Rethinking Cross-Channel Importance in Time-Series Forecasting

Multivariate time-series analysis involves extracting informative representations from sequences of multiple interdependent variables, supporting tasks such as forecasting, imputation, and anomaly detection. In real-world scenarios, these variables are typically collected from a shared context or underlying phenomenon, suggesting the presence of latent dependencies across time and channels that can be leveraged to improve performance. However, recent findings show that channel-independent (CI) models, which assume no inter-variable dependencies, often outperform channel-dependent (CD) models that explicitly model such relationships. This surprising result indicates that current CD models may not fully exploit their potential due to limitations in how dependencies are captured. Recent studies have revisited channel dependence modeling with various approaches; however, these methods often employ indirect modeling strategies, which can lead to meaningful dependencies being overlooked. To address this issue, we introduce XCTFormer, a transformer-based channel-dependent (CD) model that explicitly captures cross-temporal and cross-channel dependencies via an enhanced attention mechanism. The model operates in a token-to-token fashion, modeling pairwise dependencies between every pair of tokens across time and channels. The architecture comprises (i) a data processing module, (ii) a novel Cross-Relational Attention Block (CRAB) that increases capacity and expressiveness, and (iii) an optional Dependency Compression Plugin (DeCoP) that improves scalability. Through extensive experiments on three time-series benchmarks, we show that XCTFormer achieves strong results compared to widely recognized baselines; in particular, it attains state-of-the-art performance on the imputation task, outperforming the second-best method by an average of 20.8% in MSE and 15.3% in MAE.

Multivariate time series forecasting is critical in many real-world systems, and thus modeling cross-channel dependencies is essential. Although existing methods improve overall accuracy by enhancing representations and cross-channel interactions, it remains challenging to reliably capture inter-variable dependencies under specific conditions. We observe that dependencies in real data are often state-dependent and noisy; in such cases, dense interactions can amplify spurious correlations and lead to representation over-smoothing, which may yield unreliable predictions in certain scenarios. Motivated by this, we propose MS-FLOW, a sparse-bottleneck framework that explicitly models inter-variable interaction as capacity-limited information flow. Specifically, MS-FLOW replaces fully connected communication with selective sparse routing, retaining only a few critical dependency paths and injecting cross-variable signals under a strict communication budget, thereby suppressing redundant connections and spurious-correlation propagation. Extensive experiments demonstrate that MS-FLOW learns more reliable multivariate correlations, achieving state-of-the-art forecasting accuracy on 12 real-world benchmarks while producing fewer yet more reliable dependencies, shifting multivariate forecasting from "more interaction" to "more effective interaction".

Recent advances in explaining time series (TS) models have produced methods that identify which past values a prediction depends on. However, most existing methods return a single importance vector, assuming that every predicted step depends on the same past values. In this paper, we show that this assumption does not hold, as different forecast steps depend on different past values. Motivated by this observation, we propose Horizon-Resolved eXplanation (HRX), which adds a horizon axis to the explanation, so that every forecast step receives its own importance map. HRX is a simple yet effective plug-in framework with three components: 1) an estimator that reads these maps out of any differentiable forecaster without modifying the TS backbone, 2) an evaluation protocol that validates the horizon axis by measuring how much a single forecast step changes when the inputs an importance map ranks highest are removed, and 3) a rank criterion that predicts in advance whether the axis is worth resolving on a given TS. We further show that this step-wise dependence is low-dimensional, as the explanations of all steps are built from a few shared maps whose number does not grow with the forecast length. Extensive experiments across various backbones and datasets show that the improvement comes from the horizon axis and holds for estimators of previous explanation methods. Code is available at https://github.com/seunghan96/HRX.