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| data_mining:neural_network:tuning [2018/05/20 15:05] – [Batch normalization] phreazer | data_mining:neural_network:tuning [2018/05/20 15:21] (current) – [Batch norm at test time] phreazer | ||
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| But with mini-batch mean gets zeroed, no $b$ needed, instead $\beta$. | But with mini-batch mean gets zeroed, no $b$ needed, instead $\beta$. | ||
| $\tilde{Z}^l = \gamma^l Z^{l} + \beta^l$ | $\tilde{Z}^l = \gamma^l Z^{l} + \beta^l$ | ||
| + | |||
| + | ==== Algo ==== | ||
| + | |||
| + | * For minibatch t: | ||
| + | * Compute forward prop for $X^{\{t\}}$ | ||
| + | * In each hidden layer use BN to replace $Z^l$ with $\tilde{Z}^l$ | ||
| + | * Use backprop to compute $dW^{l}, d\beta^{l}, d\gamma^{l}$ | ||
| + | * Update parameters ... | ||
| + | |||
| + | ==== Why does it work ==== | ||
| + | |||
| + | Covariance shift (shifting input distribution) | ||
| + | |||
| + | * Batch norm reduces amount in which hidden units shifts around, become more stable (input to later layers) | ||
| + | * Slight regularization effect: Adds some noise, because it's normed on the mini batch | ||
| + | |||
| + | ==== Batch norm at test time ==== | ||
| + | |||
| + | Here no mini-batch, but one sample at a time | ||
| + | |||
| + | Estimate $\sigma^2, \mu$ using exponentially weighted average across mini-batches | ||