\n",
"

\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import torch\n",
"import torch.nn as nn\n",
"import torch.nn.functional as F\n",
"torch.manual_seed(0)\n",
"\n",
"# Here's a simple CNN and loss function:\n",
"\n",
"class SimpleCNN(nn.Module):\n",
" def __init__(self):\n",
" super(SimpleCNN, self).__init__()\n",
" self.conv1 = nn.Conv2d(1, 32, 3, 1)\n",
" self.conv2 = nn.Conv2d(32, 64, 3, 1)\n",
" self.fc1 = nn.Linear(9216, 128)\n",
" self.fc2 = nn.Linear(128, 10)\n",
"\n",
" def forward(self, x):\n",
" x = self.conv1(x)\n",
" x = F.relu(x)\n",
" x = self.conv2(x)\n",
" x = F.relu(x)\n",
" x = F.max_pool2d(x, 2)\n",
" x = torch.flatten(x, 1)\n",
" x = self.fc1(x)\n",
" x = F.relu(x)\n",
" x = self.fc2(x)\n",
" output = F.log_softmax(x, dim=1)\n",
" return output\n",
"\n",
"def loss_fn(predictions, targets):\n",
" return F.nll_loss(predictions, targets)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's generate a batch of dummy data and pretend that we're working with\n",
"an MNIST dataset. The dummy images are 28 by 28 and we use a minibatch\n",
"of size 64.\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"device = 'cuda'\n",
"\n",
"num_models = 10\n",
"batch_size = 64\n",
"data = torch.randn(batch_size, 1, 28, 28, device=device)\n",
"\n",
"targets = torch.randint(10, (64,), device=device)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In regular model training, one would forward the minibatch through the\n",
"model, and then call .backward() to compute gradients. This would\n",
"generate an \\'average\\' gradient of the entire mini-batch:\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"model = SimpleCNN().to(device=device)\n",
"predictions = model(data) # move the entire mini-batch through the model\n",
"\n",
"loss = loss_fn(predictions, targets)\n",
"loss.backward() # back propagate the 'average' gradient of this mini-batch"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In contrast to the above approach, per-sample-gradient computation is\n",
"equivalent to:\n",
"\n",
"- for each individual sample of the data, perform a forward and a\n",
" backward pass to get an individual (per-sample) gradient.\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def compute_grad(sample, target):\n",
" sample = sample.unsqueeze(0) # prepend batch dimension for processing\n",
" target = target.unsqueeze(0)\n",
"\n",
" prediction = model(sample)\n",
" loss = loss_fn(prediction, target)\n",
"\n",
" return torch.autograd.grad(loss, list(model.parameters()))\n",
"\n",
"\n",
"def compute_sample_grads(data, targets):\n",
" \"\"\" manually process each sample with per sample gradient \"\"\"\n",
" sample_grads = [compute_grad(data[i], targets[i]) for i in range(batch_size)]\n",
" sample_grads = zip(*sample_grads)\n",
" sample_grads = [torch.stack(shards) for shards in sample_grads]\n",
" return sample_grads\n",
"\n",
"per_sample_grads = compute_sample_grads(data, targets)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`sample_grads[0]` is the per-sample-grad for model.conv1.weight.\n",
"`model.conv1.weight.shape` is `[32, 1, 3, 3]`; notice how there is one\n",
"gradient, per sample, in the batch for a total of 64.\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"print(per_sample_grads[0].shape)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Per-sample-grads, *the efficient way*, using function transforms\n",
"================================================================\n",
"\n",
"We can compute per-sample-gradients efficiently by using function\n",
"transforms.\n",
"\n",
"The `torch.func` function transform API transforms over functions. Our\n",
"strategy is to define a function that computes the loss and then apply\n",
"transforms to construct a function that computes per-sample-gradients.\n",
"\n",
"We\\'ll use the `torch.func.functional_call` function to treat an\n",
"`nn.Module` like a function.\n",
"\n",
"First, let's extract the state from `model` into two dictionaries,\n",
"parameters and buffers. We\\'ll be detaching them because we won\\'t use\n",
"regular PyTorch autograd (e.g. Tensor.backward(), torch.autograd.grad).\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from torch.func import functional_call, vmap, grad\n",
"\n",
"params = {k: v.detach() for k, v in model.named_parameters()}\n",
"buffers = {k: v.detach() for k, v in model.named_buffers()}"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, let\\'s define a function to compute the loss of the model given a\n",
"single input rather than a batch of inputs. It is important that this\n",
"function accepts the parameters, the input, and the target, because we\n",
"will be transforming over them.\n",
"\n",
"Note - because the model was originally written to handle batches, we'll\n",
"use `torch.unsqueeze` to add a batch dimension.\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def compute_loss(params, buffers, sample, target):\n",
" batch = sample.unsqueeze(0)\n",
" targets = target.unsqueeze(0)\n",
"\n",
" predictions = functional_call(model, (params, buffers), (batch,))\n",
" loss = loss_fn(predictions, targets)\n",
" return loss"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, let's use the `grad` transform to create a new function that\n",
"computes the gradient with respect to the first argument of\n",
"`compute_loss` (i.e. the `params`).\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"ft_compute_grad = grad(compute_loss)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `ft_compute_grad` function computes the gradient for a single\n",
"(sample, target) pair. We can use `vmap` to get it to compute the\n",
"gradient over an entire batch of samples and targets. Note that\n",
"`in_dims=(None, None, 0, 0)` because we wish to map `ft_compute_grad`\n",
"over the 0th dimension of the data and targets, and use the same\n",
"`params` and buffers for each.\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"ft_compute_sample_grad = vmap(ft_compute_grad, in_dims=(None, None, 0, 0))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally, let\\'s used our transformed function to compute\n",
"per-sample-gradients:\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"ft_per_sample_grads = ft_compute_sample_grad(params, buffers, data, targets)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"we can double check that the results using `grad` and `vmap` match the\n",
"results of hand processing each one individually:\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"for per_sample_grad, ft_per_sample_grad in zip(per_sample_grads, ft_per_sample_grads.values()):\n",
" assert torch.allclose(per_sample_grad, ft_per_sample_grad, atol=3e-3, rtol=1e-5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A quick note: there are limitations around what types of functions can\n",
"be transformed by `vmap`. The best functions to transform are ones that\n",
"are pure functions: a function where the outputs are only determined by\n",
"the inputs, and that have no side effects (e.g. mutation). `vmap` is\n",
"unable to handle mutation of arbitrary Python data structures, but it is\n",
"able to handle many in-place PyTorch operations.\n",
"\n",
"Performance comparison\n",
"======================\n",
"\n",
"Curious about how the performance of `vmap` compares?\n",
"\n",
"Currently the best results are obtained on newer GPU\\'s such as the A100\n",
"(Ampere) where we\\'ve seen up to 25x speedups on this example, but here\n",
"are some results on our build machines:\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def get_perf(first, first_descriptor, second, second_descriptor):\n",
" \"\"\"takes torch.benchmark objects and compares delta of second vs first.\"\"\"\n",
" second_res = second.times[0]\n",
" first_res = first.times[0]\n",
"\n",
" gain = (first_res-second_res)/first_res\n",
" if gain < 0: gain *=-1 \n",
" final_gain = gain*100\n",
"\n",
" print(f\"Performance delta: {final_gain:.4f} percent improvement with {first_descriptor} \")\n",
"\n",
"from torch.utils.benchmark import Timer\n",
"\n",
"without_vmap = Timer(stmt=\"compute_sample_grads(data, targets)\", globals=globals())\n",
"with_vmap = Timer(stmt=\"ft_compute_sample_grad(params, buffers, data, targets)\",globals=globals())\n",
"no_vmap_timing = without_vmap.timeit(100)\n",
"with_vmap_timing = with_vmap.timeit(100)\n",
"\n",
"print(f'Per-sample-grads without vmap {no_vmap_timing}')\n",
"print(f'Per-sample-grads with vmap {with_vmap_timing}')\n",
"\n",
"get_perf(with_vmap_timing, \"vmap\", no_vmap_timing, \"no vmap\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There are other optimized solutions (like in\n",
"This tutorial requires PyTorch 2.0.0 or later.

\n", "