Interpretable Bidirectional Network for Forecasting

• The paper introduces IBN, which integrates Uncertainty-Aware Interpolation, Gaussian-kernel Graph Convolution, and a Bidirectional Recursive Unit to address variable missingness in multivariate time series forecasting.
• IBN employs uncertainty-aware interpolation and explicit graph construction to yield reliable reconstructions and interpretable spatial relations, mitigating biases from absent historical data.
• Empirical evaluations show IBN achieves state-of-the-art performance, particularly under severe missingness scenarios, with ablation studies confirming the contribution of each module.

Searching arXiv for the specified paper and closely related work to ground the article with current citations. {"^^^^^^^^8query8 (Ma et al., 9 Sep 2025) IBN Interpretable Bidirectional-modeling Network for Multivariate Time Series Forecasting with Variable Missing GinAR8^^^^^^^^", "^^^^^^^^8max_results8 ^^^^8arXiv (Ma et al., 9 Sep 2025) IBN Interpretable Bidirectional-modeling Network for Multivariate Time Series Forecasting with Variable Missing GinAR8query8^^^^} {"^^^^^^^^8query8 multivariate time series forecasting variable missing arXiv8^^^^^^^^", "^^^^^^^^8max_results8 ^^^^8arXiv (Ma et al., 9 Sep 2025) IBN Interpretable Bidirectional-modeling Network for Multivariate Time Series Forecasting with Variable Missing GinAR8query8^^^^} {"^^^^^^^^8query8 Bidirectional-modeling Network for Multivariate Time Series Forecasting with Variable Missing^^^^^^^^8\8 "^^^^^^^^8max_results8 ^^^^8max_results8^^^^} Interpretable Bidirectional-modeling Network (IBN) is a forecasting architecture for multivariate time series forecasting under variable missingness, a setting in which entire variables may be absent throughout the historical window rather than only individual observations being missing. It is introduced as an extension beyond conventional spatial-temporal graph neural networks, which depend on complete variable histories and reliable inter-variable graph learning, and therefore become unstable or biased when missingness artifacts contaminate reconstruction and message passing. The model integrates Uncertainty-Aware Interpolation (UAI), Gaussian kernel-based Graph Convolution (GGCN), and a bidirectional recursive unit (Bi-RU) to improve reconstruction reliability, spatial interpretability, and temporal expressiveness (&&&^^^^8query8^^^^&&&).

^^^^8arXiv (Ma et al., 9 Sep 2025) IBN Interpretable Bidirectional-modeling Network for Multivariate Time Series Forecasting with Variable Missing GinAR8^^^^. Problem setting and motivation

IBN is defined for multivariate time series forecasting with missing-input data

PRESERVED_PLACEHOLDER_^^^^8query8^^^^

where the observed input can include a missing-input version PRESERVED_PLACEHOLDER_^^^^8arXiv (Ma et al., 9 Sep 2025) IBN Interpretable Bidirectional-modeling Network for Multivariate Time Series Forecasting with Variable Missing GinAR8^^^^ in which entire variables are zero-filled (&&&^^^^8query8^^^^&&&). This formulation targets a stricter regime than ordinary random pointwise missingness: a whole sensor channel or variable can be unavailable across the historical window, so downstream spatial-temporal modeling must proceed from a partially observed multivariate history.

The motivating claim is that standard spatial-temporal graph neural networks usually rely on two assumptions: complete variable histories and reliable inter-variable graph learning. Under variable missingness, these assumptions fail in several linked ways. Graph learning becomes unstable or biased because absent histories provide little reliable signal; spatial correlation estimation is degraded because missingness artifacts can be confounded with actual correlations; temporal modeling is weakened because noisy reconstructions accumulate errors in recurrent modules; and interpretability remains poor when learned relations depend mainly on latent adaptive embeddings (&&&^^^^8query8^^^^&&&).

Within this problem setting, GinAR is described as the first method to address variable missingness using interpolation attention and adaptive graph learning. IBN is positioned as a response to three shortcomings attributed to that baseline: it makes reconstruction uncertainty-aware, replaces implicit graph adaptation with a graph mechanism grounded in node-feature distances and a Gaussian kernel, and replaces a simple unidirectional recursive unit with bidirectional temporal modeling (&&&^^^^8query8^^^^&&&).

^^^^8max_results8^^^^. Architectural composition

The architecture is organized around three design goals: reliability in reconstruction, interpretable spatial modeling, and stronger temporal modeling. These goals correspond directly to the three main components: UAI, GGCN, and Bi-RU (&&&^^^^8query8^^^^&&&).

Component	Function	Interpretability contribution
UAI	Reconstruct missing variables with MC Dropout-based uncertainty estimation	Exposes reconstructed values and uncertainty scores
GGCN	Learn spatial dependencies from predefined topology and Gaussian-kernel feature similarity	Separates static topology from dynamic feature-driven relations
Bi-RU	Encode temporal dependencies in both directions	Makes temporal contribution depend on both ends of the observed window

The resulting pipeline begins from GinAR-style interpolation attention, refines the reconstructed variables through uncertainty-aware weighting, propagates them through graph convolution using both predefined and feature-derived adjacency structure, and then models temporal dependencies bidirectionally before decoding the forecast (&&&^^^^8query8^^^^&&&). A plausible implication is that IBN is designed so that each stage reduces a distinct failure mode introduced by variable missingness: unreliable reconstruction, ambiguous spatial relations, and limited temporal context.

^^^^8query8^^^^. Uncertainty-Aware Interpolation

UAI is the reconstruction module. Starting from a time-step input PRESERVED_PLACEHOLDER_^^^^8max_results8^^^^, interpolation attention produces

PRESERVED_PLACEHOLDER_^^^^8query8^^^^

IBN then applies a linear transform with MC Dropout over multiple stochastic passes,

PRESERVED_PLACEHOLDER_^^^^8GinAR multivariate time series forecasting variable missing arXiv8^^^^

where PRESERVED_PLACEHOLDER_^^^^8max_results8^^^^, PRESERVED_PLACEHOLDER_^^^^8query8^^^^, the dropout rate is PRESERVED_PLACEHOLDER_^^^^8\8^^^^, and the number of Monte Carlo samples is $S=10$ (&&&^^^^8query8^^^^&&&).

From these samples, the model computes a predictive mean and predictive standard deviation,

$$\mu = \frac{1}{S}\sum_{s=1}^{S}\mathbf{m}^{(s)}, \qquad \sigma = \sqrt{\frac{1}{S}\sum_{s=1}^{S}\left(\mathbf{m}^{(s)} - \mu\right)^2}.$$

The final reconstruction is then

PRESERVED_PLACEHOLDER_^^^^8arXiv (Ma et al., 9 Sep 2025) IBN Interpretable Bidirectional-modeling Network for Multivariate Time Series Forecasting with Variable Missing GinAR8query8^^^^

This uncertainty-weighted interpolation is the defining step of UAI: low uncertainty preserves the reconstructed value, whereas high uncertainty suppresses it (&&&^^^^8query8^^^^&&&).

The paper interprets MC Dropout as a Bayesian approximation for uncertainty estimation. In this framework, stochastic forward passes approximate a distribution over reconstructions without requiring an explicit probabilistic decoder. The interpretability claim is concrete rather than merely rhetorical: UAI outputs both a reconstructed value and an uncertainty score, allowing inspection of which reconstructions are risky. The reported qualitative analysis states that higher reconstruction error correlates with higher estimated uncertainty, and that this uncertainty lowers the weight assigned to the reconstruction in later processing (&&&^^^^8query8^^^^&&&). This suggests that IBN treats imputation not as a hidden preprocessing step but as an inspectable and confidence-modulated part of forecasting.

^^^^8GinAR multivariate time series forecasting variable missing arXiv8^^^^. Gaussian kernel-based graph convolution

GGCN is the spatial module. Its purpose is to combine static spatial structure with dynamic feature-driven correlations. The model uses two graph components: a predefined graph PRESERVED_PLACEHOLDER_^^^^8arXiv (Ma et al., 9 Sep 2025) IBN Interpretable Bidirectional-modeling Network for Multivariate Time Series Forecasting with Variable Missing GinAR8arXiv (Ma et al., 9 Sep 2025) IBN Interpretable Bidirectional-modeling Network for Multivariate Time Series Forecasting with Variable Missing GinAR8^^^^, built from known external information such as geographical distance or physical connectivity, and a dynamic Gaussian graph PRESERVED_PLACEHOLDER_^^^^8arXiv (Ma et al., 9 Sep 2025) IBN Interpretable Bidirectional-modeling Network for Multivariate Time Series Forecasting with Variable Missing GinAR8max_results8^^^^, built from reconstructed node features (&&&^^^^8query8^^^^&&&).

For nodes PRESERVED_PLACEHOLDER_^^^^8arXiv (Ma et al., 9 Sep 2025) IBN Interpretable Bidirectional-modeling Network for Multivariate Time Series Forecasting with Variable Missing GinAR8query8^^^^ and PRESERVED_PLACEHOLDER_^^^^8arXiv (Ma et al., 9 Sep 2025) IBN Interpretable Bidirectional-modeling Network for Multivariate Time Series Forecasting with Variable Missing GinAR8GinAR multivariate time series forecasting variable missing arXiv8^^^^, feature distance is computed as

PRESERVED_PLACEHOLDER_^^^^8arXiv (Ma et al., 9 Sep 2025) IBN Interpretable Bidirectional-modeling Network for Multivariate Time Series Forecasting with Variable Missing GinAR8max_results8^^^^

and then transformed by a Gaussian kernel,

PRESERVED_PLACEHOLDER_^^^^8arXiv (Ma et al., 9 Sep 2025) IBN Interpretable Bidirectional-modeling Network for Multivariate Time Series Forecasting with Variable Missing GinAR8query8^^^^

where PRESERVED_PLACEHOLDER_^^^^8arXiv (Ma et al., 9 Sep 2025) IBN Interpretable Bidirectional-modeling Network for Multivariate Time Series Forecasting with Variable Missing GinAR8\8^^^^ is the embedding size (&&&^^^^8query8^^^^&&&). The dynamic adjacency is subsequently normalized with self-loops and softmax. The graph-convolved representation combines both graph sources,

PRESERVED_PLACEHOLDER_^^^^8arXiv (Ma et al., 9 Sep 2025) IBN Interpretable Bidirectional-modeling Network for Multivariate Time Series Forecasting with Variable Missing GinAR88^^^^

The Gaussian kernel is central to the claimed interpretability and robustness of the module. The paper attributes four effects to this choice: it compresses extreme distances, stabilizes optimization, avoids gradient explosion or vanishing, and yields edge weights with a natural similarity interpretation. Because closer features receive larger edge weights, the learned dynamic graph remains readable in terms of variable similarity rather than opaque latent affinity (&&&^^^^8query8^^^^&&&).

The interpretability of GGCN follows from the explicit separation between PRESERVED_PLACEHOLDER_^^^^8arXiv (Ma et al., 9 Sep 2025) IBN Interpretable Bidirectional-modeling Network for Multivariate Time Series Forecasting with Variable Missing GinAR8^^^^9 and PRESERVED_PLACEHOLDER_^^^^8max_results8query8^^^^. The former exposes stable physical or topological structure; the latter exposes time-varying feature-based relations. The qualitative discussion reports that the learned graph can distinguish stable physical relations from dynamic dependencies. This suggests that the model’s spatial reasoning is intended to remain inspectable even when some variables are reconstructed rather than directly observed.

^^^^8max_results8^^^^. Bidirectional recursive modeling and decoding

The temporal backbone of IBN consists of a bidirectional recursive unit followed by a simpler unidirectional recursive unit and a decoder (&&&^^^^8query8^^^^&&&). The recursive cell uses gated updates defined from UAI and GGCN outputs: PRESERVED_PLACEHOLDER_^^^^8max_results8arXiv (Ma et al., 9 Sep 2025) IBN Interpretable Bidirectional-modeling Network for Multivariate Time Series Forecasting with Variable Missing GinAR8^^^^

PRESERVED_PLACEHOLDER_^^^^8max_results8max_results8^^^^

PRESERVED_PLACEHOLDER_^^^^8max_results8query8^^^^

PRESERVED_PLACEHOLDER_^^^^8max_results8GinAR multivariate time series forecasting variable missing arXiv8^^^^

The observed sequence is processed in both directions, producing forward states

PRESERVED_PLACEHOLDER_^^^^8max_results8max_results8^^^^

and backward states

PRESERVED_PLACEHOLDER_^^^^8max_results8query8^^^^

with each hidden state in PRESERVED_PLACEHOLDER_^^^^8max_results8\8^^^^ (&&&^^^^8query8^^^^&&&). These are concatenated and passed to a second unidirectional recursive unit whose input dimension is PRESERVED_PLACEHOLDER_^^^^8max_results88^^^^.

The stated reason for bidirectionality is that a simple recursive unit uses only past-to-future information, whereas Bi-RU allows the model to exploit temporal context from both ends of the observed window. The paper associates this with three advantages: capturing symmetric temporal patterns, modeling dependencies that become clearer when viewed backward, and building richer latent temporal representations before decoding (&&&^^^^8query8^^^^&&&).

The decoder concatenates the last hidden states from the Bi-RU and the second recursive unit, and then applies two PRESERVED_PLACEHOLDER_^^^^8max_results8^^^^9 convolution layers: the first with kernel size PRESERVED_PLACEHOLDER_^^^^8query8query8^^^^, the second with kernel size PRESERVED_PLACEHOLDER_^^^^8query8arXiv (Ma et al., 9 Sep 2025) IBN Interpretable Bidirectional-modeling Network for Multivariate Time Series Forecasting with Variable Missing GinAR8^^^^, and PRESERVED_PLACEHOLDER_^^^^8query8max_results8^^^^ kernels in both layers, producing a forecast of length PRESERVED_PLACEHOLDER_^^^^8query8query8^^^^ (&&&^^^^8query8^^^^&&&). The provided formulation does not specify a separate standalone loss equation; training is described as standard regression-based forecasting, with performance reported through RMSE, MAE, and MAPE (&&&^^^^8query8^^^^&&&).

^^^^8query8^^^^. Empirical evaluation and ablation results

IBN is evaluated on four public benchmarks: METR-LA, PEMS-BAY, PEMS^^^^8query8GinAR multivariate time series forecasting variable missing arXiv8^^^^, and PEMS^^^^8query88^^^^, with random variable masking rates of PRESERVED_PLACEHOLDER_^^^^8query8GinAR multivariate time series forecasting variable missing arXiv8^^^^, PRESERVED_PLACEHOLDER_^^^^8query8max_results8^^^^, and PRESERVED_PLACEHOLDER_^^^^8query8query8^^^^ (&&&^^^^8query8^^^^&&&). The reported baselines are MegaCRN, LGnet, GC-VRNN, TriD-MAE, BiTGraph, and GinAR. Evaluation uses RMSE, MAPE, and MAE.

The principal empirical claim is that IBN achieves state-of-the-art or near-best performance overall, especially under more severe variable missingness. Average MAE improvements over GinAR across the four datasets are reported as PRESERVED_PLACEHOLDER_^^^^8query8\8^^^^ at PRESERVED_PLACEHOLDER_^^^^8query88^^^^ missingness, PRESERVED_PLACEHOLDER_^^^^8query8^^^^9 at PRESERVED_PLACEHOLDER_^^^^8GinAR multivariate time series forecasting variable missing arXiv8query8^^^^, and PRESERVED_PLACEHOLDER_^^^^8GinAR multivariate time series forecasting variable missing arXiv8arXiv (Ma et al., 9 Sep 2025) IBN Interpretable Bidirectional-modeling Network for Multivariate Time Series Forecasting with Variable Missing GinAR8^^^^ at PRESERVED_PLACEHOLDER_^^^^8GinAR multivariate time series forecasting variable missing arXiv8max_results8^^^^ (&&&^^^^8query8^^^^&&&). The growth of the gain with missingness is presented as evidence that uncertainty-aware reconstruction and bidirectional temporal modeling become more valuable as input reliability declines.

The dataset-level observations are more qualified. On METR-LA, IBN improves MAE over GinAR and often improves RMSE, though not on every metric. On PEMS-BAY, GinAR remains slightly stronger on some metrics, but IBN is competitive and improves certain settings. On PEMS^^^^8query8GinAR multivariate time series forecasting variable missing arXiv8^^^^ and PEMS^^^^8query88^^^^, IBN shows strong gains, especially under severe missingness (&&&^^^^8query8^^^^&&&). These details matter because they place the model’s reported advantages within a non-uniform empirical landscape rather than as a universal dominance claim.

Ablation studies are conducted at PRESERVED_PLACEHOLDER_^^^^8GinAR multivariate time series forecasting variable missing arXiv8query8^^^^ missingness with three substitutions: UAI PRESERVED_PLACEHOLDER_^^^^8GinAR multivariate time series forecasting variable missing arXiv8GinAR multivariate time series forecasting variable missing arXiv8^^^^ IA, GGCN PRESERVED_PLACEHOLDER_^^^^8GinAR multivariate time series forecasting variable missing arXiv8max_results8^^^^ AGCN, and Bi-RU PRESERVED_PLACEHOLDER_^^^^8GinAR multivariate time series forecasting variable missing arXiv8query8^^^^ Uni-RU. Replacing each of these components degrades performance, supporting the claim that all three modules contribute materially to the final system (&&&^^^^8query8^^^^&&&). The interpretation of the ablations is explicit: uncertainty modeling improves reconstruction robustness, Gaussian-kernel spatial modeling outperforms more implicit adaptive graph construction, and bidirectional temporal context captures richer dependencies than unidirectional recurrence.

^^^^8\8^^^^. Interpretability, limitations, and acronym disambiguation

The interpretability claim of IBN is modular. UAI is interpretable because it surfaces both reconstructed values and uncertainty estimates, so risky imputations can be identified directly. GGCN is interpretable because it separates static topology from dynamic feature similarity and applies a Gaussian distance-to-similarity transform with a transparent geometric meaning. Temporal interpretability is attributed to Bi-RU, which makes the forecast depend on context from both ends of the observed window rather than only on forward recurrence (&&&^^^^8query8^^^^&&&).

The limitations stated or inferable from the provided formulation are correspondingly specific. The model still relies on interpolation attention as the starting point for reconstruction. Its experiments use random variable masking, which may not represent all real-world missingness patterns. The interpretability it offers is at the level of uncertainty-aware reconstruction and graph structure rather than full causal interpretability. Its performance is strong overall but not uniformly best on every metric and dataset, particularly in some PEMS-BAY and PEMS^^^^8query88^^^^ settings (&&&^^^^8query8^^^^&&&). This suggests that the architecture is best understood as a reliability- and inspection-oriented extension of graph-based forecasting under missingness, not as a universal solution to all forms of distributional shift or structural incompleteness.

The acronym “IBN” is also used in unrelated literatures and therefore requires disambiguation. In recommender systems, “IBN” can refer to an attention-based bidirectional LSTM path-reasoning model over heterogeneous information networks, where interpretability comes from explicit user-item paths and attention over nodes or paths (&&&^^^^8max_results8GinAR multivariate time series forecasting variable missing arXiv8^^^^&&&). In computer vision, “IBN-Net” denotes an Instance-Batch Normalization Network that combines IN and BN inside CNN backbones to improve source-domain learning and cross-domain appearance robustness (&&&^^^^8max_results8max_results8^^^^&&&). These usages are architecturally and methodologically distinct from the Interpretable Bidirectional-modeling Network for multivariate time series forecasting.