{
"cells": [
{
"cell_type": "markdown",
"source": [
"Building on [PonderNet](https://arxiv.org/abs/2107.05407), this notebook implements a neural alternative of the [Variable Rate Coding](https://doi.org/10.32470/CCN.2019.1397-0) model to produce human-like responses.\n",
"\n",
"Given stimulus symbols as inputs, the model produces two outputs:\n",
"\n",
"- Response symbol, which, in comparison with the input stimuli, can be used to measure accuracy).\n",
"- Remaining entropy (to be contrasted against a decision threshold and ultimateely halt the process).\n",
"\n",
"Under the hood, the model uses a RNN along with multiple Poisson processes to...\n",
"\n",
"\n",
"## Resources\n",
"\n",
"- [Network model](https://drive.google.com/file/d/16eiUUwKGWfh9pu9VUxzlx046hQNHV0Qe/view?usp=sharinghttps://drive.google.com/file/d/16eiUUwKGWfh9pu9VUxzlx046hQNHV0Qe/view?usp=sharing)\n"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## Problem setting\n",
"\n",
"### Model\n",
"Given input and output data, we want to learn a supervised model of the function $X \\to y$ as follows:\n",
"\n",
"$\n",
"f: X,h_n \\mapsto \\tilde{y},h_{n+1}, \\lambda_n\n",
"$\n",
"\n",
"where $X$ and $y$ denote stimulus and response symbols, $\\lambda_n$ denotes halting probability at time $n$, and $h_{n}$ is the latent state of the model. The learninig continious up to the time point $N$.\n",
"\n",
"For the brevity and compatibility, both data are one-hot encoded.\n",
"\n",
"\n",
"### Input\n",
"\n",
"One-hot encoded symbols.\n",
"\n",
"### Output\n",
"\n",
"One-hot encoded symbols.\n",
"\n",
"### Criterion\n",
"\n",
"L = L_cross_entropy + L_halting"
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 114,
"source": [
"# Setup and imports\n",
"import torch\n",
"from torch import nn\n",
"import torch.nn.functional as F\n",
"from torch.utils.tensorboard import SummaryWriter\n",
"\n",
"from tqdm import tqdm\n",
"\n",
"from sklearn.metrics import accuracy_score\n",
"\n",
"import numpy as np\n",
"from scipy import stats\n",
"import pandas as pd\n",
"\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns; sns.set()\n",
"\n",
"import tensorflow as tf\n",
"import tensorboard as tb\n",
"tf.io.gfile = tb.compat.tensorflow_stub.io.gfile #FIX storing embeddings using tensorboard"
],
"outputs": [],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 2,
"source": [
"# produce a tarin of spikes and store timestamps of each spike in `spike_timestamps`.\n",
"\n",
"signal_rate = 2\n",
"noise_rate = 1\n",
"rate = signal_rate + noise_rate\n",
"max_duration_in_sec = 10.\n",
"resolution_in_sec = .1\n",
"\n",
"n_total_timesteps = int(max_duration_in_sec / resolution_in_sec)\n",
"n_spikes = np.random.poisson(rate * max_duration_in_sec)\n",
"\n",
"# method 1: shuffle timesteps\n",
"spike_timesteps = np.sort(np.random.choice(n_total_timesteps, size=n_spikes, replace=False))\n",
"\n",
"# method 2: exponential isi -> timestamps\n",
"# isi = np.random.exponential(1 / rate, n_spikes)\n",
"# spike_timestamps = np.cumsum(isi)\n",
"\n",
"# method 3: homogenous spikes -> timestamps\n",
"# spike_timestamps = stats.uniform.rvs(loc=0, scale=max_duration_in_sec, size=n_spikes)"
],
"outputs": [],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## Mock data"
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 3,
"source": [
"\n",
"\n",
"def generate_mock_data(n_subjects, n_trials, n_stimuli):\n",
" \"\"\"[summary]\n",
"\n",
" # TODO required data columns: subject_index, trial_index, stimulus_index, accuracy, response_time\n",
"\n",
" Args:\n",
" n_subjects (int): [description]\n",
" n_trials (int): [description]\n",
" n_stimuli (int): [description]\n",
"\n",
" Returns:\n",
" (X, accuracies, response_times): A tuple containing generated mock X, accuracies, and response_times (in sec).\n",
" \"\"\"\n",
" # stimuli\n",
" X = np.random.randint(low=1, high=n_stimuli+1, size=(n_subjects, n_trials))\n",
"\n",
" # response accuracy\n",
" subject_accuracies = np.random.uniform(low=0.2, high=1.0, size=n_subjects)\n",
" subject_accuracies = np.round(subject_accuracies * n_trials) / n_trials\n",
" accuracies = np.empty(shape=(n_subjects, n_trials))\n",
" for subj in range(n_subjects):\n",
" accuracies[subj,:] = np.random.choice(\n",
" [0,1],\n",
" p=[1-subject_accuracies[subj],subject_accuracies[subj]],\n",
" size=n_trials)\n",
"\n",
" # generate output w.r.t the accuracy (and fill incorrect trials with invalid response)\n",
" y = np.where(accuracies == 1., X, X+1 % (n_stimuli+1))\n",
"\n",
" # response time\n",
" response_times = np.random.exponential(.5, size=accuracies.shape)\n",
"\n",
" return X, y, accuracies, response_times"
],
"outputs": [],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 4,
"source": [
"# mock data parameters\n",
"n_subjects = 1\n",
"n_trials = 20\n",
"n_stimuli = 6\n",
"\n",
"X, y, accuracies, response_times = generate_mock_data(n_subjects, n_trials, n_stimuli)"
],
"outputs": [],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 117,
"source": [
"class PonderRNN(nn.Module):\n",
" def __init__(self, n_inputs, n_channels, n_outputs, halting_prob_prior=0.0):\n",
" super(PonderRNN, self).__init__()\n",
" self.encode = nn.Sequential( # encode: x -> sent_msg\n",
" nn.Linear(n_inputs, n_channels, bias=False),\n",
" )\n",
" self.transmit = nn.Sequential( # transmit: sent_msg -> rcvd_msg\n",
" nn.RNN(n_channels, n_channels),\n",
" )\n",
" self.decode = nn.Sequential( # decode: rcvd_msg -> action\n",
" nn.Linear(n_channels,n_outputs, bias=False),\n",
" nn.Softmax(dim=2)\n",
" )\n",
"\n",
" # \\lambda_p\n",
" self.halting_prob_prior = halting_prob_prior\n",
"\n",
" def forward(self, x):\n",
" # x: one stimulus category, output: y[1..N] + halting_prob[1..N]\n",
" # step 1: x -> x_n (repeat)\n",
" # step 2: x_n -> y_n\n",
"\n",
" # VRC\n",
" msg = F.one_hot(x).type(torch.float)\n",
" msg = self.encode(msg)\n",
" msg, _ = self.transmit(msg)\n",
" msg = self.decode(msg)\n",
" y = msg.squeeze()\n",
"\n",
" # TODO\n",
" halting_prob = 0.\n",
" # lambda_n = ...\n",
" # halting_prob = torch.distributions.Geometric(self.halting_prob_prior)\n",
" # self.halting_dist = torch.distributions.Geometric(prob)\n",
" # self.halting_probs = torch.cat(halting_prob, halting_prob)\n",
"\n",
" return y, halting_prob\n",
"\n",
"\n",
"n_epoches = 1500\n",
"\n",
"logs = SummaryWriter()\n",
"\n",
"model = PonderRNN(n_stimuli+1, n_stimuli, n_stimuli+1)\n",
"optimizer = torch.optim.Adam(model.parameters(), lr=0.001)\n",
"criterion = torch.nn.CrossEntropyLoss()\n",
"\n",
"X_train = torch.tensor(X)\n",
"y_train = torch.tensor(y) - 1\n",
"\n",
"for epoch in tqdm(range(n_epoches), desc='Epochs'):\n",
" model.train()\n",
" optimizer.zero_grad()\n",
" y_pred, _ = model(X_train)\n",
"\n",
" # logs.add_embedding(h.reshape(n_trials,n_stimuli), global_step=epoch, tag='embedding')\n",
"\n",
" model_accuracy = accuracy_score(y_train.squeeze(), torch.argmax(y_pred.detach(),dim=1))\n",
" logs.add_scalar('accurracy/train', model_accuracy, epoch) \n",
"\n",
" loss = criterion(y_pred, y_train.squeeze())\n",
"\n",
" logs.add_scalar('loss/train', loss, epoch)\n",
" loss.backward()\n",
" optimizer.step()\n",
"\n",
"# tensorboard --logdir=runs"
],
"outputs": [
{
"output_type": "stream",
"name": "stderr",
"text": [
"Epochs: 100%|██████████| 1500/1500 [00:02<00:00, 659.68it/s]\n"
]
}
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 137,
"source": [
"model.eval()\n",
"y_pred, _ = model(X_train)\n",
"y_pred = np.argmax(y_pred.detach().numpy(), axis=1) + 1\n",
"y_pred, y"
],
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"(array([2, 6, 5, 2, 6, 4, 4, 7, 3, 7, 5, 3, 4, 3, 3, 6, 3, 5, 7, 2]),\n",
" array([[2, 6, 5, 1, 6, 4, 4, 6, 3, 7, 5, 3, 4, 3, 3, 6, 3, 5, 7, 2]]))"
]
},
"metadata": {},
"execution_count": 137
}
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 107,
"source": [
"torch.distributions.Geometric(.01).sample()"
],
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"tensor(56.)"
]
},
"metadata": {},
"execution_count": 107
}
],
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