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@vfdev-5
Last active March 14, 2017 10:21
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Neural network tryouts to produce a image channel's formula learning
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"# Formula learning - regression\n",
"\n",
"Idea is to learn a function : $f(\\mathbf{x}) = \\frac{x_1 - x_n}{x_1 + x_n}$ with $\\mathbf{x}=(x_1, x_2, ...,x_n)$"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pylab as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"## Prepare input data\n",
"\n",
"Let's $n=5$ and $x_i$ to be normalized between 0 and 1."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"n_samples = 5000\n",
"ndim = 5\n",
"inputs = np.random.rand(n_samples, ndim)\n",
"targets = (inputs[:, 0] - inputs[:, ndim-1])/(inputs[:, 0] + inputs[:, ndim-1])"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0xbb72908>"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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lW5ZzqcwTkCc5B8frWLf5RO1DE/W5zhTJ6utcqsdRbYyVUu+KyNwUh9wM/Juy4r5tEJFp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KdM2bw8MzdDFxgXZKbisSUleL8mZFkxSgRKna3UjU2iPADsjoyAEAICZty0UaNxHEj3Yd+FLrWJ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\nGg/pqkJ2hkJg2DtHbmlRNm2BkQlbO3f0X6Q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5RMKp3iF+e6R9QuYPeuYaFhVk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Z48IWr7kz32Xao9xmLPKxGcIvGbu0rw5uNLUZLjxftHmvDmgQY8uOk7PPv293hldw3eOtCA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\nIiIigE6MRUREREQA+Av/LdyhzpEZYQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xb52f320>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"args = targets.argsort()\n",
"\n",
"plt.figure(figsize=(12,6))\n",
"plt.suptitle(\"Input data sorted by ascending targets\")\n",
"plt.subplot(231)\n",
"plt.plot(inputs[args,0], '.')\n",
"plt.title(\"x_0\")\n",
"plt.subplot(232)\n",
"plt.plot(inputs[args,1], '.')\n",
"plt.title(\"x_1\")\n",
"plt.subplot(233)\n",
"plt.plot(inputs[args,2], '.')\n",
"plt.title(\"x_2\")\n",
"plt.subplot(234)\n",
"plt.plot(inputs[args,3], '.')\n",
"plt.title(\"x_3\")\n",
"plt.subplot(235)\n",
"plt.plot(inputs[args,4], '.')\n",
"plt.title(\"x_4\")\n",
"plt.subplot(236)\n",
"plt.plot(targets[args], '.r')\n",
"plt.title(\"targets\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"## Try a simple Deep Neural Network"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Using Theano backend.\n",
"WARNING (theano.sandbox.cuda): The cuda backend is deprecated and will be removed in the next release (v0.10). Please switch to the gpuarray backend. You can get more information about how to switch at this URL:\n",
" https://github.com/Theano/Theano/wiki/Converting-to-the-new-gpu-back-end%28gpuarray%29\n",
"\n",
"Using gpu device 0: GeForce GTX 750 Ti (CNMeM is enabled with initial size: 50.0% of memory, cuDNN 5110)\n"
]
}
],
"source": [
"from keras.models import Model, Sequential\n",
"from keras.layers import Dense, Dropout, Input"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"x_in = Input((ndim,))\n",
"x = Dense(100, activation='relu', init='normal')(x_in)\n",
"x = Dense(100, activation='relu', init='normal')(x)\n",
"x = Dense(50, activation='relu', init='normal')(x)\n",
"x_out = Dense(1)(x)\n",
"model = Model(input=x_in, output=x_out)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"____________________________________________________________________________________________________\n",
"Layer (type) Output Shape Param # Connected to \n",
"====================================================================================================\n",
"input_1 (InputLayer) (None, 5) 0 \n",
"____________________________________________________________________________________________________\n",
"dense_1 (Dense) (None, 100) 600 input_1[0][0] \n",
"____________________________________________________________________________________________________\n",
"dense_2 (Dense) (None, 100) 10100 dense_1[0][0] \n",
"____________________________________________________________________________________________________\n",
"dense_3 (Dense) (None, 50) 5050 dense_2[0][0] \n",
"____________________________________________________________________________________________________\n",
"dense_4 (Dense) (None, 1) 51 dense_3[0][0] \n",
"====================================================================================================\n",
"Total params: 15,801\n",
"Trainable params: 15,801\n",
"Non-trainable params: 0\n",
"____________________________________________________________________________________________________\n"
]
}
],
"source": [
"model.summary()"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"from keras import backend as K\n",
"\n",
"def K_max_error_percentage(y_true, y_pred):\n",
" return K.max(K.abs(y_true - y_pred)) * 100.0\n",
"\n",
"\n",
"def max_error_percentage(y_true, y_pred):\n",
" return np.max(np.abs(y_true - y_pred)) * 100.0"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"model.compile(loss='mae', optimizer='adam', metrics=['mae', K_max_error_percentage])"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"batch_size = 64\n",
"history = model.fit(inputs, targets, shuffle=True, batch_size=batch_size, validation_split=0.3, nb_epoch=1000, verbose=0)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x2e856a90>"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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ZOVcE/BaYAMwBRjnnvjWzu8zsXAAzO9LMcoGfAU+Z2bfB7ocBOWY2C5gEDCkz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\nrkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0xb9fb630>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(12,4))\n",
"plt.subplot(121)\n",
"plt.plot(history.history['loss'], label='Train loss')\n",
"plt.plot(history.history['val_loss'], label='Val loss')\n",
"plt.title(\"Loss vs # epoch\")\n",
"plt.legend()\n",
"plt.subplot(122)\n",
"plt.plot(history.history['K_max_error_percentage'], label='Train metrics')\n",
"plt.plot(history.history['val_K_max_error_percentage'], label='Val metrics')\n",
"plt.title(\"Validation metrics vs # epoch\")\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"X_test = np.random.rand(100, ndim)\n",
"Y_test = (X_test[:, 0] - X_test[:, ndim-1])/(X_test[:, 0] + X_test[:, ndim-1])"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"Y_pred = model.predict(X_test)"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"args = Y_test.argsort()\n",
"y_true = Y_test[args]\n",
"y_pred = Y_pred.ravel()[args]"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"from sklearn.metrics import mean_absolute_error"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"text/plain": [
"(0.0016198964827205272, 1.2429603137116607)"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mean_absolute_error(Y_test, Y_pred), max_error_percentage(y_true, y_pred)"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"image/png": 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SWKQV6bkb11OjeSfO//azgnJTPotj/YlNmNeuFzsaNKXviv/Sd/1n5IZWpHfU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\nERGRKCmoFhERERGJkoJqEREREZEo/X8E7PQuQTUckgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x2e870c50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(12, 4))\n",
"plt.plot(y_true, 'o-')\n",
"_ = plt.plot(y_pred, '*-r')"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"After a lot of epoch of training, we manage to predict the function with a small mean absolute error."
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"### Show weights of the trained network\n",
"\n",
"We can observe that :\n",
"- variations of weights for the first and the last channels of the first Dense layer"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true,
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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MgG7fITEzsxGuUXVVRNwI3Nhj2sdL6XvJmmPVWvZy4PKGFCTngMTMxjzfITEzs5Eu5brK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\nginYPp8AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x2e44ae10>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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cNDNrnWIb2MKMOeoH+dizlT9lT5ghYd985TgRtgKzxbe2ljFhOVdOXsnsAFvR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wkJ+hF9HpW7TCdpVDLaGo44h+0ysSzcNhdo5HFSqpgYU9Q9ZbviGWM3tJqvgxCK+Ff2UEHCwIC0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\nRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x2f2dbe48>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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okiNFvGKSJEmS7GN69ZwyszrwceAZwArgBjNb7u63tq32CmC9ux9tZmcBHwBe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"text/plain": [
"<matplotlib.figure.Figure at 0x2f7259b0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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kmeX2mcADjfa1vdT2fNvzBw46oBt1joioUGcPZE6EhzIjIqIXJU4Nadtio6Jp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\ngg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x2fb40358>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"layers = list(model.layers)\n",
"layers.remove(model.input_layers[0])\n",
"for layer in layers:\n",
" weights = layer.W.eval()\n",
" b = layer.b.eval()\n",
" plt.figure(figsize=(14, 4))\n",
" plt.subplot(121)\n",
" plt.title(\"Layer {} : weights {}\".format(layer.name, weights.shape))\n",
" plt.imshow(weights, interpolation='none', aspect='auto') \n",
" plt.colorbar()\n",
" plt.subplot(122)\n",
" plt.title(\"Layer {} : bias {}\".format(layer.name, b.shape)) \n",
" b = np.expand_dims(b, axis=0) \n",
" plt.imshow(b, interpolation='none') \n",
" plt.colorbar()\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"Display the transformation on a data by each layer"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"import keras.backend as K\n",
"\n",
"def get_layer_output_func(layer_name, model):\n",
" inputs = [K.learning_phase()] + model.inputs\n",
" output_layer = model.get_layer(name=layer_name)\n",
" outputs = output_layer.output\n",
" return K.function(inputs, [outputs])\n",
" \n",
" \n",
"def compute_layer_output(input_data, layer_output_f):\n",
" return layer_output_f([0] + [input_data])\n",
"\n",
"\n",
"def compute_layer_outputs(input_data, model, layer_output_f_dict={}, layer_names=None):\n",
" \"\"\"\n",
" Method to compute (all or only those specified by `layer_names`) layer outputs on `input_data` for a given `model`\n",
" :return: tuple of pairs: [(\"layer_name_1\", ndarray), ...]\n",
" \"\"\"\n",
" if layer_names is None:\n",
" inputs_outputs = model.input_layers\n",
" inputs_outputs.extend(model.output_layers)\n",
" layer_names = [layer.name for layer in model.layers if layer not in inputs_outputs] \n",
" else:\n",
" all_layer_names = [layer.name for layer in model.layers]\n",
" assert set(layer_names) & set(all_layer_names) == set(layer_names), \\\n",
" \"Items {} of layer_names are not in model\".format(set(layer_names) - set(layer_names))\n",
"\n",
" layer_outputs = []\n",
" for layer_name in layer_names:\n",
" print(\"-- %s\" % layer_name)\n",
" if layer_name not in layer_output_f_dict:\n",
" layer_output_f_dict[layer_name] = get_layer_output_func(layer_name, model)\n",
" layer_outputs.append((layer_name, compute_layer_output(input_data, layer_output_f_dict[layer_name])))\n",
" return layer_outputs"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true,
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-- dense_1\n",
"-- dense_2\n",
"-- dense_3\n",
"\n",
"dense_1\n",
"[[ 0.00713318 0. 0. 0. 0. 0. 0.\n",
" 0. 0. 0.02638724 0. 0. 0.09311543\n",
" 0. 0. 0. 0.02588161 0. 0. 0.\n",
" 0. 0.08477767 0. 0. 0. 0.11117039\n",
" 0.08006843 0. 0. 0. 0. 0.03883591\n",
" 0. 0. 0.074395 0. 0. 0. 0.\n",
" 0. 0. 0. 0. 0.09120937 0. 0.\n",
" 0. 0.06009833 0.01551573 0. 0. 0.0397177\n",
" 0. 0. 0. 0. 0.06370535 0.\n",
" 0.01876367 0. 0. 0. 0. 0. 0.\n",
" 0. 0. 0.0540036 0. 0.03073817 0.\n",
" 0.06116246 0. 0. 0.03125905 0. 0. 0.\n",
" 0. 0. 0. 0. 0. 0.07750863\n",
" 0. 0.05117805 0. 0.00432306 0.00436122 0. 0.\n",
" 0. 0.07647017 0. 0. 0. 0.\n",
" 0.09216902 0.10743336 0. ]] (1L, 100L)\n",
"\n",
"dense_2\n",
"[[ 0.00640852 0. 0.16642483 0. 0. 0. 0.\n",
" 0. 0. 0. 0.07931623 0.17536864 0.1780152\n",
" 0. 0. 0. 0. 0.02460485 0. 0.\n",
" 0.13954461 0. 0.14416681 0.20200634 0. 0.02854967\n",
" 0.17193732 0. 0. 0.14635663 0. 0.0705931\n",
" 0. 0. 0. 0. 0.12874059 0.\n",
" 0.0572267 0. 0. 0.13223886 0.07687651 0. 0.\n",
" 0. 0. 0. 0.02044425 0.01675753 0.\n",
" 0.10902136 0. 0. 0.02596737 0. 0.\n",
" 0.01786062 0. 0.19924177 0.1023946 0. 0. 0.\n",
" 0. 0.02644203 0. 0. 0.06922066 0.145136 0.\n",
" 0. 0.0801416 0. 0. 0.11167388 0. 0.\n",
" 0.0277135 0. 0. 0. 0.10887429 0.10111415\n",
" 0. 0. 0. 0. 0. 0. 0.\n",
" 0.15770569 0. 0. 0. 0. 0. 0.\n",
" 0. 0.12619066]] (1L, 100L)\n",
"\n",
"dense_3\n",
"[[ 0.3618333 0.22800405 0.29952747 0.10755686 0. 0.18587071\n",
" 0.08668483 0. 0.19642872 0. 0. 0.\n",
" 0.10339622 0.18050502 0.13066486 0. 0. 0. 0.\n",
" 0.01402315 0. 0. 0. 0. 0. 0.\n",
" 0. 0.41603723 0. 0.11676823 0. 0.\n",
" 0.25442815 0.23253798 0. 0. 0.04096696 0. 0.\n",
" 0.25453833 0.06805512 0. 0. 0.15383859 0. 0.\n",
" 0.05323473 0. 0. 0. ]] (1L, 50L)\n",
"\n",
" Predictions :\n",
"[[ -4.99602020e-01]\n",
" [ -3.32706571e-01]\n",
" [ 5.97978175e-01]\n",
" [ 7.48892315e-04]\n",
" [ 1.00136828e+00]]\n"
]
}
],
"source": [
"x = np.array([\n",
" [0.1, 0.2, 0.0, 0.1, 0.3],\n",
" [0.2, 0.3, 0.2, 0.4, 0.4],\n",
" [0.4, 0.8, 0.3, 0.5, 0.1],\n",
" [0.7, 0.8, 0.2, 0.1, 0.7],\n",
" [0.7, 0.8, 0.8, 0.6, 0.0], \n",
"])\n",
"\n",
"# Targets should be \n",
"# (0.1 - 0.3) / (0.1 + 0.3) = -0.2 / 0.4 = -0.5\n",
"# (0.2 - 0.4) / (0.2 + 0.4) = -0.2 / 0.6 = -0.3333\n",
"# (0.4 - 0.1) / (0.4 + 0.1) = 0.3 / 0.5 = 0.6\n",
"# (0.7 - 0.7) / (0.7 + 0.7) = 0.0 / 1.4 = 0.0\n",
"# (0.7 - 0.0) / (0.7 + 0.0) = 0.7 / 0.7 = 1.0\n",
"\n",
"layer_output_f_dict = {}\n",
"layer_outputs = compute_layer_outputs(x[:1,:], model, layer_output_f_dict)\n",
"\n",
"for layer_name, layer_output in layer_outputs:\n",
" print \"\\n\", layer_name\n",
" print layer_output[0], layer_output[0].shape\n",
"\n",
"print \"\\n Predictions :\"\n",
"print model.predict(x)"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"This architecture make target function's $f(\\mathbf{x}) = \\frac{x_0 - x_{n-1}}{x_0 + x_{n-1}}$ approximation by the following expression:\n",
"\n",
"$$\n",
"NN(\\mathbf{x}) = b_4 + \\langle \\mathbf{W}_4, \\text{relu}( \\mathbf{b}_3 + \\langle \\mathbf{W}_3, \\text{relu}( \\mathbf{b}_2 + \\langle \\mathbf{W}_2, \\text{relu}( \\mathbf{b}_1 + \\langle \\mathbf{W}_1, \\mathbf{x} \\rangle ) \\, \\rangle ) \\, \\rangle )\n",
"$$\n",
"\n",
"15,801 of weights trained to make an approximation of the function\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"## Fraction architecture\n",
"\n",
"Let $\\mathbf{x}$ be an input, then a $i$-th feature map defines as $\\mathbf{f}_i = \\text{relu}(\\mathbf{b}_i + \\langle \\mathbf{W}_i,\\mathbf{x} \\rangle)$.\n",
"\n",
"We would like to obtain something similar to\n",
"$$\n",
"f_{fraction} = \\frac{\\sum_{\\mathbf{\\alpha}} \\langle \\mathbf{\\alpha}, \\mathbf{x} \\rangle }{\\sum_{\\mathbf{\\beta}} \\langle \\mathbf{\\beta}, \\mathbf{x} \\rangle }\n",
"$$\n",
"\n",
"Numerator and denominator parts can be achieved with two fully-connected layers: `input -> Dense(2) -> Dense(1) -> output`. It gives the following expression:\n",
"$$\n",
"f = b_{2} + \\langle \\mathbf{W}_2, \\text{relu}(\\mathbf{b}_1 + \\langle \\mathbf{W}_1, \\mathbf{x}\\rangle) \\rangle\n",
"$$\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"from keras.layers import merge"
]
},
{
"cell_type": "code",
"execution_count": 111,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"max_power = 1\n",
"\n",
"x_in = Input((ndim,))\n",
"\n",
"def create_powers(input_layer, max_power, nb_layers=1, n_filters=100):\n",
" # Create `max_power` of combinations [c + w*x_in]\n",
" xs = []\n",
" x = input_layer\n",
" for i in range(max_power):\n",
" for i in range(nb_layers):\n",
" x = Dense(n_filters, activation='relu', init='one')(x) \n",
" xs.append(x)\n",
"\n",
" # Merge multiply:\n",
" if len(xs) > 1:\n",
" x = merge([xs[0], xs[1]], mode='mul')\n",
" for i in range(max_power - 2):\n",
" x = merge([x, xs[i+2]], mode='mul')\n",
" else:\n",
" x = xs[0]\n",
" return x\n",
"\n",
"# Create numerator & denominator\n",
"x_numerator = create_powers(x_in, max_power, nb_layers=1, n_filters=2)\n",
"x_numerator = Dense(1, init='one', name='numerator')(x_numerator)\n",
"x_denominator = create_powers(x_in, max_power, nb_layers=1, n_filters=2)\n",
"x_denominator = Dense(1, init='one', name='denominator')(x_denominator)\n",
" \n",
"# Divide\n",
"def division(list_of_tensors): \n",
" return list_of_tensors[0] / (list_of_tensors[1] + K.epsilon())\n",
"\n",
"x = merge([x_numerator, x_denominator], mode=division, output_shape=x_numerator._keras_shape[1:], name='fraction')\n",
"x_out = x\n",
"\n",
"model = Model(input=x_in, output=x_out)"
]
},
{
"cell_type": "code",
"execution_count": 112,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true,
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"____________________________________________________________________________________________________\n",
"Layer (type) Output Shape Param # Connected to \n",
"====================================================================================================\n",
"input_6 (InputLayer) (None, 5) 0 \n",
"____________________________________________________________________________________________________\n",
"dense_19 (Dense) (None, 2) 12 input_6[0][0] \n",
"____________________________________________________________________________________________________\n",
"dense_20 (Dense) (None, 2) 12 input_6[0][0] \n",
"____________________________________________________________________________________________________\n",
"numerator (Dense) (None, 1) 3 dense_19[0][0] \n",
"____________________________________________________________________________________________________\n",
"denominator (Dense) (None, 1) 3 dense_20[0][0] \n",
"____________________________________________________________________________________________________\n",
"fraction (Merge) (None, 1) 0 numerator[0][0] \n",
" denominator[0][0] \n",
"====================================================================================================\n",
"Total params: 30\n",
"Trainable params: 30\n",
"Non-trainable params: 0\n",
"____________________________________________________________________________________________________\n"
]
}
],
"source": [
"model.summary()"
]
},
{
"cell_type": "code",
"execution_count": 113,
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"from keras.metrics import mean_absolute_error, mean_squared_error\n",
"\n",
"def K_mix_loss(y_true, y_pred):\n",
" return 100.0 * (K.square(mean_absolute_error(y_true, y_pred)) + mean_squared_error(y_true, y_pred))"
]
},
{
"cell_type": "code",
"execution_count": 114,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"model.compile(loss=K_mix_loss, optimizer='nadam', metrics=[K_max_error_percentage])"
]
},
{
"cell_type": "code",
"execution_count": 115,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true,
"scrolled": true
},
"outputs": [],
"source": [
"batch_size = 64\n",
"history = model.fit(inputs, targets, shuffle=True, batch_size=batch_size, validation_split=0.3, nb_epoch=1000, verbose=0)"
]
},
{
"cell_type": "code",
"execution_count": 116,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x3792b278>"
]
},
"execution_count": 116,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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D9kjYbYRflhZqSBYRCY8ay1JLsoiERptaks3sq8BPgdOcc+UJm2YD55hZjpnt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\nMaaCTZKNMcYYY4ypYJNkY4wxxhhjKvwNcoKAxsjmkqAAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x319d32e8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(12,4))\n",
"plt.subplot(121)\n",
"plt.plot(history.history['loss'], label='Train loss')\n",
"plt.plot(history.history['val_loss'], label='Val loss')\n",
"plt.title(\"Loss vs # epoch\")\n",
"plt.legend()\n",
"plt.subplot(122)\n",
"plt.plot(history.history['K_max_error_percentage'], label='Train metrics')\n",
"plt.plot(history.history['val_K_max_error_percentage'], label='Val metrics')\n",
"plt.title(\"Validation metrics vs # epoch\")\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 117,
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"X_test = np.random.rand(100, ndim)\n",
"Y_test = (X_test[:, 0] - X_test[:, ndim-1])/(X_test[:, 0] + X_test[:, ndim-1])"
]
},
{
"cell_type": "code",
"execution_count": 118,
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"Y_pred = model.predict(X_test)"
]
},
{
"cell_type": "code",
"execution_count": 119,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"args = Y_test.argsort()\n",
"y_true = Y_test[args]\n",
"y_pred = Y_pred.ravel()[args]"
]
},
{
"cell_type": "code",
"execution_count": 120,
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"from sklearn.metrics import mean_absolute_error"
]
},
{
"cell_type": "code",
"execution_count": 121,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"5.61979161464e-05 0.0240512646172\n"
]
}
],
"source": [
"print mean_absolute_error(y_true, y_pred), max_error_percentage(y_true, y_pred)"
]
},
{
"cell_type": "code",
"execution_count": 122,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x36694198>]"
]
},
"execution_count": 122,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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kJioTJC/fto95yz/nz69MKy7BmL95Pf+cW3YJRnB8qGldWsT7Xb3mda5e83q5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\nquj/AVAHZDUa0ASrAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x332a97b8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(12, 4))\n",
"plt.plot(y_true, 'o-')\n",
"plt.plot(y_pred, '*-r')"
]
},
{
"cell_type": "code",
"execution_count": 123,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-- numerator\n",
"-- denominator\n",
"\n",
"numerator\n",
"[[ -3.25934172e-01]\n",
" [ -3.25936198e-01]\n",
" [ 4.88781333e-01]\n",
" [ 5.72204590e-05]\n",
" [ 1.14070451e+00]]\n",
"\n",
"denominator\n",
"[[ 0.65188605]\n",
" [ 0.97777581]\n",
" [ 0.81469119]\n",
" [ 2.28168249]\n",
" [ 1.14068913]]\n",
"\n",
" Predictions :\n",
"[[ -4.99986321e-01]\n",
" [ -3.33344460e-01]\n",
" [ 5.99958956e-01]\n",
" [ 2.50781868e-05]\n",
" [ 1.00001335e+00]]\n"
]
}
],
"source": [
"x = np.array([\n",
" [0.1, 0.2, 0.0, 0.1, 0.3],\n",
" [0.2, 0.3, 0.2, 0.4, 0.4],\n",
" [0.4, 0.8, 0.3, 0.5, 0.1],\n",
" [0.7, 0.8, 0.2, 0.1, 0.7],\n",
" [0.7, 0.8, 0.8, 0.6, 0.0], \n",
"])\n",
"\n",
"# Targets should be \n",
"# (0.1 - 0.3) / (0.1 + 0.3) = -0.2 / 0.4 = -0.5\n",
"# (0.2 - 0.4) / (0.2 + 0.4) = -0.2 / 0.6 = -0.3333\n",
"# (0.4 - 0.1) / (0.4 + 0.1) = 0.3 / 0.5 = 0.6\n",
"# (0.7 - 0.7) / (0.7 + 0.7) = 0.0 / 1.4 = 0.0\n",
"# (0.7 - 0.0) / (0.7 + 0.0) = 0.7 / 0.7 = 1.0\n",
"\n",
"layer_output_f_dict = {}\n",
"layer_outputs = compute_layer_outputs(x, model, layer_output_f_dict, layer_names=['numerator', 'denominator'])\n",
"\n",
"for layer_name, layer_output in layer_outputs:\n",
" print \"\\n\", layer_name\n",
" print layer_output[0]\n",
"\n",
"print \"\\n Predictions :\"\n",
"print model.predict(x)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"source": [
"Let's compute the derivatives on $\\mathbf{x}$ (Jacobian and Hessian matricies) of the output to observe a non-linearity of the output of the feature map. Implementation continues using `theano`\n",
"\n",
"Derivatives of the feature map function $f(\\mathbf{x}) = \\frac{x_0 - x_{n-1}}{x_0 + x_{n-1}}$ is \n",
"\n",
"$$\\frac{\\partial f}{\\partial x_i} = \\frac{2 x_{n-1} } {(x_0 + x_{n-1})^2} \\delta_{i\\,0} - \\frac{2 x_{0} } {(x_0 + x_{n-1})^2} \\delta_{i\\, n-1}$$\n",
"\n",
"If function approximation by NN is a ratio function then \n",
"$$\\frac{\\partial f}{\\partial x_0} \\sim \\frac{1}{x_0^2} \\text{ and } \\frac{\\partial f}{\\partial x_{n-1}} \\sim -\\frac{1}{x_{n-1}^2} $$\n"
]
},
{
"cell_type": "code",
"execution_count": 124,
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"import theano\n",
"from theano import tensor as T"
]
},
{
"cell_type": "code",
"execution_count": 125,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"x_in = model.inputs[0]\n",
"feature_map = T.flatten(model.outputs[0])"
]
},
{
"cell_type": "code",
"execution_count": 126,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"Jacobian = T.jacobian(feature_map, x_in)\n",
"jacobian = theano.function([x_in], Jacobian)"
]
},
{
"cell_type": "code",
"execution_count": 127,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"x0 = np.arange(-5.0, 5.0, 0.025, dtype=np.float32)\n",
"x = np.ones((len(x0), ndim), dtype=np.float32)\n",
"x[:, 0] = x0"
]
},
{
"cell_type": "code",
"execution_count": 128,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"dfdx = np.array([jacobian(x[i:i+1,:])[0, 0] for i in range(x.shape[0])])"
]
},
{
"cell_type": "code",
"execution_count": 129,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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