02_1_MLP_micrograd.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# implementing Optimization iteration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\" %matplotlib inline sets the backend of matplotlib to\\nthe 'inline' backend. When using the 'inline' backend,\\nyour matplotlib graphs will be included in your notebook,\\nnext to the code.\""
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "''' %matplotlib inline sets the backend of matplotlib to\n",
    "the 'inline' backend. When using the 'inline' backend,\n",
    "your matplotlib graphs will be included in your notebook,\n",
    "next to the code.'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from graphviz import Digraph\n",
    "\n",
    "def trace(root):\n",
    "    '''\n",
    "    Build a set of all nodes and edges in a graph,\n",
    "    the order does not matter\n",
    "    '''\n",
    "    nodes, edges = set(), set()\n",
    "    \n",
    "    def build(v): # a heuristic to get the nodes without order\n",
    "        if v not in nodes:\n",
    "            nodes.add(v)\n",
    "            for child in v._prev:\n",
    "                edges.add((child, v)) # define edge like this\n",
    "                build(child)\n",
    "\n",
    "    build(root)\n",
    "    return nodes, edges\n",
    "\n",
    "# first have an scheme of your desired graph based on the nodes and operations\n",
    "def draw_dot(root):\n",
    "    dot = Digraph(format='svg', graph_attr={'rankdir': 'LR'}) # LR : left to right\n",
    "\n",
    "    nodes, edges = trace(root)\n",
    "    for n in nodes:\n",
    "        uid = str(id(n))\n",
    "        # for any value in the graph, create a rectangular (record') node for it\n",
    "        # a visual node\n",
    "        dot.node(name=uid, label=f'{n.label} | data: {n.data} | grad: {n.grad}', shape='record')\n",
    "        if n._op:\n",
    "            # if this value is result of some operation, create an operation node for it\n",
    "            dot.node(name=uid+n._op , label=n._op) # n._op is a string\n",
    "            # and connect the op node to the value node\n",
    "            dot.edge(uid+n._op , uid)\n",
    "            for child in n._prev:\n",
    "                dot.edge( str(id(child)) , uid+n._op)\n",
    "    return dot"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A NN that subscribes to the PyTorch api"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we have our class Value\n",
    "class Value:\n",
    "    \n",
    "    def __init__(self, data, _prev=(), _op='', label=''):\n",
    "        self.data = data\n",
    "        self._prev = set(_prev) # the order does not matter, use set instead of list\n",
    "        self._op = _op\n",
    "        self.label = label\n",
    "\n",
    "        self.grad = 0.0\n",
    "\n",
    "        # After the forwrd path (when we have the data vlaue of all nodes)\n",
    "        # we start the backprop (to get the gradients for each node)\n",
    "        # the output node of each operation knows the operation and children\n",
    "        # since we dont have a backprop for leaf nodes, and \n",
    "        # each operation has different local gradient\n",
    "        # we can't define a general method in the class.\n",
    "        # so at the time of doing the operation,\n",
    "        # we can both define the local gradiant function\n",
    "        # and store the whole chain rule function in an attribute to call later.\n",
    "        # then call the local this function attribute from end node to the begining.\n",
    "        self._backprop = lambda: None\n",
    "    \n",
    "    def __repr__(self) -> str:\n",
    "        return f'Value({self.label} | data:{self.data} | grad:{self.grad})'\n",
    "    \n",
    "    def __add__(self, other):\n",
    "        # check if 'other' is an instance of 'Value'\n",
    "        other = other if isinstance(other, Value) else Value(other)\n",
    "\n",
    "        out = Value(self.data + other.data, (self, other), _op='+')\n",
    "        \n",
    "        def _backprop():\n",
    "            # partial derivatives for each input:\n",
    "            self.grad += out.grad\n",
    "            other.grad += out.grad\n",
    "\n",
    "        out._backprop = _backprop\n",
    "        return out\n",
    "    \n",
    "    def __radd__(self, other):\n",
    "        return self + other\n",
    "    \n",
    "    def __sub__(self, other):\n",
    "        return self + -1*other\n",
    "    \n",
    "    def __rsub__(self, other):\n",
    "        return -1*(self + -1*other)\n",
    "    \n",
    "    def __neg__(self):\n",
    "        return self * -1\n",
    "\n",
    "    def __mul__(self, other):\n",
    "        # check if 'other' is an instance of 'Value'\n",
    "        other = other if isinstance(other, Value) else Value(other)\n",
    "\n",
    "        out = Value(self.data * other.data, (self, other), _op='*')\n",
    "        \n",
    "        def _backprop():\n",
    "            # partial derivatives for each input:\n",
    "            self.grad += other.data * out.grad\n",
    "            other.grad += self.data * out.grad\n",
    "        \n",
    "        out._backprop = _backprop\n",
    "        return out\n",
    "    \n",
    "    def __rmul__(self, other):\n",
    "        return self * other\n",
    "\n",
    "    def __truediv__(self, other):\n",
    "        return self * other**-1\n",
    "    \n",
    "    def __rtruediv__(self, other):\n",
    "        return other * self**-1\n",
    "    \n",
    "    def __pow__(self, other):\n",
    "        # only support int or float powers for now!!\n",
    "        # in case of other of type 'Value', we would need another method\n",
    "        assert isinstance(other, (int, float))\n",
    "        \n",
    "        out = Value(self.data**other, (self,), _op=f'**{other}')\n",
    "\n",
    "        def _backprop():\n",
    "            self.grad += (other * self.data**(other - 1)) * out.grad\n",
    "        \n",
    "        out._backprop = _backprop\n",
    "        return out\n",
    "\n",
    "    def relu(self):\n",
    "        out = Value( self.data if self.data > 0.0 else 0.0 , (self,), _op='ReLU' )\n",
    "        \n",
    "        def _backprop():\n",
    "            self.grad += out.grad * (out.data > 0.0)\n",
    "        \n",
    "        out._backprop = _backprop\n",
    "        return out\n",
    "    \n",
    "    def exp(self):\n",
    "        out = Value(np.exp(self.data), (self,), _op='exp')\n",
    "        \n",
    "        def _backprop():\n",
    "            self.grad += out.data * out.grad\n",
    "        \n",
    "        out._backprop = _backprop\n",
    "        return out\n",
    "    \n",
    "    def tanh(self):\n",
    "        tanh = (np.exp(2*self.data) - 1)/(np.exp(2*self.data) + 1)\n",
    "        out = Value( tanh, (self,), _op='tanh')\n",
    "        \n",
    "        def _backprop():\n",
    "            self.grad += (1 - tanh**2) * out.grad\n",
    "        \n",
    "        out._backprop = _backprop\n",
    "        return out\n",
    "    \n",
    "    def backprop(self):\n",
    "        topo_sort_list = []\n",
    "        visited = set() # the order does not matter, use set instead of list\n",
    "        \n",
    "        def build_topo(root):\n",
    "            if root not in visited:\n",
    "                visited.add(root)\n",
    "                # Appending to topo_sort before its children are processed\n",
    "                # will give us out-to-left sort,\n",
    "                # but not out to leaf sort in case of b (bias leaf), try it & see it\n",
    "                for child in root._prev:\n",
    "                    build_topo(child)\n",
    "                # Appending after its children are processed\n",
    "                # will give us leaf-to-out sort\n",
    "                topo_sort_list.append(root)\n",
    "        \n",
    "        build_topo(root=self)\n",
    "        \n",
    "        self.grad = 1.0\n",
    "        for node in reversed(topo_sort_list):\n",
    "            node._backprop()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MLP\n",
    "we can call an object of a class to give us an output:\n",
    "for that we need to use `__call__` method:\n",
    "\n",
    "n = Neuron(x) # object\n",
    "\n",
    "a = n(x) # calling object\n",
    "\n",
    "here we use it to give us the value of the forward pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Neuron:\n",
    "    # nin: number of inputs\n",
    "    def __init__(self, nin: int):\n",
    "        self.w = [ Value( random.uniform(-1,1), label=f'w{i}' ) for i in range(nin)]\n",
    "        self.b = Value(random.uniform(-1,1), label='b')\n",
    "    \n",
    "    def __call__(self, x: list) -> float:\n",
    "        # w * x + b -> a scalar value\n",
    "        activation = sum( ( wi*xi for wi,xi in zip(self.w, x) ) , start=self.b) # pair up w & x point wise\n",
    "        return activation.tanh()\n",
    "    \n",
    "    def parameters(self):\n",
    "        return self.w + [self.b]\n",
    "\n",
    "\n",
    "class OneMLPLayer:\n",
    "\n",
    "    def __init__(self, nin: int, nout: int):\n",
    "        '''\n",
    "        so we need a bunch of Neurons:\n",
    "        Data structure? -> order matters -> list\n",
    "        '''\n",
    "        self.neurons = [Neuron(nin) for _ in range(nout)]\n",
    "    \n",
    "    def __call__(self, x: list) -> list:\n",
    "        outs = [n(x) for n in self.neurons]\n",
    "        return outs[0] if len(outs) == 1 else outs\n",
    "    \n",
    "    def parameters(self) -> list:\n",
    "        # list comprehension with double for:\n",
    "        # write the for loops in a way you write it as usual !! \n",
    "        return [parameter for neuron in self.neurons for parameter in neuron.parameters()]\n",
    "        \n",
    "\n",
    "class MLP:\n",
    "    '''\n",
    "    we want a bunch of layers -> order matters -> list\n",
    "    input layer: nin - hidden layer: hs - output layer: nout\n",
    "    '''\n",
    "    def __init__(self, nin: int, hs: list, nout: int) -> None:\n",
    "        layer_width = [nin] + [nout] if hs is None else [nin] + hs + [nout]\n",
    "        self.layers = [OneMLPLayer(nin= layer_width[idx], nout=layer_width[idx+1]) for idx in range(len(layer_width)-1) ]\n",
    "\n",
    "    def __call__(self, x) -> list:\n",
    "        out = x\n",
    "        for layer in self.layers:\n",
    "            out = layer(out)\n",
    "        return out\n",
    "    \n",
    "    def parameters(self):\n",
    "        return [parameter for layer in self.layers for parameter in layer.parameters()]\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value( | data:-0.9196001508680245 | grad:0.0)\n",
      "[Value( | data:-0.8860367500680455 | grad:0.0), Value( | data:-0.748862963005636 | grad:0.0), Value( | data:0.9317577313364696 | grad:0.0)]\n",
      "Value( | data:0.5909961972202941 | grad:0.0)\n"
     ]
    }
   ],
   "source": [
    "x = [2.0, 3.0 -1.0]\n",
    "n = Neuron(3)\n",
    "l = OneMLPLayer(3, 3)\n",
    "model = MLP(nin=3, hs=[4, 4], nout=1)\n",
    "print(n(x))\n",
    "print(l(x))\n",
    "print(model(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "# input data points\n",
    "x_batch = [\n",
    "    [2.0, 3.0, -1.0],\n",
    "    [3.0, -1.0, 0.5],\n",
    "    [0.5, 1.0, 1.0],\n",
    "    [1.0, 1.0, -1.0]\n",
    "]\n",
    "\n",
    "# desires targets\n",
    "y_batch = [\n",
    "    1.0,\n",
    "    -1.0,\n",
    "    -1.0,\n",
    "    1.0\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Value( | data:0.094487047176856 | grad:0.0),\n",
       " Value( | data:0.8506407358536986 | grad:0.0),\n",
       " Value( | data:0.41161202276479 | grad:0.0),\n",
       " Value( | data:0.6335144924921988 | grad:0.0)]"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_preds = [model(x) for x in x_batch]\n",
    "y_preds"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Optimization Iterations"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### choosing a loss function\n",
    "1. When we have a single continuous output for each input data point:\n",
    "    \n",
    "    1.1. if it's a binary classification problem:\n",
    "\n",
    "        1.1.1. Mean Squared Error\n",
    "        \n",
    "        1.1.2. SVM Max Margin\n",
    "    \n",
    "    1.2. if it's a regression problem:\n",
    "\n",
    "        1.2.1. Mean Squared Error\n",
    "\n",
    "2. When we have multiple continuous outputs for each input data point:\n",
    "\n",
    "    2.1. if it's a categorical classification problem:\n",
    "\n",
    "        2.1.1. Softmax & Expected Negative Log Likelihood\n",
    "    \n",
    "    2.2. if it's a regression problem:\n",
    "\n",
    "        2.2.1. Mean Squared Error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "bach:0 | loss:6.371784970958961 \n",
      "bach:1 | loss:4.267611751809959 \n",
      "bach:2 | loss:3.149025388830487 \n",
      "bach:3 | loss:1.8953339476602427 \n",
      "bach:4 | loss:1.02824232278247 \n",
      "bach:5 | loss:0.6403924026797565 \n",
      "bach:6 | loss:0.43978108590644216 \n",
      "bach:7 | loss:0.3244709508442955 \n",
      "bach:8 | loss:0.2518664689388759 \n",
      "bach:9 | loss:0.20308114895264462 \n",
      "bach:10 | loss:0.16858429675600806 \n",
      "bach:11 | loss:0.14317243105696859 \n",
      "bach:12 | loss:0.12382230029699129 \n",
      "bach:13 | loss:0.10868190618296965 \n",
      "bach:14 | loss:0.09656467048795067 \n",
      "bach:15 | loss:0.08668077414640021 \n",
      "bach:16 | loss:0.07848703763449148 \n",
      "bach:17 | loss:0.07159923447829653 \n",
      "bach:18 | loss:0.06573884690579443 \n",
      "bach:19 | loss:0.06069961584343876 \n",
      "bach:20 | loss:0.05632588629558951 \n",
      "bach:21 | loss:0.05249821096032464 \n",
      "bach:22 | loss:0.049123549824031894 \n",
      "bach:23 | loss:0.046128455468424465 \n",
      "bach:24 | loss:0.04345424318434603 \n",
      "bach:25 | loss:0.04105350824492328 \n",
      "bach:26 | loss:0.03888757494870043 \n",
      "bach:27 | loss:0.03692460128549705 \n",
      "bach:28 | loss:0.035138152213243415 \n",
      "bach:29 | loss:0.0335061127313546 \n",
      "bach:30 | loss:0.03200985062853186 \n",
      "bach:31 | loss:0.030633564940256132 \n",
      "bach:32 | loss:0.029363774109223292 \n",
      "bach:33 | loss:0.028188910348035313 \n",
      "bach:34 | loss:0.027098995528992833 \n",
      "bach:35 | loss:0.026085380231349865 \n",
      "bach:36 | loss:0.02514053213360911 \n",
      "bach:37 | loss:0.024257863267758535 \n",
      "bach:38 | loss:0.02343158810927677 \n",
      "bach:39 | loss:0.02265660630711741 \n",
      "bach:40 | loss:0.02192840523370069 \n",
      "bach:41 | loss:0.021242978577796917 \n",
      "bach:42 | loss:0.02059675799994866 \n",
      "bach:43 | loss:0.01998655548339406 \n",
      "bach:44 | loss:0.019409514488919973 \n",
      "bach:45 | loss:0.018863068393155852 \n",
      "bach:46 | loss:0.01834490498128849 \n",
      "bach:47 | loss:0.017852935995509765 \n",
      "bach:48 | loss:0.017385270923572966 \n",
      "bach:49 | loss:0.01694019435814159 \n"
     ]
    }
   ],
   "source": [
    "# Bach Iterations\n",
    "nbatches = 50\n",
    "verbos = False\n",
    "\n",
    "for b in range(nbatches):\n",
    "    ## Forward Path\n",
    "    y_preds = [model(x) for x in x_batch]\n",
    "    losses = [(ygt-y_pred)**2 for ygt, y_pred in zip(y_batch, y_preds)]\n",
    "    loss = sum(losses)\n",
    "    loss.label = 'loss'\n",
    "\n",
    "    ## Backprop or Backward Path\n",
    "    loss.backprop()\n",
    "\n",
    "    ## Update `p_new = p_old - lr*grad`\n",
    "    ### Learning rate decay\n",
    "    lr = 1.0 - b/100\n",
    "    for p in model.parameters():\n",
    "        p.data -= lr*p.grad\n",
    "    \n",
    "    print(f'bach:{b} | loss:{loss.data} ')\n",
    "    if verbos:\n",
    "        print(f'w0: {model.layers[0].neurons[0].w[0]}')\n",
    "        print(f'losses: {losses}\\n')\n",
    "    \n",
    "    # Flush the gradients!! zero_grad in PyTorch!!\n",
    "    # Without flushing gradients,\n",
    "    # they get larger and larger -> larger update steps\n",
    "    # you will miss the optimal point!!\n",
    "    # if you still converge that's just bc\n",
    "    # your toy problem is easy to slve for NN!! \n",
    "    # In real life problem it's not gonna work!!\n",
    "    for p in model.parameters():\n",
    "        p.grad = 0.0\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Value( | data:0.9635565854273805 | grad:-0.07288682914523892),\n",
       " Value( | data:-0.9208371223712718 | grad:0.1583257552574564),\n",
       " Value( | data:-0.9429091063401198 | grad:0.11418178731976036),\n",
       " Value( | data:0.921987561510455 | grad:-0.15602487697908995)]"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_preds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value( | data:-0.08097670121382998 | grad:0.0)\n"
     ]
    }
   ],
   "source": [
    "x = [2.0, 3.0 -1.0]\n",
    "# n = Neuron(nin=3)\n",
    "# l = OneMLPLayer(nin=3, nout=2)\n",
    "model = MLP(nin=3, hs=[2], nout=1)\n",
    "# print(n(x))\n",
    "# print(l(x))\n",
    "print(model(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# input data points\n",
    "x_batch = [\n",
    "    [2.0, 3.0, -1.0],\n",
    "    [3.0, -1.0, 0.5],\n",
    "    [0.5, 1.0, 1.0],\n",
    "    [1.0, 1.0, -1.0]\n",
    "]\n",
    "\n",
    "# desires targets\n",
    "y_batch = [\n",
    "    1.0,\n",
    "    -1.0,\n",
    "    -1.0,\n",
    "    1.0\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Value( | data:-0.3262983596018056 | grad:0.0),\n",
       " Value( | data:-0.8934802089224874 | grad:0.0),\n",
       " Value( | data:0.16804425715317675 | grad:0.0),\n",
       " Value( | data:-0.7200496274046135 | grad:0.0)]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_preds = [model(x) for x in x_batch]\n",
    "y_preds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Bach Iterations\n",
    "nbatches = 50\n",
    "verbos = False\n",
    "\n",
    "# for b in range(nbatches):\n",
    "    ## Forward Path\n",
    "y_preds = [model(x) for x in x_batch]\n",
    "losses = [(ygt-y_pred)**2 for ygt, y_pred in zip(y_batch, y_preds)]\n",
    "loss = sum(losses)\n",
    "loss.label = 'loss'\n",
    "\n",
    "## Backprop or Backward Path\n",
    "loss.backprop()\n",
    "\n",
    "lr = 1.0 \n",
    "for p in model.parameters():\n",
    "    p.data -= lr*p.grad\n",
    "\n",
    "# print(f'bach:{b} | loss:{loss.data} ')\n",
    "if verbos:\n",
    "    print(f'w0: {model.layers[0].neurons[0].w[0]}')\n",
    "    print(f'losses: {losses}\\n')\n",
    "\n",
    "for p in model.parameters():\n",
    "        p.grad = 0.0\n",
    "    # break\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# y_preds.backprop()\n",
    "draw_dot(loss)"
   ]
  }
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