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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Recurrent Neural Networks"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import tensorflow as tf\n",
"import numpy as np"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Problem Definition**\n",
"\n",
"Prediction one-to-many (eg : given 'a', predict \\[ 'b', 'c', 'd' \\]"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"import string\n",
"vocab = string.ascii_lowercase\n",
"ch2idx = { ch:float(idx) for idx, ch in enumerate(vocab) }"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"samples = []\n",
"for i,ch in enumerate(vocab[:23]):\n",
" samples.append((i, [i+1, i+2, i+3]))"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[(0, [1, 2, 3]),\n",
" (1, [2, 3, 4]),\n",
" (2, [3, 4, 5]),\n",
" (3, [4, 5, 6]),\n",
" (4, [5, 6, 7]),\n",
" (5, [6, 7, 8]),\n",
" (6, [7, 8, 9]),\n",
" (7, [8, 9, 10]),\n",
" (8, [9, 10, 11]),\n",
" (9, [10, 11, 12]),\n",
" (10, [11, 12, 13]),\n",
" (11, [12, 13, 14]),\n",
" (12, [13, 14, 15]),\n",
" (13, [14, 15, 16]),\n",
" (14, [15, 16, 17]),\n",
" (15, [16, 17, 18]),\n",
" (16, [17, 18, 19]),\n",
" (17, [18, 19, 20]),\n",
" (18, [19, 20, 21]),\n",
" (19, [20, 21, 22]),\n",
" (20, [21, 22, 23]),\n",
" (21, [22, 23, 24]),\n",
" (22, [23, 24, 25])]"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"samples"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"def exec_graph(t, sample):\n",
" with tf.Session() as sess:\n",
" sess.run(tf.global_variables_initializer())\n",
" x, y = sample\n",
" return sess.run(t, feed_dict = {\n",
" pl_input : np.array(x).reshape([1,1]),\n",
" pl_output : np.array(y).reshape([1,3])\n",
" })"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [
{
"ename": "ValueError",
"evalue": "Tensor(\"Ws:0\", shape=(1, 3), dtype=float32_ref) must be from the same graph as Tensor(\"input:0\", shape=(1, 1), dtype=float32).",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-52-2ef071435e33>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 14\u001b[0m \u001b[0moutputs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 15\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 16\u001b[0;31m \u001b[0mstate\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmatmul\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minput_\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mWs\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mtf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmatmul\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstate_prev\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mWss\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 17\u001b[0m \u001b[0mstates\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstate\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[0moutput\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmatmul\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstate\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mWo\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m/usr/local/lib/python3.6/dist-packages/tensorflow/python/ops/math_ops.py\u001b[0m in \u001b[0;36mmatmul\u001b[0;34m(a, b, transpose_a, transpose_b, adjoint_a, adjoint_b, a_is_sparse, b_is_sparse, name)\u001b[0m\n\u001b[1;32m 2002\u001b[0m \u001b[0mare\u001b[0m \u001b[0mboth\u001b[0m \u001b[0mset\u001b[0m \u001b[0mto\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2003\u001b[0m \"\"\"\n\u001b[0;32m-> 2004\u001b[0;31m \u001b[0;32mwith\u001b[0m \u001b[0mops\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mname_scope\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"MatMul\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2005\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mtranspose_a\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0madjoint_a\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2006\u001b[0m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Only one of transpose_a and adjoint_a can be True.\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m/usr/local/lib/python3.6/dist-packages/tensorflow/python/framework/ops.py\u001b[0m in \u001b[0;36m__enter__\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m 5614\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_values\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5615\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_values\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 5616\u001b[0;31m \u001b[0mg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_get_graph_from_inputs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_values\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 5617\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_g_manager\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mas_default\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5618\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_g_manager\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__enter__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m/usr/local/lib/python3.6/dist-packages/tensorflow/python/framework/ops.py\u001b[0m in \u001b[0;36m_get_graph_from_inputs\u001b[0;34m(op_input_list, graph)\u001b[0m\n\u001b[1;32m 5282\u001b[0m \u001b[0mgraph\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgraph_element\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgraph\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5283\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0moriginal_graph_element\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 5284\u001b[0;31m \u001b[0m_assert_same_graph\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0moriginal_graph_element\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgraph_element\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 5285\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0mgraph_element\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgraph\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mgraph\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5286\u001b[0m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"%s is not from the passed-in graph.\"\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mgraph_element\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m/usr/local/lib/python3.6/dist-packages/tensorflow/python/framework/ops.py\u001b[0m in \u001b[0;36m_assert_same_graph\u001b[0;34m(original_item, item)\u001b[0m\n\u001b[1;32m 5218\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0moriginal_item\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgraph\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mitem\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgraph\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5219\u001b[0m raise ValueError(\"%s must be from the same graph as %s.\" % (item,\n\u001b[0;32m-> 5220\u001b[0;31m original_item))\n\u001b[0m\u001b[1;32m 5221\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5222\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mValueError\u001b[0m: Tensor(\"Ws:0\", shape=(1, 3), dtype=float32_ref) must be from the same graph as Tensor(\"input:0\", shape=(1, 1), dtype=float32)."
]
}
],
"source": [
"tf.reset_default_graph()\n",
"pl_input = tf.placeholder(tf.float32, [1, 1], 'input')\n",
"pl_output= tf.placeholder(tf.int32, [1, 3], 'output')\n",
"\n",
"Ws = tf.get_variable('Ws', [1, 3], tf.float32, \n",
" initializer=tf.random_uniform_initializer(-0.01, 0.01))\n",
"Wo = tf.get_variable('Wo', [3, 26], tf.float32, \n",
" initializer=tf.random_uniform_initializer(-0.01, 0.01))\n",
"Wss = tf.get_variable('Wss', [3, 3], tf.float32, \n",
" initializer=tf.random_uniform_initializer(-0.01, 0.01))\n",
"Woi = tf.get_variable('Woi', [26, 1], tf.float32,\n",
" initializer=tf.random_uniform_initializer(-0.01, 0.01))\n",
"\n",
"# initialization\n",
"state_prev = tf.zeros([1, 3], tf.float32, 'init_state')\n",
"input_ = pl_input\n",
"states = []\n",
"outputs = []\n",
"for i in range(3):\n",
" state = tf.matmul(input_, Ws) + tf.matmul(state_prev, Wss)\n",
" states.append(state)\n",
" output = tf.matmul(state, Wo)\n",
" outputs.append(output)\n",
" state_prev = state\n",
" input_ = tf.matmul(output, Woi)\n",
"\n",
"ce = tf.nn.sparse_softmax_cross_entropy_with_logits(\n",
" labels=pl_output,logits=tf.transpose(tf.stack(outputs), [1, 0, 2]))\n",
"loss = tf.reduce_mean(ce)\n",
"train_op = tf.train.AdamOptimizer().minimize(loss)"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0 (0, [1, 2, 3]) 3.2580965\n",
"0 (1, [2, 3, 4]) 3.258111\n",
"0 (2, [3, 4, 5]) 3.2580929\n",
"0 (3, [4, 5, 6]) 3.2580774\n",
"0 (4, [5, 6, 7]) 3.2580564\n",
"0 (5, [6, 7, 8]) 3.2579482\n",
"0 (6, [7, 8, 9]) 3.2581627\n",
"0 (7, [8, 9, 10]) 3.2581465\n",
"0 (8, [9, 10, 11]) 3.2580984\n",
"0 (9, [10, 11, 12]) 3.2579381\n",
"0 (10, [11, 12, 13]) 3.2585194\n",
"0 (11, [12, 13, 14]) 3.2580853\n",
"0 (12, [13, 14, 15]) 3.2584038\n",
"0 (13, [14, 15, 16]) 3.2586508\n",
"0 (14, [15, 16, 17]) 3.2586567\n",
"0 (15, [16, 17, 18]) 3.2583144\n",
"0 (16, [17, 18, 19]) 3.2585688\n",
"0 (17, [18, 19, 20]) 3.2580273\n",
"0 (18, [19, 20, 21]) 3.2583797\n",
"0 (19, [20, 21, 22]) 3.2581885\n",
"0 (20, [21, 22, 23]) 3.2585828\n",
"0 (21, [22, 23, 24]) 3.2585409\n",
"0 (22, [23, 24, 25]) 3.2582524\n",
"1 (0, [1, 2, 3]) 3.2580965\n",
"1 (1, [2, 3, 4]) 3.2580988\n",
"1 (2, [3, 4, 5]) 3.2581155\n",
"1 (3, [4, 5, 6]) 3.2581747\n",
"1 (4, [5, 6, 7]) 3.2582586\n",
"1 (5, [6, 7, 8]) 3.258406\n",
"1 (6, [7, 8, 9]) 3.2582371\n",
"1 (7, [8, 9, 10]) 3.2582982\n",
"1 (8, [9, 10, 11]) 3.258373\n",
"1 (9, [10, 11, 12]) 3.2585309\n",
"1 (10, [11, 12, 13]) 3.2583187\n",
"1 (11, [12, 13, 14]) 3.258422\n",
"1 (12, [13, 14, 15]) 3.258096\n",
"1 (13, [14, 15, 16]) 3.2582655\n",
"1 (14, [15, 16, 17]) 3.2583578\n",
"1 (15, [16, 17, 18]) 3.258386\n",
"1 (16, [17, 18, 19]) 3.2580726\n",
"1 (17, [18, 19, 20]) 3.2583215\n",
"1 (18, [19, 20, 21]) 3.2579937\n",
"1 (19, [20, 21, 22]) 3.258417\n",
"1 (20, [21, 22, 23]) 3.2573977\n",
"1 (21, [22, 23, 24]) 3.257549\n",
"1 (22, [23, 24, 25]) 3.2575037\n",
"2 (0, [1, 2, 3]) 3.2580965\n",
"2 (1, [2, 3, 4]) 3.2581196\n",
"2 (2, [3, 4, 5]) 3.258159\n",
"2 (3, [4, 5, 6]) 3.258215\n",
"2 (4, [5, 6, 7]) 3.2582772\n",
"2 (5, [6, 7, 8]) 3.2583935\n",
"2 (6, [7, 8, 9]) 3.2581174\n",
"2 (7, [8, 9, 10]) 3.2581809\n",
"2 (8, [9, 10, 11]) 3.2581618\n",
"2 (9, [10, 11, 12]) 3.258255\n",
"2 (10, [11, 12, 13]) 3.2581127\n",
"2 (11, [12, 13, 14]) 3.2580853\n",
"2 (12, [13, 14, 15]) 3.257639\n",
"2 (13, [14, 15, 16]) 3.257973\n",
"2 (14, [15, 16, 17]) 3.2581367\n",
"2 (15, [16, 17, 18]) 3.2579887\n",
"2 (16, [17, 18, 19]) 3.2576053\n",
"2 (17, [18, 19, 20]) 3.2576132\n",
"2 (18, [19, 20, 21]) 3.2573054\n",
"2 (19, [20, 21, 22]) 3.2579014\n",
"2 (20, [21, 22, 23]) 3.2561443\n",
"2 (21, [22, 23, 24]) 3.256376\n",
"2 (22, [23, 24, 25]) 3.2558613\n",
"3 (0, [1, 2, 3]) 3.2580965\n",
"3 (1, [2, 3, 4]) 3.2582734\n",
"3 (2, [3, 4, 5]) 3.258382\n",
"3 (3, [4, 5, 6]) 3.2585099\n",
"3 (4, [5, 6, 7]) 3.2585986\n",
"3 (5, [6, 7, 8]) 3.2587059\n",
"3 (6, [7, 8, 9]) 3.2579615\n",
"3 (7, [8, 9, 10]) 3.257974\n",
"3 (8, [9, 10, 11]) 3.2578022\n",
"3 (9, [10, 11, 12]) 3.2578633\n",
"3 (10, [11, 12, 13]) 3.2576876\n",
"3 (11, [12, 13, 14]) 3.2571929\n",
"3 (12, [13, 14, 15]) 3.2559726\n",
"3 (13, [14, 15, 16]) 3.2568653\n",
"3 (14, [15, 16, 17]) 3.257101\n",
"3 (15, [16, 17, 18]) 3.2564132\n",
"3 (16, [17, 18, 19]) 3.2551749\n",
"3 (17, [18, 19, 20]) 3.2548141\n",
"3 (18, [19, 20, 21]) 3.253765\n",
"3 (19, [20, 21, 22]) 3.254851\n",
"3 (20, [21, 22, 23]) 3.2494547\n",
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]
},
{
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]
},
{
"name": "stdout",
"output_type": "stream",
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]
},
{
"name": "stdout",
"output_type": "stream",
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{
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{
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]
},
{
"name": "stdout",
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]
},
{
"name": "stdout",
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]
},
{
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]
},
{
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]
},
{
"name": "stdout",
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},
{
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]
},
{
"name": "stdout",
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]
},
{
"name": "stdout",
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]
},
{
"name": "stdout",
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]
},
{
"name": "stdout",
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{
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]
},
{
"name": "stdout",
"output_type": "stream",
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]
},
{
"name": "stdout",
"output_type": "stream",
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]
},
{
"name": "stdout",
"output_type": "stream",
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]
},
{
"name": "stdout",
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]
},
{
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"428 (6, [7, 8, 9]) 3.329995\n",
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"429 (9, [10, 11, 12]) 3.2026908\n",
"429 (10, [11, 12, 13]) 3.1508791\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
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]
},
{
"name": "stdout",
"output_type": "stream",
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]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
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"478 (18, [19, 20, 21]) 2.601269\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
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]
},
{
"name": "stdout",
"output_type": "stream",
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]
},
{
"name": "stdout",
"output_type": "stream",
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]
},
{
"name": "stdout",
"output_type": "stream",
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]
},
{
"name": "stdout",
"output_type": "stream",
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},
{
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},
{
"name": "stdout",
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]
},
{
"name": "stdout",
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"648 (6, [7, 8, 9]) 3.3255312\n",
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]
},
{
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"668 (12, [13, 14, 15]) 3.0345066\n",
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]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
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]
},
{
"name": "stdout",
"output_type": "stream",
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"703 (12, [13, 14, 15]) 3.034198\n",
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"704 (11, [12, 13, 14]) 3.092199\n",
"704 (12, [13, 14, 15]) 3.03419\n"
]
},
{
"name": "stdout",
"output_type": "stream",
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]
},
{
"name": "stdout",
"output_type": "stream",
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"730 (8, [9, 10, 11]) 3.2450504\n",
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]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
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]
},
{
"name": "stdout",
"output_type": "stream",
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]
},
{
"name": "stdout",
"output_type": "stream",
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"843 (14, [15, 16, 17]) 2.8999817\n",
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"846 (21, [22, 23, 24]) 2.2228498\n",
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"847 (20, [21, 22, 23]) 2.4279363\n",
"847 (21, [22, 23, 24]) 2.2230442\n",
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]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"848 (5, [6, 7, 8]) 3.35433\n",
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]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"869 (19, [20, 21, 22]) 2.5149097\n",
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]
},
{
"name": "stdout",
"output_type": "stream",
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]
},
{
"name": "stdout",
"output_type": "stream",
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"933 (12, [13, 14, 15]) 3.0326235\n",
"933 (13, [14, 15, 16]) 2.9688761\n",
"933 (14, [15, 16, 17]) 2.8982637\n",
"933 (15, [16, 17, 18]) 2.833741\n",
"933 (16, [17, 18, 19]) 2.7509964\n",
"933 (17, [18, 19, 20]) 2.6818762\n",
"933 (18, [19, 20, 21]) 2.5984156\n",
"933 (19, [20, 21, 22]) 2.513861\n",
"933 (20, [21, 22, 23]) 2.4261334\n",
"933 (21, [22, 23, 24]) 2.2445018\n",
"933 (22, [23, 24, 25]) 2.4682772\n",
"934 (0, [1, 2, 3]) 3.2580965\n",
"934 (1, [2, 3, 4]) 3.3890913\n",
"934 (2, [3, 4, 5]) 3.3886251\n",
"934 (3, [4, 5, 6]) 3.3868876\n",
"934 (4, [5, 6, 7]) 3.3740642\n",
"934 (5, [6, 7, 8]) 3.35368\n",
"934 (6, [7, 8, 9]) 3.3224087\n",
"934 (7, [8, 9, 10]) 3.2873242\n",
"934 (8, [9, 10, 11]) 3.2424905\n",
"934 (9, [10, 11, 12]) 3.2015269\n",
"934 (10, [11, 12, 13]) 3.1435392\n",
"934 (11, [12, 13, 14]) 3.0896766\n",
"934 (12, [13, 14, 15]) 3.032616\n",
"934 (13, [14, 15, 16]) 2.968867\n",
"934 (14, [15, 16, 17]) 2.8982441\n",
"934 (15, [16, 17, 18]) 2.8337421\n",
"934 (16, [17, 18, 19]) 2.7509718\n",
"934 (17, [18, 19, 20]) 2.6818745\n
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