批量归一化中运行平均值和样本平均值之间的量纲差异

Question

我最近通过 cs231n 在线自学，在批量归一化分配中，特别是运行均值计算：
running_mean = momentum * running_mean + (1 - momentum) * sample_mean
running_mean由
running_mean = bn_param.get("running_mean", np.zeros(D, dtype=x.dtype)) 。
所以当你有多个batchnorm层时， running_mean值继承自最后一个batchnorm层，但sample_mean是当前层输入获得的，这导致

File ~/assignment/assignment2/cs231n/layers.py:217, in batchnorm_forward(x, gamma, beta, bn_param)
    213 out = x_hat * gamma + beta
    215 print(running_mean.shape, miu.shape)
--> 217 running_mean = momentum * running_mean + (1 - momentum) * miu
    218 running_var = momentum * running_var + (1 - momentum) * sigma_squared
    220 cache = miu, sigma_squared, eps, N, x_hat, x, gamma

ValueError: operands could not be broadcast together with shapes (1,20) (1,30) 

我在这里错过了什么？ 推导似乎是正确的

我尝试实现 batchnorm 层，但 running_mean 和 sample_mean 的维度不同。

Answer 1

这就是我所拥有的：

        miu = np.mean(x, axis=0)
        var = np.var(x, axis=0)
        x_hat = (x - miu) / np.sqrt(var + eps)
        out = x_hat * gamma + beta
        print(running_mean.shape, miu.shape)
        running_mean = momentum * running_mean + (1 - momentum) * miu
        running_var = momentum * running_var + (1 - momentum) * var
        cache = miu, var, eps, N, x_hat, x, gamma