TabGRU Model: Dual Architectures

• TabGRU is a dual-use model that integrates bidirectional GRU networks with Transformer encoders for spatiotemporal rainfall estimation and sequential labeling for table extraction.
• It achieves superior performance by combining attention pooling and morphological preprocessing, yielding high accuracy in both urban weather forecasting and document analysis.
• The architecture effectively mitigates common challenges like wet-antenna effects and OCR errors, setting new benchmarks against physics-based and traditional models.

The term “TabGRU” denotes two distinct architectures as described in peer-reviewed sources: a hybrid deep learning model for urban rainfall intensity estimation using commercial microwave links (CMLs) (Li et al., 2 Dec 2025), and a bidirectional GRU-based model for table structure extraction in document images (Khan et al., 2020). Both approaches leverage bidirectional gated recurrent unit networks, yet they address fundamentally different domains—spatiotemporal rainfall retrieval versus document understanding.

1. Dual Usage: Overview of TabGRU Architectures

TabGRU is used to describe hybrid or sequential architectures centered on bidirectional GRU networks. In the rainfall estimation context, TabGRU integrates a Transformer encoder with BiGRU layers for CML signal analysis (Li et al., 2 Dec 2025). In table structure extraction, TabGRU denotes a deep pipeline where BiGRU networks scan preprocessed table images to identify row and column separators (Khan et al., 2020). Both models achieve benchmark performance through direct sequence modeling, yet with distinct data modalities, architectures, and objectives.

2. Rainfall Intensity Estimation: TabGRU Hybrid Architecture

TabGRU for CML-based rainfall estimation operates on rolling windows of 1-min-averaged received signal levels from multiple sub-links:

• Input: $L=30$ min window ($d_{\text{in}}=3$) plus optional clock-time features. Each $x_t\in\mathbb{R}^{d_{\text{in}}}$ is linearly projected to $d_{\mathrm{model}}$.
• Positional Encoding: Learnable matrix $P\in\mathbb{R}^{L\times d_{\mathrm{model}}}$ is added: $X' = XW^{\mathrm{proj}} + P$.
• Transformer Encoder: Three layers, each with four multi-head self-attention blocks. Attention computes $$\mathrm{softmax}\left(QK^\mathsf{T}/\sqrt{d_k}\right)V$$.
• BiGRU Layer: Single-layer bidirectional GRU (hidden size 64) processes Transformer outputs, concatenating hidden states. GRU update equations:

$$r_t=\sigma(W_r z_t+U_r h_{t-1}), \quad u_t=\sigma(W_u z_t+U_u h_{t-1}),$$

$$\tilde h_t=\tanh(W_h z_t+U_h(r_t\odot h_{t-1})), \quad h_t=(1-u_t)\odot h_{t-1}+u_t\odot \tilde h_t.$$

• Attention Pooling: Scalar scores $e_t=f(h_t^{\mathrm{bi}})$, softmax normalization to $\alpha_t$, pooled $z=\sum_{t=1}^L \alpha_t h_t^{\mathrm{bi}}$, mapped to output scalar $\hat y$.
• Loss & Regularization: Mean squared error with dropout (p=0.3).
• Training Dataset: 12 sub-links over Gothenburg (June–Aug 2015), 1-min RSL inputs, mm/h rain gauge targets.

This architecture is quantitatively superior to both deep learning and physics-based baselines. At Torp site, TabGRU RMSE=0.34 mm/h, $R^2=0.91$, PCC=0.96. At Barl site, RMSE=0.25 mm/h, $R^2=0.96$, PCC=0.98. Compared to the power-law physics model (PL), TabGRU shows higher accuracy, mitigating PL’s overestimation during heavy rainfall. The attention-pooling mechanism improves peak alignment, while the BiGRU layer reduces lag and bias due to wet-antenna effects (Li et al., 2 Dec 2025).

3. Table Structure Extraction: Bidirectional GRU-Based Pipeline

TabGRU for document table structure extraction applies bidirectional GRU networks in a sequential labeling paradigm:

• Input & Preprocessing: Detected table regions are cropped, subjected to morphological filtering, adaptive binarization, resized to $1600 \times 512$, and dilated to accentuate separators.
• Separator Identification: Columns and rows are scanned via two distinct BiGRU networks, each treating pixel vectors ($x_t$) as time-steps.
• Network Structure—Columns:
  • Input: Each column ($x_t \in \mathbb{R}^{512}$), $t=1 \dots 1600$.
  • Two-layer BiGRU (hidden 512), output $h_t$.
  • FC layer: $y_t = W_{\mathrm{fc}} h_t + b_{\mathrm{fc}}$ ($W_{\mathrm{fc}} \in \mathbb{R}^{2 \times 512}$), softmax on separator vs. content.
• Network Structure—Rows:
  • Input: Each row ($x_t \in \mathbb{R}^{1600}$), $t=1 \dots 512$.
  • Two-layer BiGRU (hidden 1024).
  • FC layer as above.
• Postprocessing: Segmentation bands extracted by thresholding softmax outputs; outermost bands discarded.

TabGRU demonstrates high precision and recall against state-of-the-art baselines. On UNLV, correct column segmentation: TabGRU 55.31% (versus Bi-LSTM 49.05%); row segmentation: TabGRU 58.45% (Bi-LSTM 51.62%). On ICDAR 2013, TabGRU achieves precision 96.92%, recall 90.12%, F1 93.39% (Khan et al., 2020). This architecture’s reliance on raw pixel-patterns ensures immunity to OCR errors and robustness across table layouts.

4. Mathematical Formulation and Learning Dynamics

Both TabGRU models utilize the canonical GRU unit equations: $$z_t = \sigma(W_z x_t + U_z h_{t-1} + b_z), \quad r_t = \sigma(W_r x_t + U_r h_{t-1} + b_r),$$

$$\tilde h_t = \tanh(W_h x_t + U_h(r_t \odot h_{t-1}) + b_h),$$

$$h_t = z_t \odot h_{t-1} + (1-z_t) \odot \tilde h_t.$$

In the rainfall estimator, Transformer self-attention is defined as $$\mathrm{Attention}(Q,K,V) = \mathrm{softmax}(QK^\mathsf{T}/\sqrt{d_k})V$$, aggregating contextual temporal dependencies. The table extractor models sequential dependencies along spatial axes, translating softmax predictions into segmentation maps via weighted binary cross-entropy (class-balanced) loss.

5. Performance and Benchmarking

TabGRU consistently surpasses contemporaneous architectures in respective domains.

Application	Dataset	Benchmark (F1, R²)	TabGRU Result
Rainfall Estimation	Gothenburg CML	R² (PL): 0.83–0.88	R²: 0.91, 0.96
Table Segmentation	ICDAR 2013	F1 (S17): 91.44%	F1: 93.39%
Table Segmentation	UNLV	Corr (BiLSTM): 49%	Corr: 55–58%

TabGRU’s performance improvement traces to its hybrid or sequential sequence modeling design, explicit use of attention mechanisms, and feature embedding for temporal/spatial dynamics (Li et al., 2 Dec 2025, Khan et al., 2020).

6. Limitations and Prospective Directions

Both TabGRU implementations highlight domain-specific constraints:

• The rainfall model is validated solely on Gothenburg CML data; transferability to other climates remains untested. Micro-rain event detection is challenging, and simple RNNs may suffice in very low-signal regimes. Wet-antenna effects are modeled implicitly; architectural and loss function modifications (e.g., focal loss) could address class imbalance or event detection (Li et al., 2 Dec 2025).
• The table extraction pipeline’s generalization benefits from morphological preprocessing, but relies on precise cropping and fixed input sizes. It does not use OCR features, which points to potential hybridization with LLMs for cell-content recognition. Real-time inference is feasible on GPUs given the configuration (Khan et al., 2020).

A plausible implication is that further integration of Transformer-based modules, relative positional encoding, and state-aware event labeling may enhance robustness for both applications.

7. Contextual Significance and Research Trajectory

TabGRU illustrates the adaptability of the bidirectional GRU paradigm to heterogeneous sequence data, enabling robust segmentation in spatial domains and highly accurate forecasting in spatiotemporal sensing networks. The architectures sidestep heuristic-driven, feature-engineered baselines, with direct sequence-to-label mapping. The approach epitomizes current trends in deep learning: hybrid combinations of attention mechanisms, learnable embeddings, and sequential modeling for structured prediction tasks. The name “TabGRU” thus references versatile instantiations unified by bidirectional GRU sequence modeling and superior empirical benchmark attainment (Li et al., 2 Dec 2025, Khan et al., 2020).