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Intermediate•Deep Learning
RNNs & LSTMs
Backpropagation Through Time (BPTT), vanishing gradients, forget gates, and long-range sequence memory.
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Research-Level Deep Dive & Equations
Sequential data (time-series, speech, natural language text) possesses temporal dependencies where the current token depends on past sequence history . Standard feedforward neural networks cannot process variable-length inputs without fixed context windows. **Recurrent Neural Networks (RNNs)** introduce a recurrent hidden state vector passed forward step-by-step across time steps .
•Standard Vanilla RNN Recurrence Equations:
•Parameter Sharing: The same weight matrices , , and are reused across all time steps. This parameter sharing enables RNNs to generalize to arbitrary sequence lengths .
Key Equations
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