Model ensembling

This tutorial illustrates how to vectorize model ensembling using torch.vmap.

What is model ensembling?

Model ensembling combines the predictions from multiple models together. Traditionally this is done by running each model on some inputs separately and then combining the predictions. However, if you’re running models with the same architecture, then it may be possible to combine them together using torch.vmap. vmap is a function transform that maps functions across dimensions of the input tensors. One of its use cases is eliminating for-loops and speeding them up through vectorization.

Let’s demonstrate how to do this using an ensemble of simple MLPs.

Note

This tutorial requires PyTorch 2.0.0 or later.

import torch
import torch.nn as nn
import torch.nn.functional as F
torch.manual_seed(0)

# Here's a simple MLP
class SimpleMLP(nn.Module):
    def __init__(self):
        super(SimpleMLP, self).__init__()
        self.fc1 = nn.Linear(784, 128)
        self.fc2 = nn.Linear(128, 128)
        self.fc3 = nn.Linear(128, 10)

    def forward(self, x):
        x = x.flatten(1)
        x = self.fc1(x)
        x = F.relu(x)
        x = self.fc2(x)
        x = F.relu(x)
        x = self.fc3(x)
        return x

Let’s generate a batch of dummy data and pretend that we’re working with an MNIST dataset. Thus, the dummy images are 28 by 28, and we have a minibatch of size 64. Furthermore, lets say we want to combine the predictions from 10 different models.

device = 'cuda'
num_models = 10

data = torch.randn(100, 64, 1, 28, 28, device=device)
targets = torch.randint(10, (6400,), device=device)

models = [SimpleMLP().to(device) for _ in range(num_models)]

We have a couple of options for generating predictions. Maybe we want to give each model a different randomized minibatch of data. Alternatively, maybe we want to run the same minibatch of data through each model (e.g. if we were testing the effect of different model initializations).

Option 1: different minibatch for each model

minibatches = data[:num_models]
predictions_diff_minibatch_loop = [model(minibatch) for model, minibatch in zip(models, minibatches)]

Option 2: Same minibatch

minibatch = data[0]
predictions2 = [model(minibatch) for model in models]

Using vmap to vectorize the ensemble

Let’s use vmap to speed up the for-loop. We must first prepare the models for use with vmap.

First, let’s combine the states of the model together by stacking each parameter. For example, model[i].fc1.weight has shape [784, 128]; we are going to stack the .fc1.weight of each of the 10 models to produce a big weight of shape [10, 784, 128].

PyTorch offers the torch.func.stack_module_state convenience function to do this.

from torch.func import stack_module_state

params, buffers = stack_module_state(models)

Next, we need to define a function to vmap over. The function should, given parameters and buffers and inputs, run the model using those parameters, buffers, and inputs. We’ll use torch.func.functional_call to help out:

from torch.func import functional_call
import copy

# Construct a "stateless" version of one of the models. It is "stateless" in
# the sense that the parameters are meta Tensors and do not have storage.
base_model = copy.deepcopy(models[0])
base_model = base_model.to('meta')

def fmodel(params, buffers, x):
    return functional_call(base_model, (params, buffers), (x,))

Option 1: get predictions using a different minibatch for each model.

By default, vmap maps a function across the first dimension of all inputs to the passed-in function. After using stack_module_state, each of the params and buffers have an additional dimension of size ‘num_models’ at the front, and minibatches has a dimension of size ‘num_models’.

print([p.size(0) for p in params.values()]) # show the leading 'num_models' dimension

assert minibatches.shape == (num_models, 64, 1, 28, 28) # verify minibatch has leading dimension of size 'num_models'

from torch import vmap

predictions1_vmap = vmap(fmodel)(params, buffers, minibatches)

# verify the ``vmap`` predictions match the
assert torch.allclose(predictions1_vmap, torch.stack(predictions_diff_minibatch_loop), atol=1e-3, rtol=1e-5)

Option 2: get predictions using the same minibatch of data.

vmap has an in_dims argument that specifies which dimensions to map over. By using None, we tell vmap we want the same minibatch to apply for all of the 10 models.

predictions2_vmap = vmap(fmodel, in_dims=(0, 0, None))(params, buffers, minibatch)

assert torch.allclose(predictions2_vmap, torch.stack(predictions2), atol=1e-3, rtol=1e-5)

A quick note: there are limitations around what types of functions can be transformed by vmap. The best functions to transform are ones that are pure functions: a function where the outputs are only determined by the inputs that have no side effects (e.g. mutation). vmap is unable to handle mutation of arbitrary Python data structures, but it is able to handle many in-place PyTorch operations.

Performance

Curious about performance numbers? Here’s how the numbers look.

from torch.utils.benchmark import Timer
without_vmap = Timer(
    stmt="[model(minibatch) for model, minibatch in zip(models, minibatches)]",
    globals=globals())
with_vmap = Timer(
    stmt="vmap(fmodel)(params, buffers, minibatches)",
    globals=globals())
print(f'Predictions without vmap {without_vmap.timeit(100)}')
print(f'Predictions with vmap {with_vmap.timeit(100)}')

There’s a large speedup using vmap!

In general, vectorization with vmap should be faster than running a function in a for-loop and competitive with manual batching. There are some exceptions though, like if we haven’t implemented the vmap rule for a particular operation or if the underlying kernels weren’t optimized for older hardware (GPUs). If you see any of these cases, please let us know by opening an issue on GitHub.