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【Wrong Fix has been Closed】Fix: Replace the wrong symbol '+' with '=' in formulation related to chain rule #1317

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Replace the wrong symbol '+' with '=' in formulation related to chain rule.

Wrong Origin:
$$\frac{\partial h_t}{\partial w_h}= \frac{\partial f(x_{t},h_{t-1},w_h)}{\partial w_h} +\frac{\partial f(x_{t},h_{t-1},w_h)}{\partial h_{t-1}} \frac{\partial h_{t-1}}{\partial w_h}.$$

Revision:
$$\frac{\partial h_t}{\partial w_h}= \frac{\partial f(x_{t},h_{t-1},w_h)}{\partial w_h} =\frac{\partial f(x_{t},h_{t-1},w_h)}{\partial h_{t-1}} \frac{\partial h_{t-1}}{\partial w_h}.$$

Replace the wrong symbol '+' with '=' in formulation related to chain rule.
@GodExious GodExious closed this Jan 4, 2024
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Sorry, I think I got some wrong understandation for the formulation, because both $h_{t - 1}$ and $w_h$ is related to $w_h$,according to chain rule,there should be:

$$\frac{\partial f(g(x), h(x))}{\partial x} = \frac{\partial f(g(x), h(x))}{\partial g(x)} \frac{\partial g(x)}{\partial x} + \frac{\partial f(g(x), h(x))}{\partial h(x)} \frac{\partial h(x)}{\partial x}$$

So the origin formulation is exactly right. Sorry for my disturbtion.

@GodExious GodExious changed the title Fix: Replace the wrong symbol '+' with '=' in formulation related to chain rule 【Wrong Fix has been Closed】Fix: Replace the wrong symbol '+' with '=' in formulation related to chain rule Jan 4, 2024
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github-actions bot commented Jan 4, 2024

Job PR-1317-9c3761c is done.
Check the results at http://preview.d2l.ai/d2l-zh/PR-1317/9c3761c

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