{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# ICNN Dual Solver "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this tutorial, we explore how to learn the solution of the Kantorovich dual based on parameterizing the two dual potentials $f$ and $g$ with two input convex neural networks ({class}`~ott.solvers.nn.icnn.ICNN`) {cite}`amos:17`, a method developed by {cite}`makkuva:20`. For more insights on the approach itself, we refer the user to the original publication.\n",
"\n",
"Given dataloaders containing samples of the *source* and the *target* distribution, `OTT`'s {class}`~ott.solvers.nn.neuraldual.NeuralDualSolver` finds the pair of optimal potentials $f$ and $g$ to solve the corresponding dual of the optimal transport problem. Once a solution has been found, these neural {class}`~ott.problems.linear.potentials.DualPotentials` can be used to transport unseen source data samples to its target distribution (or vice-versa) or compute the corresponding distance between new source and target distribution."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import sys\n",
"\n",
"if \"google.colab\" in sys.modules:\n",
" !pip install -q git+https://github.com/ott-jax/ott@main"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import jax\n",
"import jax.numpy as jnp\n",
"import numpy as np\n",
"import optax\n",
"from torch.utils.data import DataLoader, IterableDataset\n",
"\n",
"import matplotlib.pyplot as plt\n",
"\n",
"from ott.geometry import pointcloud\n",
"from ott.solvers.nn import icnn, neuraldual\n",
"from ott.tools import sinkhorn_divergence"
]
},
{
"cell_type": "markdown",
"metadata": {
"tags": []
},
"source": [
"## Helper Functions"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us define some helper functions which we use for the subsequent analysis."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def plot_ot_map(neural_dual, source, target, inverse=False):\n",
" \"\"\"Plot data and learned optimal transport map.\"\"\"\n",
"\n",
" def draw_arrows(a, b):\n",
" plt.arrow(\n",
" a[0], a[1], b[0] - a[0], b[1] - a[1], color=[0.5, 0.5, 1], alpha=0.3\n",
" )\n",
"\n",
" grad_state_s = neural_dual.transport(source, forward=not inverse)\n",
"\n",
" fig = plt.figure()\n",
" ax = fig.add_subplot(111)\n",
"\n",
" if not inverse:\n",
" ax.scatter(\n",
" target[:, 0],\n",
" target[:, 1],\n",
" color=\"#A7BED3\",\n",
" alpha=0.5,\n",
" label=r\"$target$\",\n",
" )\n",
" ax.scatter(\n",
" source[:, 0],\n",
" source[:, 1],\n",
" color=\"#1A254B\",\n",
" alpha=0.5,\n",
" label=r\"$source$\",\n",
" )\n",
" ax.scatter(\n",
" grad_state_s[:, 0],\n",
" grad_state_s[:, 1],\n",
" color=\"#F2545B\",\n",
" alpha=0.5,\n",
" label=r\"$\\nabla g(source)$\",\n",
" )\n",
" else:\n",
" ax.scatter(\n",
" target[:, 0],\n",
" target[:, 1],\n",
" color=\"#A7BED3\",\n",
" alpha=0.5,\n",
" label=r\"$source$\",\n",
" )\n",
" ax.scatter(\n",
" source[:, 0],\n",
" source[:, 1],\n",
" color=\"#1A254B\",\n",
" alpha=0.5,\n",
" label=r\"$target$\",\n",
" )\n",
" ax.scatter(\n",
" grad_state_s[:, 0],\n",
" grad_state_s[:, 1],\n",
" color=\"#F2545B\",\n",
" alpha=0.5,\n",
" label=r\"$\\nabla f(target)$\",\n",
" )\n",
"\n",
" plt.legend()\n",
"\n",
" for i in range(source.shape[0]):\n",
" draw_arrows(source[i, :], grad_state_s[i, :])"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def get_optimizer(optimizer, lr, b1, b2, eps):\n",
" \"\"\"Returns a flax optimizer object based on `config`.\"\"\"\n",
"\n",
" if optimizer == \"Adam\":\n",
" optimizer = optax.adam(learning_rate=lr, b1=b1, b2=b2, eps=eps)\n",
" elif optimizer == \"SGD\":\n",
" optimizer = optax.sgd(learning_rate=lr, momentum=None, nesterov=False)\n",
" else:\n",
" raise NotImplementedError(f\"Optimizer {optimizer} not supported yet!\")\n",
"\n",
" return optimizer"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"@jax.jit\n",
"def sinkhorn_loss(x, y, epsilon=0.1):\n",
" \"\"\"Computes transport between (x, a) and (y, b) via Sinkhorn algorithm.\"\"\"\n",
" a = jnp.ones(len(x)) / len(x)\n",
" b = jnp.ones(len(y)) / len(y)\n",
"\n",
" sdiv = sinkhorn_divergence.sinkhorn_divergence(\n",
" pointcloud.PointCloud, x, y, epsilon=epsilon, a=a, b=b\n",
" )\n",
" return sdiv.divergence"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Setup Training and Validation Datasets"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We apply the {class}`~ott.solvers.nn.neuraldual.NeuralDualSolver` to compute the transport between toy datasets. In this tutorial, the user can choose between the datasets `simple` (data clustered in one center), `circle` (two-dimensional Gaussians arranged on a circle), `square_five` (two-dimensional Gaussians on a square with one Gaussian in the center), and `square_four` (two-dimensional Gaussians in the corners of a rectangle)."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"class ToyDataset(IterableDataset):\n",
" def __init__(self, name):\n",
" self.name = name\n",
"\n",
" def __iter__(self):\n",
" return self.create_sample_generators()\n",
"\n",
" def create_sample_generators(self, scale=5.0, variance=0.5):\n",
" # given name of dataset, select centers\n",
" if self.name == \"simple\":\n",
" centers = np.array([0, 0])\n",
"\n",
" elif self.name == \"circle\":\n",
" centers = np.array(\n",
" [\n",
" (1, 0),\n",
" (-1, 0),\n",
" (0, 1),\n",
" (0, -1),\n",
" (1.0 / np.sqrt(2), 1.0 / np.sqrt(2)),\n",
" (1.0 / np.sqrt(2), -1.0 / np.sqrt(2)),\n",
" (-1.0 / np.sqrt(2), 1.0 / np.sqrt(2)),\n",
" (-1.0 / np.sqrt(2), -1.0 / np.sqrt(2)),\n",
" ]\n",
" )\n",
"\n",
" elif self.name == \"square_five\":\n",
" centers = np.array([[0, 0], [1, 1], [-1, 1], [-1, -1], [1, -1]])\n",
"\n",
" elif self.name == \"square_four\":\n",
" centers = np.array([[1, 0], [0, 1], [-1, 0], [0, -1]])\n",
"\n",
" else:\n",
" raise NotImplementedError()\n",
"\n",
" # create generator which randomly picks center and adds noise\n",
" centers = scale * centers\n",
" while True:\n",
" center = centers[np.random.choice(len(centers))]\n",
" point = center + variance**2 * np.random.randn(2)\n",
"\n",
" yield point\n",
"\n",
"\n",
"def load_toy_data(\n",
" name_source: str,\n",
" name_target: str,\n",
" batch_size: int = 1024,\n",
" valid_batch_size: int = 1024,\n",
"):\n",
" dataloaders = (\n",
" iter(DataLoader(ToyDataset(name_source), batch_size=batch_size)),\n",
" iter(DataLoader(ToyDataset(name_target), batch_size=batch_size)),\n",
" iter(DataLoader(ToyDataset(name_source), batch_size=valid_batch_size)),\n",
" iter(DataLoader(ToyDataset(name_target), batch_size=valid_batch_size)),\n",
" )\n",
" input_dim = 2\n",
" return dataloaders, input_dim"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Solve Neural Dual"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In order to solve the neural dual, we need to define our dataloaders. The only requirement is that the corresponding source and target train and validation datasets are *iterators*."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"(dataloader_source, dataloader_target, _, _), input_dim = load_toy_data(\n",
" \"square_five\", \"square_four\"\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, we define the architectures parameterizing the dual potentials $f$ and $g$. These need to be parameterized by {class}`~ott.solvers.nn.icnn.ICNN`s. You can adapt the size of the ICNNs by passing a sequence containing hidden layer sizes. While ICNNs are by default containing partially positive weights, we can run the {class}`~ott.solvers.nn.neuraldual.NeuralDualSolver` using approximations to this positivity constraint (via weight clipping and a weight penalization). For this, set `positive_weights` to `True` in both the ICNN architecture and {class}`~ott.solvers.nn.neuraldual.NeuralDualSolver` configuration. For more details on how to customize the {class}`~ott.solvers.nn.icnn.ICNN` architectures, we refer you to the documentation."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"# initialize models\n",
"neural_f = icnn.ICNN(dim_hidden=[64, 64, 64, 64], dim_data=2)\n",
"neural_g = icnn.ICNN(dim_hidden=[64, 64, 64, 64], dim_data=2)\n",
"\n",
"# initialize optimizers\n",
"optimizer_f = get_optimizer(\"Adam\", lr=0.001, b1=0.5, b2=0.9, eps=1e-8)\n",
"optimizer_g = get_optimizer(\"Adam\", lr=0.001, b1=0.5, b2=0.9, eps=1e-8)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We then initialize the {class}`~ott.solvers.nn.neuraldual.NeuralDualSolver` by passing the two {class}`~ott.solvers.nn.icnn.ICNN` models parameterizing $f$ and $g$, as well as by specifying the input dimensions of the data and the number of training iterations to execute. Once the {class}`~ott.solvers.nn.neuraldual.NeuralDualSolver` is initialized, we can obtain the neural {class}`~ott.problems.linear.potentials.DualPotentials` by passing the corresponding dataloaders to it. As here our training and validation datasets do not differ, we pass (`dataloader_source`, `dataloader_target`) for both training and validation steps. For more details on how to configure the {class}`~ott.solvers.nn.neuraldual.NeuralDualSolver`, we refer you to the documentation."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Execution of the following cell might take up to 15 minutes per 5000 iterations (depending on your system and the number of training iterations."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "31b3dff5bd2840b0b358f91fdb2b117b",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
" 0%| | 0/15000 [00:00"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plot_ot_map(neural_dual, data_source, data_target, inverse=False)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plot_ot_map(neural_dual, data_target, data_source, inverse=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We further test, how close the predicted samples are to the sampled data."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First for potential $g$, transporting source to target samples. Ideally the resulting {class}`~ott.solvers.linear.sinkhorn.Sinkhorn` distance is close to $0$."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Sinkhorn distance between predictions and data samples: 1.4665195941925049\n"
]
}
],
"source": [
"pred_target = neural_dual.transport(data_source)\n",
"print(\n",
" f\"Sinkhorn distance between predictions and data samples: {sinkhorn_loss(pred_target, data_target)}\"\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Then for potential $f$, transporting target to source samples. Again, the resulting {class}`~ott.solvers.linear.sinkhorn.Sinkhorn` distance needs to be close to $0$."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Sinkhorn distance between predictions and data samples: 6.814591884613037\n"
]
}
],
"source": [
"pred_source = neural_dual.transport(data_target, forward=False)\n",
"print(\n",
" f\"Sinkhorn distance between predictions and data samples: {sinkhorn_loss(pred_source, data_source)}\"\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Besides computing the transport and mapping source to target samples or vice versa, we can also compute the overall distance between new source and target samples."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Neural dual distance between source and target data: 21.16440200805664\n"
]
}
],
"source": [
"neural_dual_dist = neural_dual.distance(data_source, data_target)\n",
"print(\n",
" f\"Neural dual distance between source and target data: {neural_dual_dist}\"\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Which compares to the primal {class}`~ott.solvers.linear.sinkhorn.Sinkhorn` distance in the following."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Sinkhorn distance between source and target data: 21.226734161376953\n"
]
}
],
"source": [
"sinkhorn_dist = sinkhorn_loss(data_source, data_target)\n",
"print(f\"Sinkhorn distance between source and target data: {sinkhorn_dist}\")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
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