# Model ensembling¶

This example illustrates how to vectorize model ensembling using 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 `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.

```
import torch
import torch.nn as nn
import torch.nn.functional as F
from functools import partial
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]`

.

functorch offers the ‘combine_state_for_ensemble’ convenience function to do that. It returns a stateless version of the model (fmodel) and stacked parameters and buffers.

```
from functorch import combine_state_for_ensemble
fmodel, params, buffers = combine_state_for_ensemble(models)
[p.requires_grad_() for p in params];
```

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

```
[10, 10, 10, 10, 10, 10]
```

```
from functorch 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 arg 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 on Google Colab.

```
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)}')
```

```
Predictions without vmap <torch.utils.benchmark.utils.common.Measurement object at 0x7fe22c58b3d0>
[model(minibatch) for model, minibatch in zip(models, minibatches)]
3.25 ms
1 measurement, 100 runs , 1 thread
Predictions with vmap <torch.utils.benchmark.utils.common.Measurement object at 0x7fe22c50c450>
vmap(fmodel)(params, buffers, minibatches)
879.28 us
1 measurement, 100 runs , 1 thread
```

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 at our GitHub!