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| { | ||
| "cells": [ | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "# Index handling\n", | ||
| "\n", | ||
| "Sometimes moving from layer to layer in a neural network involves rearranging the size from the output of the previous layer to the input of the next layer. This notebook demonstrates how to use this functionality in OMLT.\n", | ||
| "\n", | ||
| "## Library Setup\n", | ||
| "\n", | ||
| "Start by importing the libraries used in this project:\n", | ||
| "\n", | ||
| " - `numpy`: a general-purpose numerical library\n", | ||
| " - `omlt`: the package this notebook demonstates.\n", | ||
| " \n", | ||
| "We import the following classes from `omlt`:\n", | ||
| "\n", | ||
| " - `NetworkDefinition`: class that contains the nodes in a Neural Network\n", | ||
| " - `InputLayer`, `DenseLayer`, `PoolingLayer2D`: the three types of layers used in this example\n", | ||
| " - `IndexMapper`: used to reshape the data between layers" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 1, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "import numpy as np\n", | ||
| "from omlt.neuralnet import NetworkDefinition\n", | ||
| "from omlt.neuralnet.layer import IndexMapper, InputLayer, DenseLayer, PoolingLayer2D" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "Then we define a simple network that consists of a max pooling layer and a dense layer:" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 2, | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "name": "stdout", | ||
| "output_type": "stream", | ||
| "text": [ | ||
| "0\tInputLayer(input_size=[9], output_size=[9])\n", | ||
| "1\tPoolingLayer(input_size=[1, 3, 3], output_size=[1, 2, 2], strides=[2, 2], kernel_shape=[2, 2]), pool_func_name=max\n", | ||
| "2\tDenseLayer(input_size=[4], output_size=[1])\n" | ||
| ] | ||
| } | ||
| ], | ||
| "source": [ | ||
| "# define bounds for inputs\n", | ||
| "input_size = [9]\n", | ||
| "input_bounds = {}\n", | ||
| "for i in range(input_size[0]):\n", | ||
| " input_bounds[(i)] = (-10.0, 10.0)\n", | ||
| "\n", | ||
| "net = NetworkDefinition(scaled_input_bounds=input_bounds)\n", | ||
| "\n", | ||
| "# define the input layer\n", | ||
| "input_layer = InputLayer(input_size)\n", | ||
| "\n", | ||
| "net.add_layer(input_layer)\n", | ||
| "\n", | ||
| "# define the pooling layer\n", | ||
| "input_index_mapper_1 = IndexMapper([9], [1, 3, 3])\n", | ||
| "maxpooling_layer = PoolingLayer2D(\n", | ||
| " [1, 3, 3],\n", | ||
| " [1, 2, 2],\n", | ||
| " [2, 2],\n", | ||
| " \"max\",\n", | ||
| " [2, 2],\n", | ||
| " 1,\n", | ||
| " input_index_mapper=input_index_mapper_1,\n", | ||
| ")\n", | ||
| "\n", | ||
| "net.add_layer(maxpooling_layer)\n", | ||
| "net.add_edge(input_layer, maxpooling_layer)\n", | ||
| "\n", | ||
| "# define the dense layer\n", | ||
| "input_index_mapper_2 = IndexMapper([1, 2, 2], [4])\n", | ||
| "dense_layer = DenseLayer(\n", | ||
| " [4],\n", | ||
| " [1],\n", | ||
| " activation=\"linear\",\n", | ||
| " weights=np.ones([4, 1]),\n", | ||
| " biases=np.zeros(1),\n", | ||
| " input_index_mapper=input_index_mapper_2,\n", | ||
| ")\n", | ||
| "\n", | ||
| "net.add_layer(dense_layer)\n", | ||
| "net.add_edge(maxpooling_layer, dense_layer)\n", | ||
| "\n", | ||
| "for layer_id, layer in enumerate(net.layers):\n", | ||
| " print(f\"{layer_id}\\t{layer}\")" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "In this example, `input_index_mapper_1` maps outputs of `input_layer` (with size [9]) to the inputs of `maxpooling_layer` (with size [1, 3, 3]), `input_index_mapper_2` maps the outputs of `maxpooling_layer` (with size [1, 2, 2]) to the inputs of `dense_layer` (with size [4]). Given an input, we can evaluate each layer to see how `IndexMapper` works: " | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 3, | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "name": "stdout", | ||
| "output_type": "stream", | ||
| "text": [ | ||
| "outputs of maxpooling_layer:\n", | ||
| " [[[5. 6.]\n", | ||
| " [8. 9.]]]\n", | ||
| "outputs of dense_layer:\n", | ||
| " [28.]\n" | ||
| ] | ||
| } | ||
| ], | ||
| "source": [ | ||
| "x = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9])\n", | ||
| "y1 = maxpooling_layer.eval_single_layer(x)\n", | ||
| "print(\"outputs of maxpooling_layer:\\n\", y1)\n", | ||
| "y2 = dense_layer.eval_single_layer(y1)\n", | ||
| "print(\"outputs of dense_layer:\\n\", y2)" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "markdown", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "Without `IndexMapper`, the output of `maxpooling_layer` is identical to the input of `dense_layer`. When using `IndexMapper`, using `input_indexes_with_input_layer_indexes` can provide the mapping between indexes. Therefore, there is no need to define variables for the inputs of each layer (except for `input_layer`). As shown in the following, we print both input indexes and output indexes for each layer. Also, we give the mapping between indexes of two adjacent layers, where `local_index` corresponds to the input indexes of the current layer and `input_index` corresponds to the output indexes of previous layer." | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 4, | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "name": "stdout", | ||
| "output_type": "stream", | ||
| "text": [ | ||
| "input indexes of input_layer:\n", | ||
| "[(0,), (1,), (2,), (3,), (4,), (5,), (6,), (7,), (8,)]\n", | ||
| "output indexes of input_layer:\n", | ||
| "[(0,), (1,), (2,), (3,), (4,), (5,), (6,), (7,), (8,)]\n" | ||
| ] | ||
| } | ||
| ], | ||
| "source": [ | ||
| "print(\"input indexes of input_layer:\")\n", | ||
| "print(input_layer.input_indexes)\n", | ||
| "print(\"output indexes of input_layer:\")\n", | ||
| "print(input_layer.output_indexes)" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 5, | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "name": "stdout", | ||
| "output_type": "stream", | ||
| "text": [ | ||
| "input indexes of maxpooling_layer:\n", | ||
| "[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 0), (0, 1, 1), (0, 1, 2), (0, 2, 0), (0, 2, 1), (0, 2, 2)]\n", | ||
| "output indexes of maxpooling_layer:\n", | ||
| "[(0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 1, 1)]\n", | ||
| "input_index_mapping_1:\n", | ||
| "local_index: (0, 0, 0) input_index: (0,)\n", | ||
| "local_index: (0, 0, 1) input_index: (1,)\n", | ||
| "local_index: (0, 0, 2) input_index: (2,)\n", | ||
| "local_index: (0, 1, 0) input_index: (3,)\n", | ||
| "local_index: (0, 1, 1) input_index: (4,)\n", | ||
| "local_index: (0, 1, 2) input_index: (5,)\n", | ||
| "local_index: (0, 2, 0) input_index: (6,)\n", | ||
| "local_index: (0, 2, 1) input_index: (7,)\n", | ||
| "local_index: (0, 2, 2) input_index: (8,)\n" | ||
| ] | ||
| } | ||
| ], | ||
| "source": [ | ||
| "print(\"input indexes of maxpooling_layer:\")\n", | ||
| "print(maxpooling_layer.input_indexes)\n", | ||
| "print(\"output indexes of maxpooling_layer:\")\n", | ||
| "print(maxpooling_layer.output_indexes)\n", | ||
| "print(\"input_index_mapping_1:\")\n", | ||
| "for local_index, input_index in maxpooling_layer.input_indexes_with_input_layer_indexes:\n", | ||
| " print(\"local_index:\", local_index, \"input_index:\", input_index)" | ||
| ] | ||
| }, | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 6, | ||
| "metadata": {}, | ||
| "outputs": [ | ||
| { | ||
| "name": "stdout", | ||
| "output_type": "stream", | ||
| "text": [ | ||
| "input indexes of dense_layer:\n", | ||
| "[(0,), (1,), (2,), (3,)]\n", | ||
| "output indexes of dense_layer:\n", | ||
| "[(0,)]\n", | ||
| "input_index_mapping_2:\n", | ||
| "local_index: (0,) input_index: (0, 0, 0)\n", | ||
| "local_index: (1,) input_index: (0, 0, 1)\n", | ||
| "local_index: (2,) input_index: (0, 1, 0)\n", | ||
| "local_index: (3,) input_index: (0, 1, 1)\n" | ||
| ] | ||
| } | ||
| ], | ||
| "source": [ | ||
| "print(\"input indexes of dense_layer:\")\n", | ||
| "print(dense_layer.input_indexes)\n", | ||
| "print(\"output indexes of dense_layer:\")\n", | ||
| "print(dense_layer.output_indexes)\n", | ||
| "print(\"input_index_mapping_2:\")\n", | ||
| "for local_index, input_index in dense_layer.input_indexes_with_input_layer_indexes:\n", | ||
| " print(\"local_index:\", local_index, \"input_index:\", input_index)" | ||
| ] | ||
| } | ||
| ], | ||
| "metadata": { | ||
| "kernelspec": { | ||
| "display_name": "OMLT", | ||
| "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": "3.8.16" | ||
| }, | ||
| "orig_nbformat": 4 | ||
| }, | ||
| "nbformat": 4, | ||
| "nbformat_minor": 2 | ||
| } |
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