The forward pass in a deep Recurrent Neural Network (RNN) implemented from scratch is computed iteratively across its layers. For each layer in the network stack, the sequence of inputs—which consists of either the raw input data or the processed outputs from the previous layer—is fed alongside that specific layer's current hidden state. The resultant outputs from all time steps are subsequently aggregated, for instance by stacking them along a new dimension, to be utilized as the input sequence for the succeeding layer or as the final model output.

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To implement a multilayer Recurrent Neural Network (RNN) from scratch, the network can be constructed by instantiating each layer as an individual basic recurrent unit, such as an `RNNScratch` object, possessing its own independent set of learnable parameters. The initial layer processes the original sequence data, whereas every subsequent layer receives the hidden representations produced by the layer immediately preceding it.

Stacked RNN Implementation from Scratch

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Stacked RNN Forward Computation from Scratch

Training a deep Gated Recurrent Unit (GRU) language model involves architectural decisions that closely mirror those of single-layer networks, but with the addition of multiple hidden layers. A stacked GRU architecture can be instantiated by explicitly specifying a nontrivial number of layers (e.g., setting the num_layers parameter to $$2$$), while maintaining identical hyperparameters—such as using $$32$$ hidden units and a vocabulary-sized fully connected output layer to map predictions to distinct tokens. This multilayer recurrent block is then embedded within a broader language model framework and optimized using a training loop equipped with techniques like gradient clipping to maintain numerical stability.

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