blob: 37de12591faf5b1ed779d42b50040b2ee8801c21 [file] [log] [blame]
{
"cells": [
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"cell_type": "markdown",
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"source": [
"<!--- Licensed to the Apache Software Foundation (ASF) under one -->\n",
"<!--- or more contributor license agreements. See the NOTICE file -->\n",
"<!--- distributed with this work for additional information -->\n",
"<!--- regarding copyright ownership. The ASF licenses this file -->\n",
"<!--- to you under the Apache License, Version 2.0 (the -->\n",
"<!--- \"License\"); you may not use this file except in compliance -->\n",
"<!--- with the License. You may obtain a copy of the License at -->\n",
"\n",
"<!--- http://www.apache.org/licenses/LICENSE-2.0 -->\n",
"\n",
"<!--- Unless required by applicable law or agreed to in writing, -->\n",
"<!--- software distributed under the License is distributed on an -->\n",
"<!--- \"AS IS\" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY -->\n",
"<!--- KIND, either express or implied. See the License for the -->\n",
"<!--- specific language governing permissions and limitations -->\n",
"<!--- under the License. -->\n",
"\n",
"# Activation Blocks\n",
"\n",
"Deep neural networks are a way to express a nonlinear function with lots of parameters from input data to outputs. The nonlinearities that allow neural networks to capture complex patterns in data are referred to as activation functions. Over the course of the development of neural networks, several nonlinear activation functions have been introduced to make gradient-based deep learning tractable.\n",
"\n",
"If you are looking to answer the question, 'which activation function should I use for my neural network model?', you should probably go with *ReLU*. Unless you're trying to implement something like a gating mechanism, like in LSTMs or GRU cells, then you should opt for sigmoid and/or tanh in those cells. However, if you have a working model architecture and you're trying to improve its performance by swapping out activation functions or treating the activation function as a hyperparameter, then you may want to try hand-designed activations like SELU, SiLU, or GELU. This guide describes these activation functions and others implemented in MXNet in detail.\n",
"\n",
"## Visualizing Activations\n",
"In order to compare the various activation functions and to understand the nuances of their differences we have a snippet of code to plot the activation functions (used in the forward pass) and their gradients (used in the backward pass)."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "b1fa1ceb",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import mxnet as mx\n",
"from matplotlib import pyplot as plt\n",
"%matplotlib inline\n",
"\n",
"def visualize_activation(activation_fn):\n",
" data = np.linspace(-10, 10, 501)\n",
" x = mx.np.array(data)\n",
" x.attach_grad()\n",
" with mx.autograd.record():\n",
" y = activation_fn(x)\n",
" y.backward()\n",
"\n",
" plt.figure()\n",
" plt.plot(data, y.asnumpy())\n",
" plt.plot(data, x.grad.asnumpy())\n",
" activation = activation_fn.__class__.__name__[:-1]\n",
" plt.legend([\"{} activation\".format(activation), \"{} gradient\".format(activation)])\n"
]
},
{
"cell_type": "markdown",
"id": "128601c3",
"metadata": {},
"source": [
"## Sigmoids\n",
"\n",
"### Sigmoid\n",
"\n",
"The sigmoid activation function, also known as the logistic function or logit function, is perhaps the most widely known activation owing to its [long history](http://www.cs.toronto.edu/~hinton/absps/pdp8.pdf) in neural network training and appearance in logistic regression and kernel methods for classification.\n",
"\n",
"The sigmoid activation is a non-linear function that transforms any real valued input to a value between 0 and 1, giving it a natural probabilistic interpretation. The sigmoid takes the form of the function below.\n",
"\n",
"$$ \\sigma(x) = \\dfrac{1}{1 + e^x} $$ or alternatively\n",
"\n",
"$$ \\sigma(x) = \\dfrac{e^x}{e^x + 1} $$\n",
"\n",
"Warning: the term sigmoid is overloaded and can be used to refer to the class of 's' shaped functions or particularly to the logistic function that we've just described. In MxNet the sigmoid activation specifically refers to logistic function sigmoid."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "1c2e1dce",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"[04:45:43] /work/mxnet/src/storage/storage.cc:202: Using Pooled (Naive) StorageManager for CPU\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"visualize_activation(mx.gluon.nn.Activation('sigmoid'))"
]
},
{
"cell_type": "markdown",
"id": "44cb7891",
"metadata": {},
"source": [
"![sigmoid activation and gradient](/_static/sigmoid.png)\n",
"\n",
"\n",
"The sigmoid activation has since fallen out of use as the preferred activation function in designing neural networks due to some of its properties, shown in the plot above, like not being zero-centered and inducing vanishing gradients, that leads to poor performance during neural network training. Vanishing gradients here refers to the tendency of the gradient of the sigmoid function to be nearly zero for most input values.\n",
"\n",
"### tanh\n",
"The tanh, or hyperbolic tangent, activation function is also an s shaped curve albeit one whose output values range from -1 to 1. It is defined by the mathematical equation:\n",
"\n",
"$$ tanh(x) = \\dfrac{e^x - e^{-x}}{e^x + e^{-x}}$$\n",
"\n",
"tanh addresses the issues of not being zero centered associated with the sigmoid activation function but still retains the vanishing gradient problems due to the gradient being asymptotically zero for values outside a narrow range of inputs.\n",
"\n",
"In fact, the tanh can be rewritten as,\n",
"\n",
"$$tanh(x) = \\dfrac{e^{2x} - 1}{e^{2x} + 1}$$\n",
"\n",
"which shows its direct relation to sigmoid by the following equation:\n",
"\n",
"\n",
"\n",
"$$ tanh(x) = 2\\sigma(2x) - 1$$"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "b5f2880f",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"visualize_activation(mx.gluon.nn.Activation('tanh'))"
]
},
{
"cell_type": "markdown",
"id": "460132ba",
"metadata": {},
"source": [
"![tanh activation and gradient](/_static/tanh.png)\n",
"\n",
"\n",
"The use of tanh as activation functions in place of the logistic function was popularized by the success of the [LeNet architecture](http://yann.lecun.com/exdb/publis/pdf/lecun-01a.pdf) and the [methods paper](http://yann.lecun.com/exdb/publis/pdf/lecun-98b.pdf) by LeCun et al.\n",
"\n",
"### SoftSign\n",
"\n",
"The SoftSign activation is an alternative to tanh that is also centered at zero but converges asymptotically to -1 and 1 polynomially instead of exponentially. This means that the SoftSign activation does not saturate as quickly as tanh. As such, there are a greater range of input values for which the softsign assigns an output of strictly between -1 and 1.\n",
"\n",
"$$ softsign(x) = \\dfrac{x}{abs(x) + 1} $$"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "8604e202",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"visualize_activation(mx.gluon.nn.Activation('softsign'))"
]
},
{
"cell_type": "markdown",
"id": "42638aa4",
"metadata": {},
"source": [
"![softsign activation and gradient](/_static/softsign.png)\n",
"\n",
"\n",
"The softsign function is not a commonly used activation with most neural networks and still suffers from the vanishing gradient problem as seen in the graph above.\n",
"\n",
"## Rectifiers\n",
"\n",
"### ReLU\n",
"ReLU, or Rectified Linear Unit is the most common activation function in convolutional neural networks and introduces a simple nonlinearity. When the value of the input into ReLU is positive, then it retains the same value. When the value is negative then it becomes zero. In equation form, the ReLU function is given as:\n",
"\n",
"$$ ReLU(x) = \\mathtt{max}(0, x) $$\n",
"\n",
"ReLU was introduced to neural networks in the [paper by Hahnloser et al](https://papers.nips.cc/paper/1793-permitted-and-forbidden-sets-in-symmetric-threshold-linear-networks.pdf) and gained widespread popularity after it was shown in the [paper](https://papers.nips.cc/paper/4824-imagenet-classification-with-deep-convolutional-neural-networks.pdf) by Alex Krizhevsky et al to perform much better than sigmoid and tanh. This paper also introduced the AlexNet CNN that won the ILSVRC challenge in 2012.\n",
"\n",
"ReLU is the most widely used activation due to its simplicity and performance across multiple datasets and although there have been efforts to introduce activation functions, many of them described in this tutorial, that improve on ReLU, they have not gained as much widespread adoption."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "5f6049f2",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"visualize_activation(mx.gluon.nn.Activation('relu'))"
]
},
{
"cell_type": "markdown",
"id": "7b778a95",
"metadata": {},
"source": [
"![relu activation and gradient](/_static/relu.png)\n",
"\n",
"\n",
"As shown above, the ReLU activation mitigates the vanishing gradient problem associated with the sigmoid family of activations, by having a larger (infinite) range of values where its gradient is non-zero. However, one drawback of ReLU as an activation function is a phenomenon referred to as the 'Dying ReLU', where gradient-based parameter updates can happen in such a way that the gradient flowing through a ReLU unit is always zero and the connection is never activated. This can largely be addressed by ensuring that the tuning the learning rate to ensure that it's not set too large when training ReLU networks.\n",
"\n",
"### SoftReLU\n",
"\n",
"SoftReLU also known as SmoothReLU or SoftPlus is a nonlinear activation function that takes the form\n",
"\n",
"$$ SoftReLU(x) = log(1 + e^x)$$\n",
"\n",
"The SoftReLU can be seen as a smooth version of the ReLU by observing that its derivative is the sigmoid, seen below, which is a smooth version of the gradient of the ReLU shown above."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "dd3b51a0",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"visualize_activation(mx.gluon.nn.Activation('softrelu'))"
]
},
{
"cell_type": "markdown",
"id": "0d8d1a5b",
"metadata": {},
"source": [
"![softrelu activation and gradient](/_static/softrelu.png)\n",
"\n",
"\n",
"### Leaky ReLU\n",
"\n",
"Leaky ReLUs are a variant of ReLU that multiply the input by a small positive parameter $\\alpha$ when the value is negative. Unlike the ReLU which sets the activation and gradient for negative values to zero, the LeakyReLU allows a small gradient. The equation for the LeakyReLU is:\n",
"\n",
"$$ LeakyReLU(\\alpha, x) = \\begin{cases}\n",
" x,& \\text{if } x\\geq 0\\\\\n",
" \\alpha x, & \\text{otherwise}\n",
"\\end{cases}$$\n",
"\n",
"where $\\alpha > 0$ is small positive number. In MXNet, by default the $\\alpha$ parameter is set to 0.01.\n",
"\n",
"Here is a visualization for the LeakyReLU with $\\alpha = 0.05$"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "bcad162e",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"visualize_activation(mx.gluon.nn.LeakyReLU(0.05))"
]
},
{
"cell_type": "markdown",
"id": "f399802c",
"metadata": {},
"source": [
"![leakyrelu activation and gradient](/_static/leakyrelu.png)\n",
"\n",
"\n",
"As shown in the graph, the LeakyReLU's gradient is non-zero everywhere, in an attempt to address the ReLU's gradient being zero for all negative values.\n",
"\n",
"### PReLU\n",
"The PReLU activation function, or Parametric Leaky ReLU introduced by [He et al](https://arxiv.org/pdf/1502.01852.pdf), is a version of LeakyReLU that learns the parameter $\\alpha$ during training. An initialization parameter is passed into the PreLU activation layer and this is treated as a learnable parameter that is updated via gradient descent during training. This is in contrast to LeakyReLU where $\\alpha$ is a hyperparameter."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "6a3ebd89",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"prelu = mx.gluon.nn.PReLU(mx.init.Normal(0.05))\n",
"prelu.initialize()\n",
"visualize_activation(prelu)"
]
},
{
"cell_type": "markdown",
"id": "0991ed40",
"metadata": {},
"source": [
"![prelu activation and gradient](/_static/prelu.png)\n",
"\n",
"\n",
"The activation function and activation gradient of PReLU have the same shape as LeakyRELU.\n",
"\n",
"### ELU\n",
"\n",
"The ELU or exponential linear unit introduced by [Clevert et al](https://arxiv.org/abs/1511.07289) also addresses the vanishing gradient problem like ReLU and its variants but unlike the ReLU family, ELU allows negative values which may allow them to push mean unit activations closer to zero like batch normalization.\n",
"\n",
"The ELU function has the form\n",
"\n",
"$$ ELU(\\alpha, x) = \\begin{cases}\n",
" x,& \\text{if } x\\geq 0\\\\\n",
" \\alpha (e^x - 1), & \\text{otherwise}\n",
"\\end{cases}$$"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "718f38c6",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"visualize_activation(mx.gluon.nn.ELU())"
]
},
{
"cell_type": "markdown",
"id": "16b48e6f",
"metadata": {},
"source": [
"![elu activation and gradient](/_static/elu.png)\n",
"\n",
"\n",
"### SELU\n",
"SELU stands for Scaled Exponential Linear Unit and was introduced by [Klambuer et al](https://arxiv.org/abs/1706.02515) and is a modification of the ELU that improves the normalization of its outputs towards a zero mean and unit variance.\n",
"\n",
"The SELU function has the form\n",
"\n",
"$$ SELU(\\alpha, x) = \\lambda \\cdot\\begin{cases}\n",
" x,& \\text{if } x\\geq 0\\\\\n",
" \\alpha (e^x - 1), & \\text{otherwise}\n",
"\\end{cases}$$\n",
"\n",
"In SELU, unlike ELU, the parameters $\\alpha$ and $\\lambda$ are fixed parameters calculated from the data. For standard scaled inputs, these values are $$\\alpha=1.6732, \\lambda=1.0507$$ as calculated in the paper."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "a3acbda2",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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Mn4+OgLujQuqS6sX8olNNhADURcafannfQEdHRzg6OmLHjh0oKysz8A/jLyqVCoMGDUKHDh0QGxuLd955B7Nmzaqy7ezZs7FkyRKcP38eYWFhKCwsxOOPP449e/YgLi4OAwYMwKBBg5CamqpbZ8yYMUhLS8PevXvxzTff4PPPP0d2dna19ZSXl6N///5wcnLCwYMHcejQITg6OmLAgAFQq9W6dnv37sWlS5ewd+9erF+/HuvWrdMF3W+//RbNmzfHwoULkZGRgYyMjIb5YRERmYHDSdex9OcEAMC8Qe0Q0aKpxBXVX8P0u5uK8mLgPV/jb/eNa4DtvXsrrK2tsW7dOowfPx6rV69GREQEHnroIYwcORJhYWF6bWfNmoW33npLb96uXbvw4IMP1rm8jRs3QiaT4YsvvoCdnR3atm2L9PT0u079AJWnhPr166d77OrqivDwcN3jd955B9u3b8d3332HqVOn4sKFC9i1axf+/PNPdOnSBQDwn//8B23atKm2ni1btkCr1eLLL7/U9WSsXbsWLi4u2LdvHx599FEAQNOmTfHpp59CLpcjNDQUAwcOxJ49ezB+/Hi4urpCLpfreo6IiBqLa3kleGlTHLQCGBbRHKO7tZC6pPtiWT0iZmDYsGG4du0avvvuOwwYMAD79u1DRESE7j/922bOnKkbDHx76ty5c722mZiYiLCwML3xOV27dq2y7Z3bKCwsxIwZM9CmTRu4uLjA0dER58+f1/WInD9/HtbW1oiMjNStExoaChcXl2rrOXnyJJKSkuDk5KTrJXJ1dUVpaSkuXbqka9euXTvI5X/dpMnHx6fGnhYiIktXVqHB5A2xuFGkRlsfZyx6qr3Zn5q2rB4RG4fK3gkptlsHdnZ26NevH/r164e5c+fiX//6F+bPn48xY8bo2ri7uyM4OLiBC723O8ehzJgxA7/++iuWL1+O4OBg2Nvb4+mnn9Y7hVJXhYWFiIyMrHIsiYeHh+57Gxv9i/HIZDJotdp6b5eIyNwt/P4c4tPyoLS3werRkbCzMc076taFZQURmaxWp0hMTdu2bQ16jY2QkBBER0ejrKwMCkXlYKbjx4/Xat1Dhw5hzJgxeOqppwBUhoi/DyoNDQ1FRUUFYmJidKdmEhMTkZeXV+1zRkREYMuWLfD09Lyvi9bZ2tpCo9HUe30iInOy7UQaNhxLhUwGrBjZES3c6vZPsKniqRkjunHjBh5++GFER0fj1KlTSE5OxrZt27Bs2TLdXYpvKygoQGZmpt50500AExMT7zp9c/tTJX/37LPPQqvV4sUXX8T58+exe/duLF++HADu2aXXqlUrfPvtt4iPj8fJkyd1z3VbSEgIBgwYgAkTJuDYsWOIiYnBv/71L9jbV3/L6aioKLi7u2Pw4ME4ePAgkpOTsW/fPkybNg1Xr16958/xtoCAABw4cADp6em4fv16rdcjIjI3Z9Lz8daOMwCAVx5pjT4hnhJX1HAYRIzI0dER3bp1w0cffYRevXqhffv2mDt3LsaPH49PP/1Ur+28efPg4+OjN73++ut6bUaOHIlOnTrpTXdeVh8AnJ2d8f333yM+Ph4dO3bEm2++iXnz5gHAPa/r8uGHH6Jp06bo0aMHBg0ahP79+yMiIkKvzdq1a+Hr64uHHnoIQ4cOxYsvvghPz+p/SRwcHHDgwAG0aNECQ4cORZs2bTBu3DiUlpbWqYdk4cKFuHLlClq2bKl3SoeIyJLkFasxMToGZRVaPBzqiZceNv5pe0OSCVHLz55KQKVSQalUIj8//643qNLSUiQnJyMwMLDRXyStPjZs2ICxY8ciPz+/xt6LxoSvKSIyNRqtwD/XHcf+Czlo4eqA76f+A0oH07+ZXU3v33eyrDEiVK2vvvoKQUFBaNasGU6ePIlZs2bhmWeeYQghIjJhH++5iP0XcmBnY4XVoyPNIoTUFYNII5GZmYl58+YhMzMTPj4+GD58OBYtWiR1WUREVI0957PwyZ6LAIDFQzugra9l3pGeQaSReP311+8aY0JERKbpyvUivLIlHgDwfHd/PNWpubQFGRAHqxIREZmQErUGE6NjUFBagYgWLnhrYFupSzIoBhEiIiITIYTAG9tPIyGzAO6Otvg8KhK21pb9Vm32e2fCH/ohM8PXEhFJ7asjKdgelw65lQyfPhsBb6Xlf4LPbIPI7ct/FxcXS1wJWYrbr6U7Ly1PRGQMMSm5eOeHcwCAOY+F4oEgN4krMg6zHawql8vh4uKiuwmag4OD2d/4h6QhhEBxcTGys7Ph4uKid6M9IiJjyC4oxaToWFRoBQaG+WDcPwKlLslozDaIANDd/p13ZKWG4OLiontNEREZS7lGi6kb45BdUIZWno5YNiysUf1jbdZBRCaTwcfHB56enlXeY4WotmxsbNgTQkSSWLIrAX8m58JRYY3Vz0WiicKs35rrzCL2Vi6X802EiIjMzncnr+E/fyQDAJYPD0dLD0eJKzI+sx2sSkREZM4uZBVg1jenAACTerfEgPaN89QwgwgREZGRqUrLMeHrGJSUa9Az2A2v9WstdUmSYRAhIiIyIq1W4LWtJ5F8vQi+Sjt8MrITrOWN9+248e45ERGRBFbtv4Rfz2XBVm6FVaMj4eaokLokSTGIEBERGcnBizn44JdEAMCCwe0Q7ucibUEmgEGEiIjICK7eLMa0TXHQCuCZzs0xsouf1CWZBAYRIiIiAyst12DyhljcLC5Hh2ZKLBzcvlFdtKwmDCJEREQG9vZ3Z3Hqaj5cHGzweVQE7Gx47avbGESIiIgMaPOfqdh8PA0yGfDJyE7wc3WQuiSTwiBCRERkIKeu5mHed2cBADMeDUGv1h4SV2R6GESIiIgMILdIjUnRsVBXaNG3jRcmPdRS6pJMEoMIERFRA9NoBaZtikN6XgkC3Bzw4YhwWFlxcGpVGESIiIga2Ie/JuKPpOuwt5FjzXOd4WxnI3VJJotBhIiIqAH9cjYTn+29BABYMqwDQrydJK7ItDGIEBERNZDLOYV4betJAMDYngEY3LGZxBWZPgYRIiKiBlBUVoGJ0TEoKKtAl4CmeOPxNlKXZBYYRIiIiO6TEAKz/ncKF7IK4eGkwGfPRsCmEd9Rty74UyIiIrpP/z10BT+cyoC1lQyfR0XA09lO6pLMBoMIERHRffgzORfv/XQeAPDmwDboEuAqcUXmhUGEiIionrJUpZi8IRYarcDgjr4Y0yNA6pLMDoMIERFRPagrtJi8IRbXC8sQ6u2ExUM78I669cAgQkREVA/v/XQeMSk34WRnjdWjI+Fgay11SWaJQYSIiKiOdsSlY93hKwCAj57piAD3JtIWZMYYRIiIiOrgfIYKs789BQB46eFg9G3rJXFF5o1BhIiIqJbyS8oxMToGpeVa9GrtgVf6tpa6JLNnsCCi0Wgwd+5cBAYGwt7eHi1btsQ777wDIYShNklERGQwWq3A9C3xSLlRjGYu9vh4REfIeUfd+2awkTVLly7FqlWrsH79erRr1w4nTpzA2LFjoVQqMW3aNENtloiIyCA+25uEPQnZsLW2wprnItG0ia3UJVkEgwWRw4cPY/DgwRg4cCAAICAgAJs2bcKff/5pqE0SEREZxL7EbHz42wUAwLtD2qN9M6XEFVkOg52a6dGjB/bs2YMLFyoP3MmTJ/HHH3/gscceq3adsrIyqFQqvYmIiEhKabnFeHlzPIQARnVtgWc6+0ldkkUxWI/I7NmzoVKpEBoaCrlcDo1Gg0WLFiEqKqradRYvXowFCxYYqiQiIqI6KS3XYGJ0DPJLyhHeXIm3n2wrdUkWx2A9Ilu3bsWGDRuwceNGxMbGYv369Vi+fDnWr19f7Tpz5sxBfn6+bkpLSzNUeURERDUSQuCtHWdw9poKrk1ssWp0JBTWcqnLsjgG6xGZOXMmZs+ejZEjRwIAOnTogJSUFCxevBgvvPBClesoFAooFApDlURERFRrG/9MxTcxV2ElA1aO6gRfF3upS7JIBusRKS4uhpWV/tPL5XJotVpDbZKIiKhBxKXexNvfnQUAzOwfip7B7hJXZLkM1iMyaNAgLFq0CC1atEC7du0QFxeHDz/8EP/85z8NtUkiIqL7dr2wDJM3xKJcI9C/nRcmPhQkdUkWzWBBZOXKlZg7dy4mT56M7Oxs+Pr6YsKECZg3b56hNklERHRfKjRavLQxDhn5pQjyaILlw8N5R10DkwkTvtSpSqWCUqlEfn4+nJ2dpS6HiIgs3OJd57Fm/2U42Mqxc0pPtPJykroks1SX92/ea4aIiAjArtMZWLP/MgDg/afDGUKMhEGEiIgavaTsQszYdhIAMP7BQAwM85G4osaDQYSIiBq1wrIKTPj6BIrUGjwQ5IpZA0KlLqlRYRAhIqJGSwiB1785iUs5RfB2tsPKURGwlvOt0Zj40yYiokbri4OX8dPpTNjIZfgsKgIeTryoprExiBARUaN0+NJ1LNmVAACY90RbRPo3lbiixolBhIiIGp2M/BK8tDEOWgEMjWiG0Q/4S11So8UgQkREjUpZhQaTomNxo0iNNj7OWDSkAy9aJiEGESIialTe+eEc4tPy4GxnjTWjI2FvyzvqSolBhIiIGo1vYq4i+mgqZDLg45Gd0MLNQeqSGj0GESIiahTOpOfjze2nAQAvP9IKfUI9Ja6IAAYRIiJqBPKK1Zi0IQZlFVr0CfHAtIdbSV0S3cIgQkREFk2rFXhlSzzSckvQwtUBK0Z0gpUVB6eaCgYRIiKyaB/vuYh9iTlQWFth1egIKB1spC6J/oZBhIiILNbvCVn4eM9FAMB7T3VAO1+lxBXRnRhEiIjIIqXcKMIrm+MBAM894I9hkc2lLYiqxCBCREQWp0StwcToWKhKK9CphQvmPtFW6pKoGgwiRERkUYQQeGP7aZzPUMHd0RaroiJha823O1PFI0NERBbl66Mp2B6XDrmVDCtHRcBbaSd1SVQDBhEiIrIYMSm5WPj9OQDA7AGh6N7STeKK6F4YRIiIyCJkF5Ri8oZYVGgFBnbwwb8eDJS6JKoFBhEiIjJ75Rotpm6MQ5aqDMGejlj6dBjvqGsmGESIiMjsLd2VgD+Tc+GosMbq0ZFwVFhLXRLVEoMIERGZtR9OXcOXfyQDAJYPD0Owp6PEFVFdMIgQEZHZupBVgNe/OQUAmPhQSwxo7yNxRVRXDCJERGSWVKXlmPh1DIrVGvRo6YYZj7aWuiSqBwYRIiIyO0IIzNh6EpevF8FHaYeVozrBWs63NHPEo0ZERGZn1f5L+OVcFmzlVlg1OhJujgqpS6J6YhAhIiKz8sfF61i+OxEA8PaT7dDRz0Xagui+MIgQEZHZSM8rwbTNcdAKYHhkc4zq6id1SXSfGESIiMgslJZrMCk6BrlFarRv5ox3hrTnRcssAIMIERGZhQXfn8Wpq/lwcbDBqqhI2NnIpS6JGgCDCBERmbwtx1Ox6c80yGTAJyM7wc/VQeqSqIEwiBARkUk7dTUPc3eeBQC81q81erX2kLgiakgMIkREZLJyi9SYFB0LdYUWfdt4YnLvYKlLogbGIEJERCZJoxV4eXMc0vNKEODmgA+e6QgrKw5OtTQMIkREZJI++vUCDl68DnsbOVY/FwmlvY3UJZEBMIgQEZHJ+eVsJj7dmwQAWDKsA0K9nSWuiAyFQYSIiExK8vUivLb1JABgTI8ADO7YTOKKyJAYRIiIyGQUqysw8esYFJRVoLN/U7w5sI3UJZGBMYgQEZFJEEJg9v9OIzGrAB5OCnweFQEb3lHX4vEIExGRSVh76Aq+O3kN1lYyfB4VAU9nO6lLIiNgECEiIsn9mZyL9346DwB44/E26BLgKnFFZCwMIkREJKlsVSmmbIxFhVbgyXBfjO0ZIHVJZEQGDSLp6ekYPXo03NzcYG9vjw4dOuDEiROG3CQREZmRco0WkzfEIqegDCFeTlgyrAPvqNvIWBvqiW/evImePXuiT58+2LVrFzw8PHDx4kU0bdrUUJskIiIzs+jH8ziRchNOCmusfi4SDrYGe1siE2WwI7506VL4+flh7dq1unmBgYGG2hwREZmZnfHpWHf4CgDgwxEdEejeRNqCSBIGOzXz3XffoXPnzhg+fDg8PT3RqVMnfPHFFzWuU1ZWBpVKpTcREZHlSchUYfb/TgMApvYJRr+2XhJXRFIxWBC5fPkyVq1ahVatWmH37t2YNGkSpk2bhvXr11e7zuLFi6FUKnWTn5+focojIiKJ5JeUY+LXMSgp1+DBVu54tV9rqUsiCcmEEMIQT2xra4vOnTvj8OHDunnTpk3D8ePHceTIkSrXKSsrQ1lZme6xSqWCn58f8vPz4ezM+wwQEZk7rVbgxa9P4Lfz2WjmYo8fXvoHmjaxlbosamAqlQpKpbJW798G6xHx8fFB27Zt9ea1adMGqamp1a6jUCjg7OysNxERkeX4fF8SfjufDVtrK6weHckQQoYLIj179kRiYqLevAsXLsDf399QmyQiIhO2/0IOPvj1AgDg3cHt0aG5UuKKyBQYLIi8+uqrOHr0KN577z0kJSVh48aN+Pe//40pU6YYapNERGSi0nKL8fLmOAgBjOrqh2e6cAwgVTJYEOnSpQu2b9+OTZs2oX379njnnXewYsUKREVFGWqTRERkgkrLNZi0IQZ5xeUIb67E20+2k7okMiEGvXLME088gSeeeMKQmyAiIhMmhMDcHWdwJl0F1ya2+Hx0JBTWcqnLIhPCe80QEZHBbPozDdtirsJKBqwc1QnNXOylLolMDIMIEREZRHxaHt7+7iwAYEb/EPQMdpe4IjJFDCJERNTgbhSWYVJ0DNQaLfq388Kkh1pKXRKZKAYRIiJqUBUaLV7aFIeM/FIEuTfB8uHhvKMuVYtBhIiIGtTyXy7g8KUbcLCVY/VzkXCys5G6JDJhDCJERNRgfj6TgdX7LwEAlj0dhtZeThJXRKaOQYSIiBpEUnYhZmw7BQD41z8C8USYr8QVkTlgECEiovtWWFaBidExKCyrQLdAV8x+LFTqkshMMIgQEdF9EUJg1jenkJRdCC9nBT59NgLWcr69UO3wlUJERPfly4PJ+PF0BmzkMnweFQkPJ4XUJZEZYRAhIqJ6O3LpBpb8nAAAmPtEW0T6N5W4IjI3DCJERFQvGfkleGlTLDRagaGdmuG5B/ylLonMEIMIERHVmbpCi8kbYnG9UI02Ps5Y9FQHXrSM6oVBhIiI6uydH84hLjUPznbWWD06Ava2vKMu1Q+DCBER1cn/Yq7i66MpAIAVIzvC362JxBWROWMQISKiWjt7LR9vbD8NAHj5kVZ4ONRL4orI3DGIEBFRreQXl2NidAzKKrToHeKBlx9pJXVJZAEYRIiI6J60WoFXtsQhLbcEfq72WDGiI6ysODiV7h+DCBER3dMnv1/E3sQcKKytsCoqEi4OtlKXRBaCQYSIiGq0NyEbH++5CAB476kOaN9MKXFFZEkYRIiIqFqpN4rx8uY4CAGMfqAFhkU2l7oksjAMIkREVKUStQYTomOgKq1ApxYumPdEO6lLIgvEIEJERHcRQuDN7adxPkMFd0dbfB4VAVtrvmVQw+OrioiI7hJ9NAXfxqVDbiXDylER8FHaS10SWSgGESIi0hOTchMLfzgHAJg1IATdW7pJXBFZMgYRIiLSySkow+QNMSjXCDzewRvjHwySuiSycAwiREQEAKjQaDF1YyyyVGUI9nTEsqfDeUddMjgGESIiAgAs/TkBx5Jz0cRWjtWjI+GosJa6JGoEGESIiAg/nsrAFweTAQDLh4cj2NNR4oqosWAQISJq5C5mFWDmNycBABMeCsJjHXwkrogaEwYRIqJGrKC0HBOiY1Cs1qB7kBtmPhoidUnUyDCIEBE1UkIIzNx2CpdziuCjtMPKZzvBWs63BTIuvuKIiBqp1fsv4+ezmbCVW+HzqAi4OyqkLokaIQYRIqJG6FDSdby/OwEAMP/JtujUoqnEFVFjxSBCRNTIpOeV4KVNcdAK4OnI5ni2awupS6JGjEGEiKgRKavQYHJ0DHKL1GjfzBnvDmnPi5aRpBhEiIgakbe/O4eTV/Ph4mCDVVGRsLORS10SNXIMIkREjcTW42nY9GcqZDLg45Gd4OfqIHVJRAwiRESNwemr+Xhr5xkAwPS+rfFQaw+JKyKqxCBCRGThbhapMTE6BuoKLfq28cSUPsFSl0SkwyBCRGTBNFqBaZvjkJ5XAn83B3zwTEdYWXFwKpkOBhEiIgu24rcLOHjxOuxsrLB6dCSU9jZSl0Skh0GEiMhC/XouCyt/TwIALBkahjY+zhJXRHQ3BhEiIguUfL0I07fEAwDG9AjAkE7NpC2IqBpGCyJLliyBTCbDK6+8YqxNEhE1SsXqCkz8OgYFZRXo7N8UbzzeRuqSiKpllCBy/PhxrFmzBmFhYcbYHBFRoyWEwJxvTyMxqwAeTgp8FhUBW2t2fpPpMvirs7CwEFFRUfjiiy/QtClvqkREZEjrDl/BzvhrkFvJ8NmzEfBytpO6JKIaGTyITJkyBQMHDkTfvn3v2basrAwqlUpvIiKi2jl+JReLfjwPAHjj8TboGugqcUVE92ZtyCffvHkzYmNjcfz48Vq1X7x4MRYsWGDIkoiILFK2qhSTN8SiQiswKNwX/+wZIHVJRLVisB6RtLQ0vPzyy9iwYQPs7GrXNThnzhzk5+frprS0NEOVR0RkMco1WkzZGIucgjK09nLEkqEdeEddMhsG6xGJiYlBdnY2IiIidPM0Gg0OHDiATz/9FGVlZZDL9e/6qFAooFAoDFUSEZFFeu+n8zh+5SacFNZYPToSTRQG7ewmalAGe7U+8sgjOH36tN68sWPHIjQ0FLNmzborhBARUd3tjE/H2kNXAAAfPBOOIA9HaQsiqiODBREnJye0b99eb16TJk3g5uZ213wiIqq7hEwVZv+v8h++KX1a4tF23hJXRFR3/HA5EZEZUpWWY+LXMSgp1+DBVu6Y3i9E6pKI6sWoJxL37dtnzM0REVkkrVZg+paTuHKjGM1c7PHxyE6Q8466ZKbYI0JEZGZW7b+E385nwdbaCqtGR8C1ia3UJRHVG4MIEZEZOXAhB8t/SQQAvDO4HcKau0hbENF9YhAhIjITabnFmLY5DkIAI7v4YUSXFlKXRHTfGESIiMxAabkGkzfEIq+4HGHNlXj7yXZSl0TUIBhEiIjMwPydZ3E6PR9NHWzweVQE7Gx4LSayDAwiREQmbtOfqdhyIg1WMmDlqAg0b+ogdUlEDYZBhIjIhJ1My8P8nWcBAK89GoJ/tHKXuCKihsUgQkRkom4UlmFSdAzUGi0ebeuFyb1bSl0SUYNjECEiMkEVGi2mbY7DtfxSBLk3wfJnwnlHXbJIDCJERCbog18v4FDSDdjbyLH6uUg429lIXRKRQTCIEBGZmJ/PZGLVvksAgGVPh6G1l5PEFREZDoMIEZEJuZRTiBnbTgIAxv0jEIPCfSWuiMiwGESIiExEUVkFJn4dg8KyCnQNdMXsx0KlLonI4BhEiIhMgBACr//vFC5mF8LLWYFPn+0EGzn/RJPl46uciMgE/OePZPx4KgPWVjJ8HhUBTyc7qUsiMgoGESIiiR29fAOLdyUAAOY+0RaR/q4SV0RkPAwiREQSyswvxdSNsdBoBZ7q1AzPd/eXuiQio2IQISKSiLpCi8kbYnC9UI1Qbye891QHXrSMGh0GESIiibz74znEpubByc4aa56LhL0t76hLjQ+DCBGRBL6NvYqvjqQAAFaM6Ah/tyYSV0QkDQYRIiIjO3dNhTe2nwYATHukFR5p4yVxRUTSYRAhIjKi/OJyTIyOQWm5Fg+19sDLj7SSuiQiSTGIEBEZiVYr8MqWOKTmFqN5U3t8PLIj5FYcnEqNG4MIEZGRrPw9CXsTc6CwtsLq0ZFwcbCVuiQiyTGIEBEZwd7EbKzYcwEAsOipDmjfTClxRUSmgUGEiMjAUm8U4+VNcRACiOrWAk9HNpe6JCKTwSBCRGRAJWoNJkbHQFVagY5+Lpg3qK3UJRGZFAYRIiIDEULgzR2ncS5DBbcmtlg1OgIKa160jOjvGESIiAwk+lgqvo1Nh5UMWPlsJ/go7aUuicjkMIgQERlAbOpNLPz+LABg1oBQ9GjpLnFFRKaJQYSIqIHlFJRhcnQsyjUCj7X3xou9gqQuichkMYgQETWgCo0WL22KRaaqFC09muD94eG8oy5RDRhEiIga0LLdiTh6ORdNbOVY81wkHBXWUpdEZNIYRIiIGshPpzPw7wOXAQDvDw9HsKeTxBURmT4GESKiBpCUXYCZ204CACb0CsLjHXwkrojIPDCIEBHdp4LScrz4dQyK1Bp0D3LDzP4hUpdEZDYYRIiI7oMQAq9/cwqXc4rg7WyHlc92grWcf1qJaou/LURE9+HfBy5j15lM2Mhl+Hx0BNwdFVKXRGRWGESIiOrpcNJ1LP05AQAwf1A7RLRoKnFFROaHQYSIqB6u5ZVg6qY4aAUwLKI5orq1kLokIrPEIEJEVEdlFRpM2hCL3CI12vk6Y9FT7XnRMqJ6YhAhIqqjBd+fw8m0PCjtbbB6dCTsbHhHXaL6YhAhIqqDrSfSsPFYKmQy4OORHeHn6iB1SURmzaBBZPHixejSpQucnJzg6emJIUOGIDEx0ZCbJCIymDPp+XhrxxkAwKt9W6N3iKfEFRGZP4MGkf3792PKlCk4evQofv31V5SXl+PRRx9FUVGRITdLRNTgbhapMTE6BuoKLR4J9cTUPsFSl0RkEQx6N6aff/5Z7/G6devg6emJmJgY9OrVy5CbJiJqMBqtwMtb4nH1Zgn83Rzw4YiOsLLi4FSihmDUMSL5+fkAAFdXV2Nulojovnz82wUcuJADOxsrrB4dCaW9jdQlEVkMo92fWqvV4pVXXkHPnj3Rvn37KtuUlZWhrKxM91ilUhmrPCKiKv12Lguf/J4EAFg8tAPa+DhLXBGRZTFaj8iUKVNw5swZbN68udo2ixcvhlKp1E1+fn7GKo+I6C5Xrhfh1a3xAIAXuvvjqU7NpS2IyALJhBDC0BuZOnUqdu7ciQMHDiAwMLDadlX1iPj5+SE/Px/OzvwvhIiMp1hdgaGfH0ZCZgEi/Zti0/gHYGvNKx4Q1YZKpYJSqazV+7dBT80IIfDSSy9h+/bt2LdvX40hBAAUCgUUCt4wioikJYTAnG9PIyGzAO6OCnweFcEQQmQgBg0iU6ZMwcaNG7Fz5044OTkhMzMTAKBUKmFvb2/ITRMR1dv6w1ewM/4a5FYyfPZsJ3g520ldEpHFMmjEX7VqFfLz89G7d2/4+Pjopi1bthhys0RE9XbiSi7e/fE8AGDOY6HoFuQmcUVEls3gp2aIiKq0+01AlQ4M+y9gZRqnPbILSjF5QywqtAJPhPlg3D9qPp1MRPfPNH77iahxuRoDHPkUOLsduJEkdTUAgHKNFlM3xCG7oAytvRyxdFgY76hLZAQMIkRkfIc/+ev7ctO45cPinxLw55VcOCqssXp0JJoojHaZJaJGjUGEiIwr5wJwbudfj9XSB5HvTl7Dfw8lAwA+eCYcQR6OEldE1HgwiBCRcR1cDuBv48ckDiKJmQWY9c0pAMDk3i3Rv523pPUQNTYMIkRkPDcuAae3VX6vuHWRI3WhZOWoSssxMToGJeUa/CPYHa89GiJZLUSNFYMIERnPwQ8AoQVaDwD8e1TOk6hHRKsVeG3rSSRfL0IzF3t8MqoT5LyjLpHRMYgQkXHkJgMnb91rqtfrgG2Tyu8lCiKr9l/Cr+eyYCu3wudREXBtYitJHUSNHYMIERnH/qWA0ADBfYHmkX8LIsY/NXPwYg4++CURALBwcDuE+7kYvQYiqsQgQkSGdy3+r96QPm9UfrW99ckUI/eIXL1ZjGmb4qAVwIjOfhjZtYVRt09E+hhEiMiwhAB+eQuAADoMB5pFVs7X9YgUG62U0nINJkXH4mZxOTo0U2LB4HZG2zYRVY1BhIgM6+IvwJWDgFwBPDz3r/kSjBF5+7uzOJ2ej6YONlg1OgJ2NnKjbZuIqsYgQkSGo6kAfrkVPrpNAJr6/7VMd2rGOGNENv+Zis3H0yCTAZ+M6oTmTR2Msl0iqhmDCBEZzp//Bq4nAvZNgQdf019mcysIGKFH5GRaHubtPAsAmPFoCB5s5WHwbRJR7TCIEJFh5F8Ffn+38vtH5gP2LvrLjXRqJrdIjckbYqHWaNGvrRcmPdTSoNsjorphECEiw/jp9cob2vk9AES8cPdyI5ya0WgFpm2KQ3peCQLdm+CDZ8JhxYuWEZkUBhEianjnvwcSfwSsbIBBKwCrKv7UGKFH5INfEvFH0nXY28ixenQknO1sDLYtIqofBhEialjFucBPMyu/7/ky4Nmm6nYGDiK7z2bi832XAABLnw5DiLeTQbZDRPeHQYSIGo4QwA+vAAUZgFsw0GtG9W0NGEQu5xTita0nAQD/7BmIJ8N9G3wbRNQwrKUugIgsyMlNwLmdgJU1MOxLwMa++rZ/HyPy+6IGK0Gt0eLw8TSM16jRzM0eTzk0A37f3mDPT2RxfDsBoY9LtnkGESJqGLnJf52S6fNG5R+3mtg5V44h0ZYDB5Y1WBm2AEYDlX/digAcbLCnJrJMkWMZRIjIzJWXAN+MrezdaNED6PnKvdexsa/sNUk51GBlnL2Wj+NXbsJKBvRv5w0vZ7sGe24ii+XXTdLNM4gQ0f0RAvjxNeBaHGDvCgxdA1jV8tLp7YZUTg3g2OUbePaPY9BoBd4e1BZePQMb5HmJyLA4WJWI7s/xL4H4DYDMCnj6v4CL8e9mm6UqxZSNcdBoBYZ09MULPQKMXgMR1Q+DCBHVX/JB4OfZld/3XQC07GP0EtQVWkzeEIvrhWUI9XbCe0M7QCbjRcuIzAWDCBHVT+YZYPOzgLYCaDcU6PGSJGUs+vEcYlJuwsnOGqtHR8LBlmecicwJgwgR1V1eGrDhaaBMVTk4dcgqQIJeiO1xV7H+SAoAYMWIjghwb2L0Gojo/jCIEFHdFGYD0UMrL1rm0QYYtRGwMf6nU85dU2HOt6cBANMeDsYjbbyMXgMR3T8GESKqvYJMYN1A4PoFwLkZMPobwL6p0cvILy7HxOgYlJZr0au1B17u29roNRBRw+DJVCKqHVUGsP4J4EZSZQh54XtA2dzoZWi1AtO3xiM1txjNm9rjk5EdIecddYnMFoMIEd3b9YtA9DAgLwVQ+lWGEFdprtPx6d4k7EnIhsLaCqtHR8LFwVaSOoioYTCIEFHNUo4Am0cBJTeBpgHA8zsrv0pgb2I2PvrtAgDg3SHt0b6ZUpI6iKjhMIgQUfVObga+mwZoyoBmnYFRmwFHD0lKScstxiub4yEE8Gy3Fhje2U+SOoioYTGIENHdKsqAn+cAJ/5T+ThkYOV9YWwdJCmntFyDCV/HIL+kHOF+Lpg/qK0kdRBRw2MQISJ9Ny4B344H0mMAyICHZlVOVtJ8yE4IgTe3n8G5DBXcmthiVVQEFNa1vJcNEZk8BhEiqiQEELMW2P0WUF4E2LlU9oK06idpWRuOpeJ/sVdhJQNWjuoEXxd7SeshoobFIEJElb0gP80ALv1e+TjgQWDI55LcwO7v4lJvYsH3ZwEArw8IRY9gd0nrIaKGxyBC1JiVlwKHPgYOflA5IFWuAPrOB7pNkuxUzG3XC8swKToW5RqBAe28MaFXkKT1EJFhMIgQNUaaCuDUZmDvYkB1tXJeUG/g8Q8A92BJSwOACo0WL22MQ6aqFC09muD94WG8oy6RhWIQIWpMtFog4Qfg93eB64mV85ybAY++U3kHXRN5s39/dyKOXL6BJrZyrHkuEk52NlKXREQGwiBC1BiUl1ReE+TIp5WXaAcq7xHz4Aygy78kuWlddXadzsCaA5cBAMueDkewp5PEFRGRITGIEFmy3GQgLhqIWQcUX6+cp1AC3SYAPaYCdqZ1ZdKk7ALM2HYSAPBiryAMDPORuCIiMjQGESJLU1YAJO4CYr8Crhz8a76yBdB9MtBpNKAwvV6GwrIKTPg6BkVqDR4IcsXr/UOkLomIjIBBhMgSlNysDB/nvqv8CK6m7NYCGdCyDxDxPBA6CJCb5q+8EAIzt53EpZwieDvbYeWoCFjLpf3UDhEZh2n+VSKimmk1wLV44PJe4PI+IPUIoK34a7lrEBA2Auj4rOTXAqmNLw5exq4zmbCRy/D56Ah4OCmkLomIjMTgQeSzzz7D+++/j8zMTISHh2PlypXo2rWroTdLZFnKCiqDR3oMcPV45SmX0nz9Np5tgTZPAm2frPzeRD4Bcy+HL13Hkl0JAIB5g9ohokVTiSsiImMyaBDZsmULpk+fjtWrV6Nbt25YsWIF+vfvj8TERHh6ehpy00TmSQigKAfIPg/kJACZp4D02MrHEPptFUog8MHK63+0fBhwaylFxfclI78EL22Mg1YAQyOaYXQ30++9IaKGJRNCiHs3q59u3bqhS5cu+PTTTwEAWq0Wfn5+eOmllzB79ux7rq9SqaBUKpGfnw9nZ2dDlUlkXEIAxblA3hXgZgqQlwLcvALkXKgMHyW5Va+n9AOaRQDNIgH/fwC+HQEr8735W1mFBiPWHEV8Wh7a+jjj28k9YGdjvvtDRH+py/u3wXpE1Go1YmJiMGfOHN08Kysr9O3bF0eOHKlynbKyMpSVlekeq1QqQ5VH1PC0msrTJSU3gYJMoDDrr6ng9tfMyuChLqzhiWRA0wDAs03lKZZmkZUBxMnbWHtiFIt+PI/4tDwo7W2wenQkQwhRI2WwIHL9+nVoNBp4eXnpzffy8kJCQkKV6yxevBgLFiwwVElE+oSoHOBZXgyoi299Lar8WtU8dTGgLgBK8oDSvLu/lqpw1+mTmjh6A039ARf/yq9urQDPUMC9NWBj2XeYTcwswNdHUwAAK0Z2RAs3B4krIiKpmNSnZubMmYPp06frHqtUKvj5+TX8hvLSbp1zB/TeOPTOUpnafFQz39TqvHO+qLysuNACQlP5Vav563G1y7R3t9U9FrfWvT2vAtCUAxr1ramq76tZXpfgUFs2TQAnL8Dx1uTkDTh6VgYPR6/KT7G4+Fl82KjJJ79fhBDAY+290SeE48WIGjODBRF3d3fI5XJkZWXpzc/KyoK3d9VdzAqFAgqFET62l/Qb8MMrht8OmQ+ZVWWAsHUAbBwA2yaVQUH3vUPlMltHwM4FsHe542vTW98rAWt+9LQmF7MK8NPpDADAtEdaSVwNEUnNYEHE1tYWkZGR2LNnD4YMGQKgcrDqnj17MHXqVENttnYc3ACfjn891vuYo6x+8xviOe6aj2rmS1FLPWuXWVVOVvJb39/6amV1x2P5PZbdfiyr4rmsAbkNILe9Nd3r+zvm2ThUhgcz+birufvk9yQIAfRv54U2PhyETtTYGfTUzPTp0/HCCy+gc+fO6Nq1K1asWIGioiKMHTvWkJu9t7a3rrVAREaVlF2AH05dA8DeECKqZNAgMmLECOTk5GDevHnIzMxEx44d8fPPP981gJWIGoePfqscG/JoWy+08zWtG+4RkTQMeh2R+8XriBBZjpiUmxi26jBkMuDHlx5EW1/+ThNZqrq8f/OuUkRkcEIIvPvjOQDA8MjmDCFEpMMgQkQG98OpDMSl5sHBVo7XHg2RuhwiMiEMIkRkUKXlGiz9ufIihhN6tYSXs53EFRGRKWEQISKD+veBy7h6swTeznYY3ytQ6nKIyMQwiBCRwVzKKcSnvycBAN4Y2AYOtiZ1MWciMgEMIkRkEEIIvPHtaag1WjzU2gODwnykLomITBCDCBEZxLYTV3EsORf2NnK8O6Q9ZLxyLRFVgUGEiBpcZn4pFv1UeWPJ6f1aw8+Vd9cloqoxiBBRg9JqBaZvjUd+STnCmisxtmeA1CURkQljECGiBvXFwcs4fOkG7G3kWDGiI6zl/DNDRNXjXwgiajBn0vOx/JdEAMD8QW0R5OEocUVEZOoYRIioQeQXl2PKxliUawT6t/PCiC5+UpdERGaAQYSI7ptGKzBtcxxSbhSjmYs9lgwN46dkiKhWGESI6L4t/yUR+y/kwM7GCv9+PhJNm9hKXRIRmQkGESK6Lzvj07Fq3yUAwLKnw9HOVylxRURkThhEiKjeDlzIwYxtJwEAE3oF4clwX4krIiJzwyBCRPVyMi0PE6NjUK4RGBTui1kDQqUuiYjMEIMIEdVZYmYBxq47jmK1Bv8Idsfy4WGwsuLgVCKqO94Kk4jq5Nw1FaK+PIqbxeXo0EyJ1c9FQmEtl7osIjJTDCJEVGtn0vMx+j/HkFdcefn2r//ZDY4K/hkhovrjXxAiqpX9F3IwZUMsCssq0NHPBev/2RVKexupyyIiM8cgQkT3tPnPVLy54ww0WoEHglzxxfOd4WTHEEJE949BhIiqVa7RYumuBHz5RzIA4KlOzbBkWAeOCSGiBsMgQkRVylaVYurGOPx5JRcAMO3hYLzarzUv3U5EDYpBhIjusjchGzO/OYXrhWVwVFhj+fAwDGjvI3VZRGSBGESISKewrALv/nAOm4+nAQBCvJywanQEgjwcJa6MiCwVgwgRQQiBX85lYeH355CeVwKZDPhnz0DM7B8COxuOByEiw2EQIWrkkq8XYeH3Z7E3MQcA0LypPZYPD8cDQW4SV0ZEjQGDCFEjlZFfgk/2XMTWE1eh0QrYyGWY0KslpvQJhr0te0GIyDgYRIgamSxVKb48eBnrj6RAXaEFADwc6ok3B7ZBS44FISIjYxAhaiTOZ6jwxcHL+P7kNZRrBACga4ArZg4IQZcAV4mrI6LGikGEyIKVqDX4+WwGthxPw9HLubr5XQKaYnKfYPRu7cHrghCRpBhEiCxMhUaLP6/k4odTGfg+/hoKyioAAHIrGR5r741/PRiEjn4u0hZJRHQLgwiRBSgt1+Dwpev4+Uwmfj2XhZvF5bplfq72GB7ph2GRzdHMxV7CKomI7sYgQmSGNFqBs9fycSjpBg5fuo7jV3JRWq7VLW/qYIO+bbzwVEQzPBDoBisrnn4hItPEIEJkBq4XluHU1TzEp+XjZFoe4tPykF9SrtfG29kO/dt5oX97b3QNcIW13EqiaomIao9BhMiElJZrcDmnCBezC3AxqxAXswtw9poKV2+W3NXWSWGNbkGu6Bnsjp7B7mjl6ciBp0RkdhhEiIxIqxXILVYjLbcYV2+WIO1mMdJyS3D1ZjHScouRmlsMrbh7PZkMaOnhiPDmLujop0RYcxe083VmrwcRmT0GEaL7oNEKFJSWI79Ef7pZpEZOQRmyC8qQU1CGnMLKr9cLy3TX8KiO0t4Grb0cEezphFaejgj1dkL75ko429kYaa+IiIyHQYQsjlYroNZoUa7RolwjUK7RQl1xx2ONFuUVlY/VGg2K1ZVTafmd31fcNb+orEIXOApKK+pcn0xWOZ6jeVN7+DV1QHNXB/g1tUfzpg5o6dkEHo4KnmIhokajUQaRmJRcfH8y4675Qvz1n6rQm/+37/+2RH9+1e31l9yxzn0879/bV/NtLffn3u1RmzpraCNQGQ60QkAjKrejufVYq8Wt+QJa8bd2WgEhcGu+uDUft+bf3b5CK3RBQ1PVuQ0Dc7CVQ2lvA6W9DZztbeBibwNPZwU8HO1ufVXAw0kBT2cF3JooYGvNUypEREAjDSKJmYVYd/iK1GWQkcitZLCRy2Ajt4Kt3Ao2civYWOs/treVw95GDgdbOextK7862FrDzub297eXW8NB8VfoUNrbwNnOhsGCiKieGmUQaefrjKl9gnWP/94Lrtch/rcFsqpnQ/a3JdU9z5297NV1u9/P81bXvrrtVv881bS/j5+RlUwGK9ntrzLIrWSQySoDwu15Vn9/bHXrsUwG2a32VjLcmi+7Nf+v9nKryue2tf570LCqDB9WVryGBhGRCWuUQSTczwXhvMQ1ERGR5AzSn3zlyhWMGzcOgYGBsLe3R8uWLTF//nyo1WpDbI6IiIjMlEF6RBISEqDVarFmzRoEBwfjzJkzGD9+PIqKirB8+XJDbJKIiIjMkEwIYZSPGLz//vtYtWoVLl++XOt1VCoVlEol8vPz4ezsbMDqiIiIqKHU5f3baGNE8vPz4erqWmObsrIylJWV6R6rVCpDl0VEREQSMspnDpOSkrBy5UpMmDChxnaLFy+GUqnUTX5+fsYoj4iIiCRSpyAye/ZsyG59pLK6KSEhQW+d9PR0DBgwAMOHD8f48eNrfP45c+YgPz9fN6WlpdV9j4iIiMhs1GmMSE5ODm7cuFFjm6CgINja2gIArl27ht69e+OBBx7AunXrYGVVtw4YjhEhIiIyPwYbI+Lh4QEPD49atU1PT0efPn0QGRmJtWvX1jmEEBERkeUzyGDV9PR09O7dG/7+/li+fDlycnJ0y7y9vQ2xSSIiIjJDBgkiv/76K5KSkpCUlITmzZvrLTPSp4WJiIjIDBjkfMmYMWMghKhyIiIiIrqNAzeIiIhIMgwiREREJBmTvvvu7VM5vMIqERGR+bj9vl2bIRkmHUQKCgoAgFdYJSIiMkMFBQVQKpU1tjHaTe/qQ6vV4tq1a3BycoJMJmvQ51apVPDz80NaWppFXiyN+2f+LH0fuX/mz9L30dL3DzDcPgohUFBQAF9f33teR8yke0SsrKzu+vhvQ3N2drbYFxjA/bMElr6P3D/zZ+n7aOn7BxhmH+/VE3IbB6sSERGRZBhEiIiISDKNNogoFArMnz8fCoVC6lIMgvtn/ix9H7l/5s/S99HS9w8wjX006cGqREREZNkabY8IERERSY9BhIiIiCTDIEJERESSYRAhIiIiyVhsEFm0aBF69OgBBwcHuLi4VNkmNTUVAwcOhIODAzw9PTFz5kxUVFTU+Ly5ubmIioqCs7MzXFxcMG7cOBQWFhpgD+pm3759kMlkVU7Hjx+vdr3evXvf1X7ixIlGrLz2AgIC7qp1yZIlNa5TWlqKKVOmwM3NDY6Ojhg2bBiysrKMVHHtXblyBePGjUNgYCDs7e3RsmVLzJ8/H2q1usb1TP34ffbZZwgICICdnR26deuGP//8s8b227ZtQ2hoKOzs7NChQwf89NNPRqq07hYvXowuXbrAyckJnp6eGDJkCBITE2tcZ926dXcdLzs7OyNVXDdvv/32XbWGhobWuI45Hb+q/p7IZDJMmTKlyvbmcOwOHDiAQYMGwdfXFzKZDDt27NBbLoTAvHnz4OPjA3t7e/Tt2xcXL1685/PW9fe4riw2iKjVagwfPhyTJk2qcrlGo8HAgQOhVqtx+PBhrF+/HuvWrcO8efNqfN6oqCicPXsWv/76K3744QccOHAAL774oiF2oU569OiBjIwMvelf//oXAgMD0blz5xrXHT9+vN56y5YtM1LVdbdw4UK9Wl966aUa27/66qv4/vvvsW3bNuzfvx/Xrl3D0KFDjVRt7SUkJECr1WLNmjU4e/YsPvroI6xevRpvvPHGPdc11eO3ZcsWTJ8+HfPnz0dsbCzCw8PRv39/ZGdnV9n+8OHDGDVqFMaNG4e4uDgMGTIEQ4YMwZkzZ4xcee3s378fU6ZMwdGjR/Hrr7+ivLwcjz76KIqKimpcz9nZWe94paSkGKniumvXrp1erX/88Ue1bc3t+B0/flxv33799VcAwPDhw6tdx9SPXVFREcLDw/HZZ59VuXzZsmX45JNPsHr1ahw7dgxNmjRB//79UVpaWu1z1vX3uF6EhVu7dq1QKpV3zf/pp5+ElZWVyMzM1M1btWqVcHZ2FmVlZVU+17lz5wQAcfz4cd28Xbt2CZlMJtLT0xu89vuhVquFh4eHWLhwYY3tHnroIfHyyy8bp6j75O/vLz766KNat8/LyxM2NjZi27Ztunnnz58XAMSRI0cMUGHDWrZsmQgMDKyxjSkfv65du4opU6boHms0GuHr6ysWL15cZftnnnlGDBw4UG9et27dxIQJEwxaZ0PJzs4WAMT+/furbVPd3yNTNH/+fBEeHl7r9uZ+/F5++WXRsmVLodVqq1xuTsdOCCEAiO3bt+sea7Va4e3tLd5//33dvLy8PKFQKMSmTZuqfZ66/h7Xh8X2iNzLkSNH0KFDB3h5eenm9e/fHyqVCmfPnq12HRcXF70ehr59+8LKygrHjh0zeM118d133+HGjRsYO3bsPdtu2LAB7u7uaN++PebMmYPi4mIjVFg/S5YsgZubGzp16oT333+/xlNpMTExKC8vR9++fXXzQkND0aJFCxw5csQY5d6X/Px8uLq63rOdKR4/tVqNmJgYvZ+9lZUV+vbtW+3P/siRI3rtgcrfSXM4VkDl8QJwz2NWWFgIf39/+Pn5YfDgwdX+vTEFFy9ehK+vL4KCghAVFYXU1NRq25rz8VOr1YiOjsY///nPGm+wak7H7k7JycnIzMzUO0ZKpRLdunWr9hjV5/e4Pkz6pneGlJmZqRdCAOgeZ2ZmVruOp6en3jxra2u4urpWu45U/vOf/6B///73vGngs88+C39/f/j6+uLUqVOYNWsWEhMT8e233xqp0tqbNm0aIiIi4OrqisOHD2POnDnIyMjAhx9+WGX7zMxM2Nra3jVGyMvLy+SO152SkpKwcuVKLF++vMZ2pnr8rl+/Do1GU+XvWEJCQpXrVPc7aerHCqi8U/grr7yCnj17on379tW2CwkJwX//+1+EhYUhPz8fy5cvR48ePXD27FmD3+Czrrp164Z169YhJCQEGRkZWLBgAR588EGcOXMGTk5Od7U35+O3Y8cO5OXlYcyYMdW2MadjV5Xbx6Eux6g+v8f1YVZBZPbs2Vi6dGmNbc6fP3/PAVXmpD77fPXqVezevRtbt2695/P/fXxLhw4d4OPjg0ceeQSXLl1Cy5Yt6194LdVl/6ZPn66bFxYWBltbW0yYMAGLFy822Usw1+f4paenY8CAARg+fDjGjx9f47pSHz+qNGXKFJw5c6bGMRQA0L17d3Tv3l33uEePHmjTpg3WrFmDd955x9Bl1sljjz2m+z4sLAzdunWDv78/tm7dinHjxklYWcP7z3/+g8ceewy+vr7VtjGnY2duzCqIvPbaazUmVgAICgqq1XN5e3vfNfL39qcpvL29q13nzgE6FRUVyM3NrXad+1WffV67di3c3Nzw5JNP1nl73bp1A1D5H7kx3sju55h269YNFRUVuHLlCkJCQu5a7u3tDbVajby8PL1ekaysLIMdrzvVdf+uXbuGPn36oEePHvj3v/9d5+0Z+/hVx93dHXK5/K5PKNX0s/f29q5Te1MxdepU3cD1uv5nbGNjg06dOiEpKclA1TUcFxcXtG7dutpazfX4paSk4LfffqtzL6I5HTvgr/e1rKws+Pj46OZnZWWhY8eOVa5Tn9/jemmw0SYm6l6DVbOysnTz1qxZI5ydnUVpaWmVz3V7sOqJEyd083bv3m1Sg1W1Wq0IDAwUr732Wr3W/+OPPwQAcfLkyQaurOFFR0cLKysrkZubW+Xy24NVv/nmG928hIQEkx2sevXqVdGqVSsxcuRIUVFRUa/nMKXj17VrVzF16lTdY41GI5o1a1bjYNUnnnhCb1737t1NdrCjVqsVU6ZMEb6+vuLChQv1eo6KigoREhIiXn311QauruEVFBSIpk2bio8//rjK5eZ2/G6bP3++8Pb2FuXl5XVaz9SPHaoZrLp8+XLdvPz8/FoNVq3L73G9am2wZzIxKSkpIi4uTixYsEA4OjqKuLg4ERcXJwoKCoQQlS+i9u3bi0cffVTEx8eLn3/+WXh4eIg5c+bonuPYsWMiJCREXL16VTdvwIABolOnTuLYsWPijz/+EK1atRKjRo0y+v5V57fffhMAxPnz5+9advXqVRESEiKOHTsmhBAiKSlJLFy4UJw4cUIkJyeLnTt3iqCgINGrVy9jl31Phw8fFh999JGIj48Xly5dEtHR0cLDw0M8//zzujZ37p8QQkycOFG0aNFC/P777+LEiROie/fuonv37lLsQo2uXr0qgoODxSOPPCKuXr0qMjIydNPf25jT8du8ebNQKBRi3bp14ty5c+LFF18ULi4uuk+qPffcc2L27Nm69ocOHRLW1tZi+fLl4vz582L+/PnCxsZGnD59WqpdqNGkSZOEUqkU+/bt0ztexcXFujZ37uOCBQvE7t27xaVLl0RMTIwYOXKksLOzE2fPnpViF2r02muviX379onk5GRx6NAh0bdvX+Hu7i6ys7OFEOZ//ISofFNt0aKFmDVr1l3LzPHYFRQU6N7rAIgPP/xQxMXFiZSUFCGEEEuWLBEuLi5i586d4tSpU2Lw4MEiMDBQlJSU6J7j4YcfFitXrtQ9vtfvcUOw2CDywgsvCAB3TXv37tW1uXLlinjssceEvb29cHd3F6+99ppeKt67d68AIJKTk3Xzbty4IUaNGiUcHR2Fs7OzGDt2rC7cmIJRo0aJHj16VLksOTlZ72eQmpoqevXqJVxdXYVCoRDBwcFi5syZIj8/34gV105MTIzo1q2bUCqVws7OTrRp00a89957er1Xd+6fEEKUlJSIyZMni6ZNmwoHBwfx1FNP6b25m4q1a9dW+Xr9e6elOR6/lStXihYtWghbW1vRtWtXcfToUd2yhx56SLzwwgt67bdu3Spat24tbG1tRbt27cSPP/5o5Iprr7rjtXbtWl2bO/fxlVde0f08vLy8xOOPPy5iY2ONX3wtjBgxQvj4+AhbW1vRrFkzMWLECJGUlKRbbu7HT4jKHm0AIjEx8a5l5njsbr9n3Tnd3g+tVivmzp0rvLy8hEKhEI888shd++7v7y/mz5+vN6+m3+OGIBNCiIY70UNERERUe432OiJEREQkPQYRIiIikgyDCBEREUmGQYSIiIgkwyBCREREkmEQISIiIskwiBAREZFkGESIiIhIMgwiREREJBkGESIiIpIMgwgRERFJhkGEiIiIJPN/egDcgdVlMrYAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"visualize_activation(mx.gluon.nn.SELU())"
]
},
{
"cell_type": "markdown",
"id": "0abe6cf5",
"metadata": {},
"source": [
"![selu activation and gradient](/_static/selu.png)\n",
"\n",
"\n",
"### SiLU\n",
"The SiLU is an activation function that attempts to address the shortcomings of ReLU by combining ideas from ReLU and sigmoid. The SiLU serves as a smooth approximation to the ReLU and was originally introduced in [Hendrycks et al](https://arxiv.org/abs/1606.08415).\n",
"\n",
"The silu function is given as \n",
"\n",
"$$ silu(x) = x\\cdot\\sigma(x)$$\n",
"\n",
"where $\\sigma$ is the sigmoid activation function $\\sigma(x) = \\frac{1}{1 + e^{-x}}$ described above."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "ca43abf8",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"visualize_activation(mx.gluon.nn.SiLU())"
]
},
{
"cell_type": "markdown",
"id": "3432456c",
"metadata": {},
"source": [
"![silu activation and gradient](/_static/silu.png)\n",
"\n",
"### GELU\n",
"The GELU is a smooth approximation to the ReLU and was introduced in [Hendrycks et al](https://arxiv.org/abs/1606.08415). It is a common activation function in architectures such as Transformers, BERT, and GPT.\n",
"\n",
"The gelu function is given as \n",
"\n",
"$$ gelu(x) = x\\cdot\\Phi(x),$$\n",
"\n",
"whereas the ReLU can be written as $x\\cdot\\mathbf{1}(x>0)$, so $Phi(x)$ serves as a smooth approximation to the ReLU's indicator function.\n",
"\n",
"Note $\\Phi(x) = \\frac{1}{\\sqrt{2 \\pi}} \\exp\\left\\{-\\frac{x^2}{2}\\right\\}$ is the standard normal cumulative distribution."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "ee44dee2",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"visualize_activation(mx.gluon.nn.GELU())"
]
},
{
"cell_type": "markdown",
"id": "0d5662ad",
"metadata": {},
"source": [
"![gelu activation and gradient](/_static/gelu.png)\n",
"\n",
"## Summary\n",
"\n",
"* Activation functions introduce non-linearities to deep neural network that allow the models to capture complex interactions between features of the data.\n",
"* ReLU is the activation function that is commonly used in many neural network architectures because of its simplicity and performance.\n",
"* Sigmoids like the logistic (sigmoid) function and tanh where the first kinds of activation functions used in neural networks. They have since fallen out of use because of their tendency to saturate and have vanishing gradients.\n",
"* Rectifiers like ReLU do not saturate like the Sigmoids and so address the vanishing gradient problem making them the de facto activation functions. ReLU however is still plagued by the dying ReLU problem.\n",
"* LeakyReLU and PReLU are two similar approaches to improve ReLU and address the dying ReLU by introducing a parameter $\\alpha$ (learned in PReLU) that leaks to the gradient of negative inputs\n",
"* MXNet also implements custom state-of-the-art activations like ELU, SELU, SiLU, and GELU.\n",
"\n",
"\n",
"\n",
"## Next Steps\n",
"\n",
"Activations are just one component of neural network architectures. Here are a few MXNet resources to learn more about activation functions and how they they combine with other components of neural nets.\n",
"* Learn how to create a Neural Network with these activation layers and other neural network layers in the [Gluon crash course](../../../../getting-started/crash-course/index.ipynb).\n",
"* Check out the guide to MXNet [gluon layers and blocks](../nn.ipynb) to learn about the other neural network layers in implemented in MXNet and how to create custom neural networks with these layers.\n",
"* Also check out the [guide to normalization layers](../../training/normalization/index.ipynb) to learn about neural network layers that normalize their inputs.\n",
"* Finally take a look at the [Custom Layer guide](../custom-layer.ipynb) to learn how to implement your own custom activation layer."
]
}
],
"metadata": {
"language_info": {
"name": "python"
}
},
"nbformat": 4,
"nbformat_minor": 5
}