Bidirectional GRU (BiGRU)

• Bidirectional Gated Recurrent Unit (BiGRU) is a recurrent neural network architecture that processes sequences in both forward and backward directions to capture complete temporal context.
• It is widely applied in areas such as natural language processing, energy forecasting, and network intrusion detection, demonstrating superior performance over unidirectional models.
• Leveraging efficient gating mechanisms and optimized hyperparameters, BiGRU models improve prediction accuracy and reduce errors in diverse sequential tasks.

A Bidirectional Gated Recurrent Unit (BiGRU) is a recurrent neural network layer architecture that leverages the gating mechanisms of the Gated Recurrent Unit (GRU) and augment this with bidirectional sequence processing—by running two independent GRU layers, one over the input sequence forwards and one in reverse. This configuration enables each output time-step's representation to incorporate both future and past contextual information, which is critical for temporal and sequential modeling tasks involving ambiguous or context-dependent signals. BiGRU networks have demonstrated empirical superiority and robust generalization properties across domains including physiological signal analysis, energy consumption prediction, network intrusion detection, natural language processing, and battery state-of-health forecasting.

1. Mathematical Formulation and Bidirectional Architecture

At each time step $t$, a standard GRU cell computes an update gate $z_t$, a reset gate $r_t$, a candidate activation $\tilde{h}_t$, and the new hidden state $h_t$: $z_t = \sigma(W_z x_t + U_z h_{t-1} + b_z)$

$r_t = \sigma(W_r x_t + U_r h_{t-1} + b_r)$

$$\tilde{h}_t = \tanh(W_h x_t + U_h (r_t \circ h_{t-1}) + b_h)$$

$$h_t = (1 - z_t) \circ h_{t-1} + z_t \circ \tilde{h}_t$$

where $\sigma$ is the logistic sigmoid, $\circ$ is an element-wise product, and $W_*$, $U_*$, $b_*$ are learned parameters.

The BiGRU extension deploys two independent GRU layers—one traversing the input sequence forward ($\overrightarrow{h}_t$), the other backward ($\overleftarrow{h}_t$). The combined representation at each time $t$ is typically constructed by concatenation: $$H_t = [\overrightarrow{h}_t;\ \overleftarrow{h}_t] \in \mathbb{R}^{2H}$$ Some implementations sum the two directional states instead of concatenation, as seen in data center energy prediction models (Kannan et al., 23 Dec 2025). Only the last time step (or a pooled representation) is often passed to the subsequent dense or classification layer.

2. Network Design and Hyperparameter Optimization

The canonical BiGRU network stacks multiple bidirectional GRU layers, each with a tunable number of hidden units per direction. Optimal architecture configuration—layer depth $N$, hidden size $H$, and input window length $L$—significantly impacts model performance. Hyperparameter search approaches include Bayesian optimization and grid search, targeting not only these structure parameters but also batch size, learning rates, and threshold values for classification tasks (Radzio et al., 2019). Regularization is often achieved through dropout within or after BiGRU layers and data-level normalization, though some models rely solely on preprocessing for normalization (Radzio et al., 2019).

A representative BiGRU architecture for physiological signal classification uses:

• Two stacked BiGRU layers (N=2), each with 100 units per direction (H=100).
• Input sequences of length L (optimized, typically 400–600 samples).
• Output at the final time-step, followed by a softmax dense classifier.
• Training via ADADELTA optimizer and early stopping on validation performance (Radzio et al., 2019).

Dual-module BiGRU architectures for battery health forecasting employ stacked bidirectional blocks, with sequence-level forward- and backward-GRU passes (implemented via “Flip–GRU–Flip” for backward flow). Hyperparameters such as the number of units per direction, dropout rates, learning rates, and number of epochs are optimized automatically by metaheuristic algorithms (e.g., sparrow search algorithm) for improved robustness and accuracy (Wen et al., 23 May 2025).

3. Application Domains and Empirical Performance

BiGRU networks have been successfully adapted to a broad spectrum of real-world tasks:

Application Area	Data Modality	BiGRU Configuration
Syncope/falls prediction (Radzio et al., 2019)	HR, mean BP time series	2×BiGRU(100 per direction)
Data center PUE prediction (Kannan et al., 23 Dec 2025)	21 features/time series	1×BiGRU(100 per direction)
Fake news detection (Bangla) (Roy et al., 2024)	Word sequence / text	1×BiGRU(64 per direction)
Network intrusion detection (Zhang et al., 5 Sep 2025)	Packet feature sequence	2×BiGRU(128 per direction)
Li-ion battery SOH (Wen et al., 23 May 2025)	Health indicator (1D time series)	Dual-module BiGRU

Empirical results consistently indicate that BiGRU architectures outperform unidirectional GRUs or even more complex hybrid models both in lead-time for early event detection (e.g., 10 minutes prior to syncope), regression accuracy (e.g., RMSE and $R^2$ for PUE and SOH), and classification F1-score (e.g., 99.57% for Bangla fake news) (Radzio et al., 2019, Kannan et al., 23 Dec 2025, Roy et al., 2024).

4. Impact of Bidirectionality

Bidirectional processing enables each hidden state to integrate context from both earlier and later points in the input sequence window. For physiological signals, this results in substantial reductions in false negatives and increased stability to threshold selection in classification (Radzio et al., 2019). In text data and sequence modeling tasks, BiGRU captures left and right context—a property critical for morphologically complex or free word-order languages (Roy et al., 2024). For network traffic and activity recognition, bidirectionality disambiguates patterns that only emerge when global sequence context is available (e.g., pre/post-attack packet signatures or mutual interactions in Wi-Fi CSI data) (Zhang et al., 5 Sep 2025, Khan et al., 2022).

5. Extensions: Hybrid Architectures and Attention Mechanisms

Recent work integrates BiGRUs with other model blocks, notably Transformers and attention mechanisms:

• BiGRU+Transformer: In network intrusion detection, BiGRU feature extraction precedes Transformer encoder blocks. Concatenated bidirectional states are input to multi-head self-attention, followed by pooling and dense classification (Zhang et al., 5 Sep 2025). This architecture achieves improved detection of both common and rare events, leveraging local sequence dynamics (BiGRU) and global feature relevance (Transformer).
• Attention-BiGRU: In human interaction recognition from Wi-Fi signals, multi-head self-attention operates on stacked BiGRU outputs, facilitating selective focus on key time windows. Skip connections and positional embeddings further enhance robustness to input variability (Khan et al., 2022).
• Dual-module and cascaded designs: Stacking multiple BiGRU blocks with independent hyperparameters, tuned by metaheuristic algorithms, provides gains in predictive accuracy, generalization, and stability for engineering applications such as battery SOH forecasting (Wen et al., 23 May 2025).

6. Data Preprocessing and Model Training

Successful BiGRU deployment is coupled to rigorous data cleaning, balancing, and normalization:

• Outlier removal via studentization, median filtering, and gap interpolation (for physiological signals).
• Min-max normalization of multi-variate features (HR, mBP, network packet features, etc.).
• Sequence segmentation into windows based on optimized length, often coupled with stop-word and low-content filtering for NLP tasks (Radzio et al., 2019, Roy et al., 2024).
• One-hot encoding and label balancing—especially critical in highly imbalanced binary or multi-class settings (e.g., fake news detection, intrusion classes).
• Training configurations vary: default PyTorch or Keras optimizers (Adam, ADADELTA), batch sizes range from 12 (Wi-Fi HAR) to 512 (network traffic), loss functions chosen according to task (MSE, cross-entropy), and regularization via dropout or early stopping (Radzio et al., 2019, Khan et al., 2022, Kannan et al., 23 Dec 2025).

7. Comparative Evaluation and Domain-significance

Benchmarking against unidirectional GRUs, LSTMs, CNNs, and hybrid models shows that BiGRUs yield superior accuracy for most time-sequential tasks. In physiological event prediction, BiGRUs improve early-warning lead time by five minutes and raise recall to 0.91 (Radzio et al., 2019). For data center energy forecasting, BiGRU achieves $R^2 = 0.99673$ with lower MSE and MAE than GRU (Kannan et al., 23 Dec 2025). In Bangla fake-news detection, BiGRU attains 99.16% accuracy—the highest among compared architectures (Roy et al., 2024). The ability of BiGRU to integrate future and past context underpins its wide deployment in scientific and engineering domains where windowed sequence knowledge is often incomplete if conditioned only on the unidirectional past.

In summary, the Bidirectional Gated Recurrent Unit framework combines the efficiency and gating benefits of GRU with symmetric time-context extraction, establishing it as an empirically dominant choice for sequence modeling applications requiring robust temporal reasoning and contextual integration.