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I have read somewhere (sorry, couldn't find the reference anymore), that $C_t$ (check figure below) represents the "long term" in LSMT. The reason was because "The information goes throughout the cell without being altered by synaptic weights."

Is this true? It does not make sense to me, because $C_t$ depends on $f_t$, $i_t$ and $\tilde C_t$ and all of them has their own synaptics weights.

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And $h_t$ (check figure below) represents the "short term" in LSTM. It is considered the "short term" because it is altered by synaptic weights.

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From many sources in the internet, I assume they are indeed the "long term" and "short term" memories. But, why?

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