How does an RNN calculate a new hidden state at each time step?

The mechanism by which a Recurrent Neural Network (RNN) calculates a new hidden state at each time step involves leveraging both the current input and the previous hidden state. This architecture is specifically designed to capture temporal dependencies in sequential data by maintaining information through its hidden state.

At each time step, the RNN takes in the current input and combines it with the previous hidden state. This allows the network to integrate what it has learned from past inputs with the current information, effectively enabling it to understand context and sequence in data such as text, time series, or speech. The process typically involves a mathematical operation where a weighted sum of the current input and the previous hidden state is computed, often followed by an activation function, such as tanh or ReLU. This operation produces the new hidden state that will be passed to the next time step.

The other options do not encapsulate the fundamental working of an RNN. The reliance solely on the current input neglects the critical aspect of memory that allows RNNs to make decisions based on prior information, while calculating new states based only on input and output weights does not accurately represent the recursion inherent in the RNN architecture. Additionally, while training on an extensive dataset is important for RNN effectiveness,