BN、LN、IN、GN的区别

• NLP领域和音频领域很像，只有[B,T,C]维度，因为每个batch中相同位置的元素大概率不是一个类别，直接做batch norm 效果会比较差，更适合单个样本内部做layer norm；
• 音频的时间维度如果被压缩，计算得到==【B,1,C】的统计特征，保留了不同channel的特征，压缩了随时间变化的特征，更多统计的是单个音频全局不变的特征，比如音色；如果对C维度进行压缩，得到【B,T,1】==，音频各个频率域的区别被抹掉；时间维度的信息变化很大，得到的可能更偏向于内容维度的特征；
  
• NLP中的layer norm实现

import torch

batch_size, seq_size, dim = , , 
embedding = torch.randn(batch_size, seq_size, dim)

layer_norm = torch.nn.LayerNorm(dim, elementwise_affine = False)
print("y: ", layer_norm(embedding))

eps: float = 0.00001
mean = torch.mean(embedding[:, :, :], dim=(-1), keepdim=True)
var = torch.square(embedding[:, :, :] - mean).mean(dim=(-1), keepdim=True)

print("mean: ", mean.shape)
print("y_custom: ", (embedding[:, :, :] - mean) / torch.sqrt(var + eps))

• 更适合做batch-norm 的样本类型
  

- BatchNorm：batch方向做归一化，算NxHxW的均值，对小batchsize效果不好；BN主要缺点是对batchsize的大小比较敏感，由于每次计算均值和方差是在一个batch上，所以如果batchsize太小，则计算的均值、方差不足以代表整个数据分布。- LayerNorm：channel方向做归一化，算CxHxW的均值，主要对RNN(处理序列)作用明显，目前大火的Transformer也是使用的这种归一化操作；- InstanceNorm：一个channel内做归一化，算H*W的均值，用在风格化迁移；因为在图像风格化中，生成结果主要依赖于某个图像实例，所以对整个batch归一化不适合图像风格化中，因而对HW做归一化。可以加速模型收敛，并且保持每个图像实例之间的独立。- GroupNorm：将channel方向分group，然后每个group内做归一化，算(C//G)HW的均值；这样与batchsize无关，不受其约束，在分割与检测领域作用较好。

图像风格迁移adaIN

• Arbitrary Style Transfer in Real-time with Adaptive Instance Normalization 知乎笔记
• 代码实现
  

• 作者做实验，对IN 和BN 的loss区别原因进行对比，发现图片计算的均值/方差代表图片的风格；因此设计AdaIN 对图片风格归一化，然后再迁移到目标风格；

def forward(self, content, style, alpha=1.0):
    assert 0 <= alpha <= 1
    style_feats = self.encode_with_intermediate(style)
    content_feat = self.encode(content)
    t = adain(content_feat, style_feats[-1])
    t = alpha * t + (1 - alpha) * content_feat # 控制内容和风格的比例

    g_t = self.decoder(t)
    g_t_feats = self.encode_with_intermediate(g_t)

    loss_c = self.calc_content_loss(g_t_feats[-1], t)
    loss_s = self.calc_style_loss(g_t_feats[0], style_feats[0])
    for i in range(1, 4):
        loss_s += self.calc_style_loss(g_t_feats[i], style_feats[i])
    return loss_c, loss_s

• adain 只用在encoder-decoder 之间；实验发现encoder-adain-decoder(IN) 效果会变差；
• 控制内容和风格的比例 t = alpha * t + (1 - alpha) * content_feat

DiT adaLN

import numpy as np

class LayerNorm:
    def __init__(self, epsilon=1e-6):
        self.epsilon = epsilon

    def __call__(self, x: np.ndarray, gamma: np.ndarray, beta: np.ndarray) -> np.ndarray:
        """
    Args:
        x (np.ndarray): shape: (batch_size, sequence_length, feature_dim)
            gamma (np.ndarray): shape: (batch_size, 1, feature_dim), generated by condition embedding
            beta (np.ndarray): shape: (batch_size, 1, feature_dim), generated by condition embedding
    return:
            x_layer_norm (np.ndarray): shape: (batch_size, sequence_length, feature_dim)
    """
        _mean = np.mean(x, axis=-1, keepdims=True)
        _std = np.var(x, axis=-1, keepdims=True)
        x_layer_norm = self.gamma * (x - _mean / (_std + self.epsilon)) + self.beta
        return x_layer_norm

class DiTAdaLayerNorm:
    def __init__(self,feature_dim, epsilon=1e-6):
        self.epsilon = epsilon
        self.weight = np.random.rand(feature_dim, feature_dim * 2)

    def __call__(self, x, condition):
        """
        Args:
            x (np.ndarray): shape: (batch_size, sequence_length, feature_dim)
            condition (np.ndarray): shape: (batch_size, 1, feature_dim)
                Ps: condition = time_cond_embedding + class_cond_embedding
        return:
            x_layer_norm (np.ndarray): shape: (batch_size, sequence_length, feature_dim)
        """
        affine = condition @ self.weight  # shape: (batch_size, 1, feature_dim * 2)
        gamma, beta = np.split(affine, 2, axis=-1)
        _mean = np.mean(x, axis=-1, keepdims=True)
        _std = np.var(x, axis=-1, keepdims=True)
        x_layer_norm = gamma * (x - _mean / (_std + self.epsilon)) + beta
        return x_layer_norm

class DiTBlock:
    def __init__(self, feature_dim):
        self.MultiHeadSelfAttention = lambda x: x # mock multi-head self-attention
        self.layer_norm = LayerNorm()
        self.MLP = lambda x: x # mock multi-layer perceptron
        self.weight = np.random.rand(feature_dim, feature_dim * 6)

    def __call__(self, x: np.ndarray, time_embedding: np.ndarray, class_emnedding: np.ndarray) -> np.ndarray:
        """
        Args:
            x (np.ndarray): shape: (batch_size, sequence_length, feature_dim)
            time_embedding (np.ndarray): shape: (batch_size, 1, feature_dim)
            class_emnedding (np.ndarray): shape: (batch_size, 1, feature_dim)
        return:
            x (np.ndarray): shape: (batch_size, sequence_length, feature_dim)
        """
        condition_embedding = time_embedding + class_emnedding
        affine_params = condition_embedding @ self.weight  # shape: (batch_size, 1, feature_dim * 6)
        gamma_1, beta_1, alpha_1, gamma_2, beta_2, alpha_2 = np.split(affine_params, 6, axis=-1)
        x = x + alpha_1 * self.MultiHeadSelfAttention(self.layer_norm(x, gamma_1, beta_1))
        x = x + alpha_2 * self.MLP(self.layer_norm(x, gamma_2, beta_2))
        return x

• class condition的引入，用adaLN替换常规的LN。adaLN和adaLN-Zero的区别在于，用于scale的均值方差是随机初始化的，还是可以训练的；