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June 2, 2017 17:21
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Mixture autoencoder with gumbel-softmax
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| # -*- coding: utf-8 -*- | |
| """ | |
| a bunch of lasagne code implementing gumbel softmax | |
| https://arxiv.org/abs/1611.01144 | |
| """ | |
| import numpy as np | |
| import theano | |
| import theano.tensor as T | |
| from theano.sandbox.rng_mrg import MRG_RandomStreams as RandomStreams | |
| from lasagne.random import get_rng | |
| from lasagne.layers import Layer | |
| class GumbelSoftmax: | |
| """ | |
| A gumbel-softmax nonlinearity with gumbel(0,1) noize | |
| In short, it's a quasi-one-hot nonlinearity that "samples" from softmax | |
| categorical distribution. | |
| Explaination and motivation: https://arxiv.org/abs/1611.01144 | |
| Code mostly follows http://blog.evjang.com/2016/11/tutorial-categorical-variational.html | |
| Softmax normalizes over the LAST axis (works exactly as T.nnet.softmax for 2d). | |
| :param t: temperature of sampling. Lower means more spike-like sampling. Can be symbolic. | |
| :param eps: a small number used for numerical stability | |
| :returns: a callable that can (and should) be used as a nonlinearity | |
| """ | |
| def __init__(self, | |
| t=0.1, | |
| eps=1e-20): | |
| assert t != 0 | |
| self.temperature=t | |
| self.eps=eps | |
| self._srng = RandomStreams(get_rng().randint(1, 2147462579)) | |
| def __call__(self,logits): | |
| """computes a gumbel softmax sample""" | |
| #sample from Gumbel(0, 1) | |
| uniform = self._srng.uniform(logits.shape,low=0,high=1) | |
| gumbel = -T.log(-T.log(uniform + self.eps) + self.eps) | |
| #draw a sample from the Gumbel-Softmax distribution | |
| return T.nnet.softmax((logits + gumbel) / self.temperature) | |
| def onehot_argmax(logits): | |
| """computes a hard one-hot vector encoding maximum""" | |
| return T.extra_ops.to_one_hot(T.argmax(logits,-1),logits.shape[-1]) | |
| class GumbelSoftmaxLayer(Layer): | |
| """ | |
| lasagne.layers.GumbelSoftmaxLayer(incoming,**kwargs) | |
| A layer that just applies a GumbelSoftmax nonlinearity. | |
| In short, it's a quasi-one-hot nonlinearity that "samples" from softmax | |
| categorical distribution. | |
| If you provide "hard_max=True" in lasagne.layers.get_output | |
| it will instead compute one-hot of aт argmax. | |
| Softmax normalizes over the LAST axis (works exactly as T.nnet.softmax for 2d). | |
| Explaination and motivation: https://arxiv.org/abs/1611.01144 | |
| Code mostly follows http://blog.evjang.com/2016/11/tutorial-categorical-variational.html | |
| Parameters | |
| ---------- | |
| incoming : a :class:`Layer` instance or a tuple | |
| The layer feeding into this layer, or the expected input shape | |
| t: temperature of sampling. Lower means more spike-like sampling. Can be symbolic (e.g. shared) | |
| eps: a small number used for numerical stability | |
| """ | |
| def __init__(self, incoming, t=0.1, eps=1e-20, **kwargs): | |
| super(GumbelSoftmaxLayer, self).__init__(incoming, **kwargs) | |
| self.gumbel_softmax = GumbelSoftmax(t=t,eps=eps) | |
| def get_output_for(self, input, hard_max=False, **kwargs): | |
| if hard_max: | |
| return onehot_argmax(input) | |
| else: | |
| return self.gumbel_softmax(input) |
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "from gumbel_softmax import GumbelSoftmax, GumbelSoftmaxLayer\n", | |
| "import theano.tensor as T\n", | |
| "import numpy as np" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Simple demo\n", | |
| "* Sample from gumbel-softmax\n", | |
| "* Average over samples" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 2, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "temperature = 0.01\n", | |
| "logits = np.linspace(-2,2,10).reshape([1,-1])\n", | |
| "gumbel_softmax = GumbelSoftmax(t=temperature)(logits)\n", | |
| "softmax = T.nnet.softmax(logits)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 3, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
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OvYKmBQTi0MdC0/pceP11Dh/OT/MPcOmFZwDoWxta6WbCNZncxTQR0yC8jkfurttGhSHl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| |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x7fa97c5ad2d0>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "<matplotlib.legend.Legend at 0x7fa9774990d0>" | |
| ] | |
| }, | |
| "execution_count": 3, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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XX3+9KMbt27eTmZlZ4n4bNmxInTp12Lp1K8uXLwegT58+LF68mOPHj5Ofn89nn31WVOfy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\nKM5ej+Ls9fhZbXstrKvHGGNqGUv8xhh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| |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x7fa97a4b8d10>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "import matplotlib.pyplot as plt\n", | |
| "%matplotlib inline\n", | |
| "plt.title('gumbel-softmax samples')\n", | |
| "for i in range(100):\n", | |
| " plt.plot(range(10),gumbel_softmax.eval()[0],marker='o',alpha=0.25)\n", | |
| "plt.ylim(0,1)\n", | |
| "plt.show()\n", | |
| "\n", | |
| "plt.title('average over samples')\n", | |
| "plt.plot(range(10),np.mean([gumbel_softmax.eval()[0] for _ in range(500)],axis=0),\n", | |
| " marker='o',label='gumbel-softmax average')\n", | |
| "\n", | |
| "plt.plot(softmax.eval()[0],marker='+',label='regular softmax')\n", | |
| "plt.legend(loc='best')" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "# Autoencoder with mixture distribution\n", | |
| "\n", | |
| "* We learn mixture distribution via $ z ~ \\sum _i g_i \\cdot q_i $ where\n", | |
| " * g_i is a gumbel-softmax sample for i-th mixture component\n", | |
| " * q_i is i-th mixture component\n", | |
| "* We do not use any bayesian regularization, simply optimizer by backprop\n", | |
| "* Hidden layer contains 256 units, split into 32 blocks of 8 variables\n", | |
| "* Gumbel-softmax is computed over each block" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 4, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "from lasagne.random import get_rng\n", | |
| "from theano.sandbox.rng_mrg import MRG_RandomStreams as RandomStreams\n", | |
| "from lasagne.layers import MergeLayer\n", | |
| "class MixtureLayer(MergeLayer):\n", | |
| " \"\"\"\n", | |
| " A layer that takes gumbel-softmax quasi-categorical variable \n", | |
| " and a set of normal mixture component parameters (mu,sigma).\n", | |
| " All shapes are [batch size, n_hidden_variables,n_components] \n", | |
| " \"\"\"\n", | |
| " _rng = RandomStreams(get_rng().randint(1, 2147462579))\n", | |
| " def get_output_for(self, inputs,**kwargs):\n", | |
| " g,mu,sigma = inputs\n", | |
| " \n", | |
| " #compute distribution components q_i\n", | |
| " e = self._rng.normal(mu.shape,0,1)\n", | |
| " q = mu + sigma * e\n", | |
| " \n", | |
| " #compute samples from mixture\n", | |
| " return (g*q).sum(axis=-1)\n", | |
| " \n", | |
| " def get_output_shape_for(self,input_shapes,**kwargs):\n", | |
| " return input_shapes[0][:1]\n", | |
| " " | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 5, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "from sklearn.datasets import load_digits\n", | |
| "X = load_digits().data" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 6, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "import lasagne\n", | |
| "from lasagne.layers import *\n", | |
| "import theano\n", | |
| "\n", | |
| "#graph inputs and shareds\n", | |
| "input_var = T.matrix(\"data batch\")\n", | |
| "temp = theano.shared(np.float32(1),'temperature',allow_downcast=True)\n", | |
| "\n", | |
| "#architecture: encoder\n", | |
| "nn = l_in = InputLayer((None,64),input_var)\n", | |
| "nn = DenseLayer(nn,64,nonlinearity=T.tanh)\n", | |
| "nn = DenseLayer(nn,32,nonlinearity=T.tanh)\n", | |
| "\n", | |
| "#bottleneck\n", | |
| "g_logits = DenseLayer(nn,32,nonlinearity=None,name='gumbel')\n", | |
| "mu = DenseLayer(nn,32,nonlinearity=None,name='mu')\n", | |
| "sigma = DenseLayer(nn,32,nonlinearity=lambda s: T.log1p(T.exp(s)),name='sigma')\n", | |
| "\n", | |
| "#reshape everything into blocks of 4 \n", | |
| "#so that we have 8 variables with mixtures of 4 distributions\n", | |
| "g_logits,mu,sigma = map(lambda layer: reshape(layer,(-1,4)),[g_logits,mu,sigma])\n", | |
| "\n", | |
| "#apply gumbel-softmax\n", | |
| "g = GumbelSoftmaxLayer(g_logits,t=temp)\n", | |
| "\n", | |
| "#draw samples from mixture\n", | |
| "nn = MixtureLayer([g,mu,sigma])\n", | |
| "nn = bottleneck = reshape(nn,(-1,32/4))\n", | |
| "\n", | |
| "#decoder\n", | |
| "nn = DenseLayer(nn,32,nonlinearity=T.tanh)\n", | |
| "nn = DenseLayer(nn,64,nonlinearity=T.tanh)\n", | |
| "nn = DenseLayer(nn,64,nonlinearity=None)\n", | |
| "\n", | |
| "#loss and updates\n", | |
| "loss = T.mean((get_output(nn)-input_var)**2) #+ <your KL here>\n", | |
| "updates = lasagne.updates.adam(loss,get_all_params(nn))\n", | |
| "\n", | |
| "#compile\n", | |
| "train_step = theano.function([input_var],loss,updates=updates)\n", | |
| "evaluate = theano.function([input_var],loss)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Training loop\n", | |
| "* We gradually reduce temperature from 1 to 0.01 over time" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 7, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "60.040 21.718 18.868 18.782 18.796 18.779 18.785 18.782 18.785 18.785 18.784 18.785 18.700 18.257 17.599 16.959 16.499 16.124 15.547 14.622 13.796 13.249 12.817 12.400 11.842 11.196 10.591 10.100 9.740 9.426 9.139 8.923 8.729 8.536 8.368 8.212 8.060 7.908 7.755 7.665 7.515 7.417 7.298 7.179 7.077 6.995 6.919 6.807 6.712 6.629 6.560 6.483 6.376 6.303 6.216 6.156 6.101 6.045 5.946 5.889 5.838 5.808 5.732 5.722 5.671 5.594 5.551 5.507 5.465 5.440 5.394 5.363 5.328 5.278 5.258 5.258 5.212 5.180 5.161 5.114 5.087 5.075 5.236 5.037 5.002 4.991 4.969 4.925 4.891 4.882 4.852 4.847 4.818 4.812 4.784 4.766 4.749 4.739 4.716 4.692\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "for i,t in enumerate(np.logspace(0,-2,10000)):\n", | |
| " sample = X[np.random.choice(len(X),32)]\n", | |
| " temp.set_value(t)\n", | |
| " mse = train_step(sample)\n", | |
| " if i %100 ==0:\n", | |
| " print '%.3f'%evaluate(X)," | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 8, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "#functions for visualization\n", | |
| "get_sample = theano.function([input_var],get_output(nn))\n", | |
| "get_sample_hard = theano.function([input_var],get_output(nn,hard_max=True))\n", | |
| "get_code = theano.function([input_var],get_output(bottleneck,hard_max=False))\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 12, | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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| |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x7fa96a423c90>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
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| |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x7fa96ae77890>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
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| |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x7fa96a1fccd0>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
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| |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x7fa96a110190>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
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| |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x7fa969e9e7d0>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
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| |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x7fa96ae77d10>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
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| |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x7fa96a745150>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
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| |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x7fa96acebf50>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
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| |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x7fa96a48ed90>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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BkiRtzcOr6obm9S/pTWiwJQVclOQe4NSqWrm1gEmOB44H2GWXXQ567GMfO+ckf/7zn885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\nJEmdZsMrSZKkTrPhlSRJUqf9f6UNlekYG5tRAAAAAElFTkSuQmCC\n", | |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x7fa96a479e90>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "for i in range(10):\n", | |
| " X_sample = X[np.random.randint(len(X)),None,:]\n", | |
| " plt.figure(figsize=[12,4])\n", | |
| " plt.subplot(1,4,1)\n", | |
| " plt.title(\"original\")\n", | |
| " plt.imshow(X_sample.reshape([8,8]),interpolation='none',cmap='gray')\n", | |
| " plt.subplot(1,4,2)\n", | |
| " plt.title(\"gumbel\")\n", | |
| " plt.imshow(get_sample(X_sample).reshape([8,8]),interpolation='none',cmap='gray')\n", | |
| " plt.subplot(1,4,3)\n", | |
| " plt.title(\"hard-max\")\n", | |
| " plt.imshow(get_sample_hard(X_sample).reshape([8,8]),interpolation='none',cmap='gray')\n", | |
| " plt.subplot(1,4,4)\n", | |
| " plt.title(\"code\")\n", | |
| " plt.imshow(get_code(X_sample).reshape(1,8),interpolation='none',cmap='gray')\n", | |
| " plt.show()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": "Python 2", | |
| "language": "python", | |
| "name": "python2" | |
| }, | |
| "language_info": { | |
| "codemirror_mode": { | |
| "name": "ipython", | |
| "version": 2 | |
| }, | |
| "file_extension": ".py", | |
| "mimetype": "text/x-python", | |
| "name": "python", | |
| "nbconvert_exporter": "python", | |
| "pygments_lexer": "ipython2", | |
| "version": "2.7.13" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 0 | |
| } |
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