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Weight initialization by normal distribution with various scales.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"def tanh_derivative(x):\n",
" return 1 - np.tanh(x) ** 2\n",
"\n",
"x = np.linspace(-5, 5, 100)\n",
"plt.plot(x, np.tanh(x), label='tanh(x)')\n",
"plt.plot(x, tanh_derivative(x), label='d_tanh(x)/d_x')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0xdef8470>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x11d19a20>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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"text/plain": [
"<matplotlib.figure.Figure at 0x7ef6550>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x119da470>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0xe02b9b0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"N = 1 # number of examples\n",
"D = 2 # number of input's dimensions\n",
"H = 100 # number of hidden's dimensions\n",
"\n",
"w_scale = 1.0\n",
"\n",
"x = np.random.randn(N, D)\n",
"w = w_scale * np.random.randn(D, H)\n",
"\n",
"plt.plot(w[0], w[1], '.')\n",
"plt.title('{} weight vectors in W'.format(H))\n",
"plt.xlabel('w_0')\n",
"plt.ylabel('w_1')\n",
"plt.grid()\n",
"plt.show()\n",
"\n",
"plt.hist(np.linalg.norm(w, axis=0))\n",
"plt.title('histogram of L2 norms of the weight vectors')\n",
"plt.xlabel('L2 norm')\n",
"plt.ylabel('counts')\n",
"plt.show()\n",
"\n",
"a = x.dot(w)\n",
"plt.plot(a.T, '.')\n",
"plt.title('a = x.dot(w)')\n",
"plt.xlabel('j of w_j')\n",
"plt.ylabel('x.dot(w)')\n",
"plt.show()\n",
"\n",
"h = np.tanh(a)\n",
"plt.plot(h.T, '.')\n",
"plt.title('h = tanh(a)')\n",
"plt.xlabel('j of a_j')\n",
"plt.ylabel('tanh(a_j)')\n",
"plt.show()\n",
"\n",
"dh_da = tanh_derivative(a)\n",
"plt.plot(dh_da.T, '.')\n",
"plt.title('dh/da')\n",
"plt.xlabel('j')\n",
"plt.ylabel('dh(a_j)/da')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"num_scales: 11\n",
"w_scales:\n",
"[ 1.00000000e-05 1.00000000e-04 1.00000000e-03 1.00000000e-02\n",
" 1.00000000e-01 1.00000000e+00 1.00000000e+01 1.00000000e+02\n",
" 1.00000000e+03 1.00000000e+04 1.00000000e+05]\n"
]
},
{
"data": {
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kA72TEeOSEfRORoxLRtAz+TAu+UDvtpsRmpxhh/iDPR75QO/kw7hkBL2T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\n/MreZ9NG25qtY6zfzbzcvpLMe/O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"text/plain": [
"<matplotlib.figure.Figure at 0x11832eb8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"w_scales = np.logspace(-5, 5, 11)\n",
"num_scales = len(w_scales)\n",
"print 'num_scales:', num_scales\n",
"print 'w_scales:'\n",
"print w_scales\n",
"\n",
"plt.figure(figsize=(40, 10))\n",
"for i, w_scale in enumerate(w_scales):\n",
" a = x.dot(w_scale * w)\n",
" h = np.tanh(w_scale * a)\n",
" dh_da = tanh_derivative(a)\n",
"\n",
" plt.subplot(2, num_scales, 1 + i)\n",
" plt.plot(h.T, '.')\n",
" plt.title('a = x.dot({} * w)'.format(w_scale))\n",
" plt.xlabel('j')\n",
" plt.ylabel('tanh(a_j)')\n",
"\n",
" plt.subplot(2, num_scales, 1 + i + num_scales)\n",
" plt.plot(dh_da.T, '.')\n",
" plt.xlabel('j')\n",
" plt.ylabel('dh(a_j)/da')\n",
"\n",
"plt.tight_layout()\n",
"plt.show()"
]
}
],
"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": "2.7.11"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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