393\n",
            "epoch ->1500\n",
            "cost ->0.69316256\n",
            "epoch ->2000\n",
            "cost ->0.6931605\n",
            "epoch ->2500\n",
            "cost ->0.69315857\n",
            "epoch ->3000\n",
            "cost ->0.6931565\n",
            "epoch ->3500\n",
            "cost ->0.69315624\n",
            "epoch ->4000\n",
            "cost ->0.69315535\n",
            "epoch ->4500\n",
            "cost ->0.69315463\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YriNAz8MMSRd",
        "colab_type": "code",
        "outputId": "9a4b0fd4-5fc1-4f57-a714-575828f7d91f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "plt.plot(costs_6)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f1cb13b0a90>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 40
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "w_TzN6A5NETP",
        "colab_type": "code",
        "outputId": "e954bf4e-1352-4770-dc0f-8816939d01fd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "#this looks really steep\n",
        "#lets plot out epochs 0-500 to check where it starts converging\n",
        "plt.plot(costs_6[0:500])"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f1cb129c278>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 41
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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j3hNYUhW4A7gU2AVslLQ2Ip5q1ImIG0v1bwDOT8/nAH8CdAIBbErHvpyqfyoiulvVmWZI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\nMuUAMDPLlAPAzCxT/x/c7mhB0ajuewAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "C784R99_s23v",
        "colab_type": "code",
        "outputId": "f5422913-559e-43fb-b121-2a6d62e4ff68",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "#still no, plotting out 0-100 epochs\n",
        "plt.plot(costs_6[0:100])"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f1cb12788d0>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 42
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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UjWcdRcM/F/A60CwpN9k+I+LBiFgdEavb29tL2HV5LW7N0zc4Qs+J/sv+2WZm06mUANgK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\nRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rLyn-cAf82p9",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}