【炼丹Trick】EMA的原理与实现

在进行深度学习训练时，同一模型往往可以训练出不同的效果，这就是炼丹这件事的玄学所在。使用一些trick能够让你更容易追上目前SOTA的效果，一些流行的开源代码中已经集成了不少trick，值得学习一番。本节介绍EMA这一方法。

EMA也就是指数移动平均(Exponential moving average)。其公式非常简单，如下所示：

\(\theta_{\text{EMA}, t+1} = (1 - \lambda) \cdot \theta_{\text{EMA}, t} + \lambda \cdot \theta_{t}\)

\(\theta_{t}\)是t时刻的网络参数，\(\theta_{\text{EMA}, t}\)是t时刻滑动平均后的网络参数，那么t+1时刻的滑动平均结果就是这两者的加权融合。这里 \(\lambda\)通常会取接近于1的数，比如0.9995，数字越大平均的效果就比较强。

值得注意的是，这里可以看成有两个模型，基础模型其参数按照常规的前后向传播来更新，另外一个模型则是基础模型的滑动平均版本，它并不直接参与前后向传播，仅仅是利用基础模型的参数结果来更新自己。

EMA为什么会有效呢？大概是因为在训练的时候，会使用验证集来衡量模型精度，但其实验证集精度并不和测试集一致，在训练后期阶段，模型可能已经在测试集最佳精度附近波动，所以使用滑动平均的结果会比使用单一结果更加可靠。感兴趣的话可以看看这几篇论文,论文1,论文2,论文3。

Pytorch其实已经为我们实现了这一功能，为了避免自己造轮子可能引入的错误，这里直接学习一下官方的代码。这个类的名称就叫做AveragedModel。代码如下所示。
我们需要做的是提供avg_fn这个函数，avg_fn用来指定以何种方式进行平均。

class AveragedModel(Module):
    """
    You can also use custom averaging functions with `avg_fn` parameter.
    If no averaging function is provided, the default is to compute
    equally-weighted average of the weights.
    """
    def __init__(self, model, device=None, avg_fn=None, use_buffers=False):
        super(AveragedModel, self).__init__()
        self.module = deepcopy(model)
        if device is not None:
            self.module = self.module.to(device)
        self.register_buffer('n_averaged',
                             torch.tensor(0, dtype=torch.long, device=device))
        if avg_fn is None:
            def avg_fn(averaged_model_parameter, model_parameter, num_averaged):
                return averaged_model_parameter + \
                    (model_parameter - averaged_model_parameter) / (num_averaged + 1)
        self.avg_fn = avg_fn
        self.use_buffers = use_buffers

    def forward(self, *args, **kwargs):
        return self.module(*args, **kwargs)

    def update_parameters(self, model):
        self_param = (
            itertools.chain(self.module.parameters(), self.module.buffers())
            if self.use_buffers else self.parameters()
        )
        model_param = (
            itertools.chain(model.parameters(), model.buffers())
            if self.use_buffers else model.parameters()
        )
        for p_swa, p_model in zip(self_param, model_param):
            device = p_swa.device
            p_model_ = p_model.detach().to(device)
            if self.n_averaged == 0:
                p_swa.detach().copy_(p_model_)
            else:
                p_swa.detach().copy_(self.avg_fn(p_swa.detach(), p_model_,
                                                 self.n_averaged.to(device)))
        self.n_averaged += 1


@torch.no_grad()
def update_bn(loader, model, device=None):
    r"""Updates BatchNorm running_mean, running_var buffers in the model.

    It performs one pass over data in `loader` to estimate the activation
    statistics for BatchNorm layers in the model.
    Args:
        loader (torch.utils.data.DataLoader): dataset loader to compute the
            activation statistics on. Each data batch should be either a
            tensor, or a list/tuple whose first element is a tensor
            containing data.
        model (torch.nn.Module): model for which we seek to update BatchNorm
            statistics.
        device (torch.device, optional): If set, data will be transferred to
            :attr:`device` before being passed into :attr:`model`.

    Example:
        >>> loader, model = ...
        >>> torch.optim.swa_utils.update_bn(loader, model)

    .. note::
        The `update_bn` utility assumes that each data batch in :attr:`loader`
        is either a tensor or a list or tuple of tensors; in the latter case it
        is assumed that :meth:`model.forward()` should be called on the first
        element of the list or tuple corresponding to the data batch.
    """
    momenta = {}
    for module in model.modules():
        if isinstance(module, torch.nn.modules.batchnorm._BatchNorm):
            module.running_mean = torch.zeros_like(module.running_mean)
            module.running_var = torch.ones_like(module.running_var)
            momenta[module] = module.momentum

    if not momenta:
        return

    was_training = model.training
    model.train()
    for module in momenta.keys():
        module.momentum = None
        module.num_batches_tracked *= 0

    for input in loader:
        if isinstance(input, (list, tuple)):
            input = input[0]
        if device is not None:
            input = input.to(device)

        model(input)

    for bn_module in momenta.keys():
        bn_module.momentum = momenta[bn_module]
    model.train(was_training)

这里同样参考官方的示例代码，给出滑动平均的实现。ExponentialMovingAverage继承了AveragedModel，并且复写了init方法，其实更直接的方法是将ema_avg函数作为参数传递给AveragedModel，这里可能是为了可读性，避免出现一个孤零零的ema_avg函数。

class ExponentialMovingAverage(torch.optim.swa_utils.AveragedModel):
    """Maintains moving averages of model parameters using an exponential decay.
    ``ema_avg = decay * avg_model_param + (1 - decay) * model_param``
    `torch.optim.swa_utils.AveragedModel <https://pytorch.org/docs/stable/optim.html#custom-averaging-strategies>`_
    is used to compute the EMA.
    """

    def __init__(self, model, decay, device="cpu"):
        def ema_avg(avg_model_param, model_param, num_averaged):
            return decay * avg_model_param + (1 - decay) * model_param

        super().__init__(model, device, ema_avg, use_buffers=True)

如何使用呢？方式是比较简单的，首先是利用当前模型创建出一个滑动平均模型。

model_ema = utils.ExponentialMovingAverage(model, device=device, decay=ema_decay)

然后是进行基础模型的前后向传播，更新结束后再对滑动平均版的模型进行参数更新。

output = model(image)
loss = criterion(output, target)
optimizer.zero_grad()
loss.backward()
optimizer.step()
model_ema.update_parameters(model)