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.

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.

Training a Deep GRU Language Model

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.

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Stacked RNNs consist of multiple networks where the output of one layer serves as the input to a subsequent layer. The initial layers of stacked networks can induce representations that serve as useful abstractions for further layers — representations that might prove difficult to induce in a single RNN. So it can outperform single-layer networks.

Stacked RNNs

Dive into Deep Learning

Stacked RNN Implementation from Scratch

Implementing multiple layers of a Recurrent Neural Network (RNN) from scratch involves handling numerous logistical details, but modern deep learning frameworks abstract these away through high-level APIs. A deep architecture can be concisely defined by utilizing built-in recurrent functionalities and explicitly specifying a nontrivial number of hidden layers (e.g., setting a num_layers parameter) rather than relying on the default single-layer configuration. This approach generalizes single-layer implementations, allowing developers to easily instantiate deep models like multilayer GRUs. However, in minimalist frameworks like JAX's Flax, functionalities for stacking layers or integrating dropout are not provided out of the box, requiring developers to manually build upon built-in single-layer cells by programming the iterative layer logic and injecting dropout operations.

Concise Implementation of Deep RNNs

In deep, or stacked, Recurrent Neural Networks (RNNs), the hidden state is responsible for propagating sequential information throughout the multi-layered architecture. At any specific time step, the hidden state computed by a given layer is passed in two distinct directions: horizontally to the next time step within the identical layer, and vertically to the current time step of the subsequent layer. This two-dimensional information flow enables the network to build hierarchical representations over time.

Hidden State Propagation in Deep RNNs

Training deep Recurrent Neural Networks (RNNs) is a complex process that demands careful configuration to achieve proper convergence. Because the multi-layered sequential architecture exacerbates gradient-related issues, practitioners must ensure meticulous parameter initialization before training begins. Furthermore, successfully optimizing deep RNNs typically requires significant manual tuning and the application of specialized techniques, most notably learning rate adjustments and gradient clipping, to stabilize the learning process.

Training Requirements for Deep RNNs

Deep recurrent neural networks can be constructed using various types of recurrent units to process sequential data. The most common flavors of these deep architectures include standard vanilla RNNs, Long Short-Term Memory (LSTMs) networks, and Gated Recurrent Units (GRUs). These different varieties of recurrent models are conveniently accessible and can be instantiated as pre-built components through the high-level APIs of modern deep learning frameworks.

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