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What's the intuition behind the hidden states of RNN/LSTM? Are they similar to the hidden states of HMM (Hidden Markov Model)? Thanks!

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I personally don't think they are comparable to the hidden state of a Markov model. One key difference is that, in a HMM you can explain what a given state means to someone, where in a RNN/LSTM you cannot interpret a given state.

The closest thing that you can compare the hidden state of an RNN/LSTM is to think of it as the output of an intermediate layer of a fully-connected neural network but for time-series data.

And the larger the hidden state the more memory it can retain of the past.

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