Class BatchNorm2d

imperative/python/megengine/module/batchnorm.py:266–342

r"""Applies Batch Normalization over a 4D tensor. .. math:: y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta The mean and standard-deviation are calculated per-dimension over the mini-batches and :math:`\gamma` and :math:`\beta` are learnable

class BatchNorm2d(_BatchNorm):
    r"""Applies Batch Normalization over a 4D tensor.

    .. math::

        y = \frac{x - \mathrm{E}[x]}{ \sqrt{\mathrm{Var}[x] + \epsilon}} * \gamma + \beta

    The mean and standard-deviation are calculated per-dimension over
    the mini-batches and :math:`\gamma` and :math:`\beta` are learnable
    parameter vectors.

    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 :attr:`momentum`
    of 0.9.

    If :attr:`track_running_stats` is set to ``False``, this layer will not
    keep running estimates, batch statistics is used during
    evaluation time instead.

    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.

    .. note::

        The update formula for ``running_mean`` and ``running_var`` (taking ``running_mean`` as an example) is

        .. math::

            \textrm{running_mean} = \textrm{momentum} \times \textrm{running_mean} + (1 - \textrm{momentum}) \times \textrm{batch_mean}

        which could be defined differently in other frameworks. Most notably, ``momentum`` of 0.1 in PyTorch
        is equivalent to ``mementum`` of 0.9 here.

    Args:
        num_features: usually :math:`C` from an input of shape
            :math:`(N, C, H, W)` or the highest ranked dimension of an input
            less than 4D.
        eps: a value added to the denominator for numerical stability.
            Default: 1e-5
        momentum: the value used for the ``running_mean`` and ``running_var`` computation.
            Default: 0.9
        affine: a boolean value that when set to True, this module has
            learnable affine parameters. Default: True
        track_running_stats: when set to True, this module tracks the
            running mean and variance. When set to False, this module does not
            track such statistics and always uses batch statistics in both training
            and eval modes. Default: True
        freeze: when set to True, this module does not update the
            running mean and variance, and uses the running mean and variance instead of
            the batch mean and batch variance to normalize the input. The parameter takes effect
            only when the module is initilized with track_running_stats as True.
            Default: False

    Shape:
        - Input: :math:`(N, C, H, W)`
        - Output: :math:`(N, C, H, W)` (same shape as input)