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)