Initial commit for a3

Aufgabe 3/aufgabe03.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "\n",
+    "rng = np.random.default_rng()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Aufgabe 1\n",
+    "\n",
+    "relu = np.vectorize(lambda x : max(0, x))\n",
+    "\n",
+    "sigmoid = np.vectorize(lambda x : 1 / (1 + np.exp(-x)))\n",
+    "\n",
+    "inputs  = [rng.integers(0, 1, size=(2,1), endpoint=True) for _ in range(100)]\n",
+    "outputs = [a[0] ^ b[0] for a, b in inputs]\n",
+    "data    = list(zip(inputs, outputs))\n",
+    "\n",
+    "# Aufgabe 3\n",
+    "\n",
+    "# Binary Cross Entropy Loss\n",
+    "bcel = np.vectorize(lambda y, ŷ : -(y * np.log(ŷ) + (1 - y) * np.log(1 - ŷ)))\n",
+    "\n",
+    "# Derivations\n",
+    "bcel_derivation = np.vectorize(lambda y, ŷ: (1 / (1 - ŷ)) if y == 0 else -(1 / ŷ))\n",
+    "sigmoid_derivation = np.vectorize(lambda x: (1 / (1 + np.exp(-x))) * (1 - (1 / (1 + np.exp(-x)))))\n",
+    "relu_derivation = np.vectorize(lambda x: 0 if x < 0 else 1)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.7722866010132297\n",
+      "0.7722866010132297\n",
+      "0.9354266393448504\n",
+      "0.7722866010132297\n",
+      "0.7722866010132297\n",
+      "0.7722866010132297\n",
+      "0.8102957251424703\n",
+      "0.7722866010132297\n",
+      "0.5\n",
+      "0.7722866010132297\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Aufgabe 2\n",
+    "\n",
+    "\n",
+    "class NeuralNet:\n",
+    "    def __init__(self, inputs: int = 2, hidden_layers: int = 1, hidden_layer_neurons: int = 4):\n",
+    "        self.input_shape = (inputs, 1)\n",
+    "\n",
+    "        # Construct weights for hidden layer\n",
+    "        self.weights = []\n",
+    "        for i in range(hidden_layers):\n",
+    "            num_inputs = inputs if i == 0 else hidden_layer_neurons # First hidden layer only needs 2x4 weight matrix\n",
+    "            self.weights.append(rng.uniform(low=-1.0, high=1.0, size=(hidden_layer_neurons, num_inputs)))\n",
+    "\n",
+    "        # Construct weights for output layer\n",
+    "        self.outweights = rng.uniform(low=-1.0, high=1.0, size=(1, hidden_layer_neurons))\n",
+    "\n",
+    "    def forward_pass(self, x) -> float:\n",
+    "        x = np.array(x)\n",
+    "        if x.shape != self.input_shape:\n",
+    "            raise ValueError(f\"Input must be of shape {self.input_shape}.\")\n",
+    "\n",
+    "        # Hidden layers\n",
+    "        for layer in self.weights:\n",
+    "            x = relu(np.matmul(layer, x))\n",
+    "\n",
+    "        # Output layer\n",
+    "        return sigmoid(np.matmul(self.outweights, x))[0][0]\n",
+    "    \n",
+    "    # Aufgabe 4\n",
+    "    def backward_pass(self, learning_rate: float):\n",
+    "        ...\n",
+    "\n",
+    "\n",
+    "nn = NeuralNet(hidden_layers=1)\n",
+    "\n",
+    "for input_values, expected in data[:10]:\n",
+    "    actual = nn.forward_pass(input_values)\n",
+    "\n",
+    "    print(actual)\n"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.10.1"
+  },
+  "orig_nbformat": 4
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}