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[fix] fix the math style in paddle.static.nn.batch_norm #58514

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merged 4 commits into from
Oct 31, 2023
Merged

[fix] fix the math style in paddle.static.nn.batch_norm #58514

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ooooo-create Oct 31, 2023
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Merge branch 'develop' of https://github.com/PaddlePaddle/Paddle into…
ooooo-create Oct 31, 2023
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24 changes: 12 additions & 12 deletions python/paddle/static/nn/common.py
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Original file line number Diff line number Diff line change
Expand Up @@ -2803,19 +2803,19 @@ def batch_norm(
Internal Covariate Shift <https://arxiv.org/pdf/1502.03167.pdf>`_
for more details.

:math:input is the input features over a mini-batch.
:math:`input` is the input features over a mini-batch.

.. math::

\\mu_{\\beta} &\\gets \\frac{1}{m} \\sum_{i=1}^{m} x_i \\qquad &//\\
\ mini-batch\ mean \\\\
\\sigma_{\\beta}^{2} &\\gets \\frac{1}{m} \\sum_{i=1}^{m}(x_i - \\
\\mu_{\\beta})^2 \\qquad &//\ mini-batch\ variance \\\\
\\hat{x_i} &\\gets \\frac{x_i - \\mu_\\beta} {\\sqrt{\\
\\sigma_{\\beta}^{2} + \\epsilon}} \\qquad &//\ normalize \\\\
y_i &\\gets \\gamma \\hat{x_i} + \\beta \\qquad &//\ scale\ and\ shift
\mu_{\beta} &\gets \frac{1}{m} \sum_{i=1}^{m} x_i \qquad &//
\ mini-batch\ mean \\
\sigma_{\beta}^{2} &\gets \frac{1}{m} \sum_{i=1}^{m}(x_i -
\mu_{\\beta})^2 \qquad &//\ mini-batch\ variance \\
\hat{x_i} &\gets \frac{x_i - \mu_\beta} {\sqrt{
\sigma_{\beta}^{2} + \epsilon}} \qquad &//\ normalize \\
y_i &\gets \gamma \hat{x_i} + \beta \qquad &//\ scale\ and\ shift

moving\_mean = moving\_mean * momentum + mini-batch\_mean * (1. - momentum) \\\\
moving\_mean = moving\_mean * momentum + mini-batch\_mean * (1. - momentum) \\
moving\_var = moving\_var * momentum + mini-batch\_var * (1. - momentum)


Expand All @@ -2829,9 +2829,9 @@ def batch_norm(

.. math::

\\hat{x_i} &\\gets \\frac{x_i - \\mu_\\beta} {\\sqrt{\\
\\sigma_{\\beta}^{2} + \\epsilon}} \\\\
y_i &\\gets \\gamma \\hat{x_i} + \\beta
\hat{x_i} &\gets \frac{x_i - \mu_\beta} {\sqrt{
\sigma_{\beta}^{2} + \epsilon}} \\
y_i &\gets \gamma \hat{x_i} + \beta

Note:
if build_strategy.sync_batch_norm=True, the batch_norm in network will use
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