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

I am recently teaching my self through cs231n online, and in batch normalizetion assignment, specifically in running mean calculation:
running_mean = momentum * running_mean + (1 - momentum) * sample_mean
the running_mean is set by
running_mean = bn_param.get("running_mean", np.zeros(D, dtype=x.dtype)) .
So when you have more than one batchnorm layer, the running_mean value is inherited from the last batchnorm layer, but the sample_mean is obtained by current layer input, which result in

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) 

what did I miss here? The derivation seems right though

I tried to implement the batchnorm layer, but the dimension is different between running_mean and sample_mean.

Answer 1

This is what I have:

        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