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# BatchNorm2d

class torch.nn.BatchNorm2d(num_features, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True, device=None, dtype=None)

  Applies Batch Normalization over a 4D input (a mini-batch of 2D inputs with additional channel dimension) as described in the paper Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift .

  y=x−E[x]V a r[x]+ϵ∗γ+β y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta y=Var[x]+ϵ
  ​x−E[x]​∗γ+β

  The mean and standard-deviation are calculated per-dimension over the mini-batches and γ\gamma γ and β\beta β are learnable parameter vectors of size C (where C is the input size). By default, the elements of γ\gamma γ are set to 1 and the elements of β\beta β are set to 0. At train time in the forward pass, the standard-deviation is calculated via the biased estimator, equivalent to `torch.var(input, unbiased=False)`. However, the value stored in the moving average of the standard-deviation is calculated via the unbiased estimator, equivalent to `torch.var(input, unbiased=True)`.

  Also by default, during training this layer keeps running estimates of its computed mean and variance, which are then used for normalization during evaluation. The running estimates are kept with a default `momentum` of 0.1.

  If `track_running_stats` is set to `False`, this layer then does not keep running estimates, and batch statistics are instead used during evaluation time as well.

  Note

  This `momentum` argument is different from one used in optimizer classes and the conventional notion of momentum. Mathematically, the update rule for running statistics here is x^new=(1−momentum)×x^+momentum×x t\hat{x}_\text{new} = (1 - \text{momentum}) \times \hat{x} + \text{momentum} \times x_t x^new​=(1−momentum)×x^+momentum×x t​, where x^\hat{x}x^ is the estimated statistic and x t x_t x t​ is the new observed value.

  Because the Batch Normalization is done over the C dimension, computing statistics on (N, H, W) slices, it’s common terminology to call this Spatial Batch Normalization.

  Parameters:

    - num_features (int) – C C C from an expected input of size (N,C,H,W)(N, C, H, W)(N,C,H,W)

    - eps (float) – a value added to the denominator for numerical stability. Default: 1e-5

    - momentum (float) – the value used for the running_mean and running_var computation. Can be set to `None` for cumulative moving average (i.e. simple average). Default: 0.1

    - affine (bool) – a boolean value that when set to `True`, this module has learnable affine parameters. Default: `True`

    - track_running_stats (bool) – a boolean value that when set to `True`, this module tracks the running mean and variance, and when set to `False`, this module does not track such statistics, and initializes statistics buffers `running_mean` and `running_var` as `None`. When these buffers are `None`, this module always uses batch statistics. in both training and eval modes. Default: `True`

  Shape:

    - Input: (N,C,H,W)(N, C, H, W)(N,C,H,W)

    - Output: (N,C,H,W)(N, C, H, W)(N,C,H,W) (same shape as input)

  Examples:

      >>> # With Learnable Parameters
      >>> m = nn.BatchNorm2d(100)
      >>> # Without Learnable Parameters
      >>> m = nn.BatchNorm2d(100, affine=False)
      >>> input = torch.randn(20, 100, 35, 45)
      >>> output = m(input)

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