Talk:Batch normalization
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Inference with Batch-Normalized Networks
In the formula,
![{\displaystyle y^{(k)}=BN_{\gamma ^{(k)},\beta ^{(k)}}^{\text{inf}}(x^{(k)})={\frac {\gamma }{\sqrt {\operatorname {Var} [x^{(k)}]+\epsilon }}}x^{(k)}+{\Bigg (}\beta -{\frac {\gamma E[x^{(k)}]}{\sqrt {\operatorname {Var} [x^{(k)}]+\epsilon }}}{\Bigg )}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7d214e7a7fdf2989d5e2f1079a23c539c5c66162)
the indices are missing.
Shouldn't it be
![{\displaystyle y^{(k)}=BN_{\gamma ^{(k)},\beta ^{(k)}}^{\text{inf}}(x^{(k)})={\frac {\gamma ^{(k)}}{\sqrt {\operatorname {Var} [x^{(k)}]+\epsilon }}}x^{(k)}+{\Bigg (}\beta ^{(k)}-{\frac {\gamma ^{(k)}E[x^{(k)}]}{\sqrt {\operatorname {Var} [x^{(k)}]+\epsilon }}}{\Bigg )}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/adbcefcc21ff96358a00387bbb456b998a767ca7)
doubt about the backprop derivatives
In the dl/dmu - the 2nd term has a sum of x-mu - this sum is equal to 0, since the sum of the x's is equal to the sum of the mean. Why does this term appear then? 83.48.83.202 (talk) 13:58, 14 March 2023 (UTC)