CASE-Net: Deep Spatio-Temporal Representation Learning via Causal Attention and Channel Recalibration for Multivariate Time Series Classification

1 Introduction

The surge in IoT and wearable data makes MTS classification a core AI challenge, ranging from clinical diagnostics to activity recognition [Morid et al., 2023; Liu et al., 2024a]. Unlike static data modalities, MTS exhibits profound Spatio-Temporal Complexity: temporal dimensions encapsulate non-stationary dynamics across multiple granularities, while spatial dimensions involve intricate, high-dimensional couplings between heterogeneous variables [Wang et al., 2024b]. Extracting robust representations from these complex sequences is a core challenge.

Multi-scale analysis has proven effective in capturing cross-granularity patterns. Building upon this, recent breakthroughs in Multi-scale Disentanglement have successfully introduced scale-shared and scale-specific orthogonal constraints to mitigate inter-scale redundancy [Liu et al., 2025], fostering a solid theoretical foundation for representation learning. However, these frameworks typically operate under the implicit assumption that the spatio-temporal features fed into the disentanglement module are sufficiently robust and noise-resilient. Critically, we argue that this assumption is often violated in real-world scenarios due to two representation bottlenecks in current feature extraction pipelines.

* Corresponding author: hwa229@163.com

First, existing encoders often suffer from temporal blindness: recurrent models struggle with long-range dependencies, while bidirectional processing may introduce futureinduced stochastic fluctuations into current representations. In physical systems, the arrow of time dictates that current states should not depend on future observations. For nonstationary MTS, such future observations often correspond to evolutionary noise or sensor artifacts rather than useful semantic context, leading to temporal confounding and distorted latent motifs.

Second, high-dimensional sensing systems also exhibit spatial channel heterogeneity. Variable importance is inherently dynamic and context-dependent, yet many architectures treat all channels with homogeneous priority and leave noise filtering to the downstream disentanglement module. This increases the burden on the disentanglement head and fundamentally limits the purity of the distilled features. CASENET mitigates these two bottlenecks by redefining the causal mask as a structural noise filter and introducing channel recalibration as a proactive spatial information bottleneck.

Beyond time-series analysis, compositional representation learning has also been actively explored in composed image and video retrieval, where models disentangle target semantics from modification cues to support robust cross-modal matching [Li et al., 2025; Fu et al., 2025; Huang et al., 2025; Chen et al., 2025; Zhang et al., 2026c; Li et al., 2026a; Li et al., 2026b]. Inspired by this general principle of composition-aware representation learning, we investigate compositionality along temporal-scale and channel dimensions in MTS, where future-induced stochasticity and sensor heterogeneity become the dominant obstacles. Motivated by the insight that better representation facilitates better disentanglement, we propose CASE-NET. Our objective is to implement structural manifold pre-conditioning on the upstream representations to support high-fidelity feature decoupling.

Our contributions are summarized as follows:

• Causal-Aware Temporal Reconstruction: We introduce a causal attention framework that explicitly enforces a physical arrow-of-time prior, filtering future-induced evolutionary noise to help preserve the integrity of latent action motifs. By coordinating local causal convolutions with global masked self-attention, the CASE encoder functions as a structural manifold pre-conditioner that is architecture-agnostic, empowering various downstream tasks as a high-fidelity front-end.
• Context-Adaptive Spatial Recalibration: We implement a channel-wise information bottleneck via adaptive recalibration (SE module) to execute proactive manifold pre-conditioning. By suppressing non-discriminative spatial artifacts before the disentanglement stage, this mechanism encourages high-saliency variables to propagate to the latent space, thereby enhancing the purity of the distilled features.
• Holistic Evaluation across Six Heterogeneous Domains: Unlike conventional approaches validated only in a single domain, CASE-NET was fully evaluated on six benchmark datasets with diverse physical characteristics and data distributions. Results show that CASE-NET established new state-of-the-art benchmarks on four tasks.

2 RelatedWork

2.1 Deep Temporal Modeling

Extracting temporal dependencies is central to MTS classification [Qin et al., 2017; Zhu et al., 2023]. While traditional recursive models like LSTMs and GRUs utilize inductive bias for sequential encoding, they often suffer from vanishing gradients and a critical paradigm limitation: Temporal Blindness. Most recurrent architectures lack temporal causality, leading to spurious future-information leakage that compromises reliability in sensitive domains like clinical diagnostics. Although recent works attempt to encode causality through transfer entropy [Sun et al., 2024] or spatiotemporal information transformation [Cai et al., 2025], these often incur heavy computational costs. CASE-NET mitigates this by re-engineering the encoder with causal convolutions and masked self-attention, enforcing temporal arrows to capture global dynamic motifs with high fidelity.

Recent forecasting models further exploit multi-offset temporal interactions, semantic fusion, and non-ideal data utilization to strengthen multivariate dependency learning [Zhang et al., 2026a; Zhang et al., 2026b; Qiu et al., 2025b; Wang et al., 2026b]. Nevertheless, these methods primarily emphasize predictive dependency modeling, whereas CASE-NET focuses on classification-oriented representation purification under temporal causality. In addition, ensuring high-fidelity representations remains a challenge, as explored by Zhang et al. [Zhang et al., 2022] through time-frequency consistency. In contrast, CASE-NET enforces a causal inductive bias to improve manifolds, especially in non-stationary states. This distinguishes it from latent SDE-Attention [Fang et al., 2025], which focuses on irregular sampling, as we optimize the upstream representation manifold for deterministic MTS.

Recently, Xu et al. [Xu et al., 2025] proposed a spatiotemporal fusion architecture for dynamic ECN analysis, using Granger-causality-based discovery to model the evolution of brain networks. While their approach focuses on learning the explicit causal structure from observational data, CASE-NET leverages a causal inductive bias through architectural masking. We argue that for non-stationary classification tasks, enforcing causality as a structural prior is more effective for filtering future-induced stochastic noise than explicit causal discovery, which can be sensitive to latent confounding factors.

2.2 Channel Saliency and Information Bottleneck

Attention mechanisms have shifted MTS modeling toward dynamic recalibration. Recent architectures have introduced cross-channel attention [Hao and Cao, 2020; Zhang et al., 2025] or association adapters [Lin et al., 2025] to handle multivariate dependencies. Recent developments such as iTransformer [Liu et al., 2024b] have rethought the role of channel dependencies by inverting the transformer structure. However, many frameworks still rely on a suboptimal assumption of Spatial Channel Homogeneity, treating sensors with uniform priority regardless of their varying Signal-to-Noise Ratios [Cheng et al., 2023; Huang et al., 2023]. Consistent with feature-centric explanation models like CAFO [Kim et al., 2024], CASE-NET leverages Information Bottleneck theory and integrates an adaptive recalibration mechanism to execute proactive feature-cleaning, helping high-saliency variables propagate to the latent space for robust disentanglement.

2.3 Multi-Scale Analysis and Disentanglement Fidelity

Recent milestones like DisMS-TS have introduced multiscale disentanglement to mitigate inter-scale redundancy [Liu et al., 2025]. At the benchmark and optimization levels, recent studies have emphasized fair time-series evaluation, non-ideal data utilization, and scalable optimization for time-series modeling [Qiu et al., 2024; Wang et al., 2026b; Wang et al., 2026a; Qiu et al., 2025a]. Unlike multi-scale token mixing [Zhong et al., 2025], hierarchical temporalfrequency fusion [Song et al., 2025], or multi-view metalearning [Zhang et al., 2024] that prioritize feature fusion, the efficacy of decoupling is fundamentally contingent upon the fidelity of underlying representations. Existing frameworks often overlook feature extractor quality, creating a performance bottleneck when processing noise-contaminated or temporally inconsistent inputs. Departing from efforts focused solely on downstream decoupling logic, CASE-NET focuses on optimizing the quality of the upstream representation manifold through structural pre-conditioning. By providing causal-aware spatio-temporal priors, our model bridges the gap between raw sensing data and decoupled representations, establishing new performance ceilings across heterogeneous domains.

3 Methodology

3.1 Overall Architecture

CASE-NET enhances classification through three stages (Fig. 1): Multi-scale Projection, the CASE Encoder, and decomposition. The CASE encoder is weight-shared across all S branches. This allows the model to learn a scale-invariant causal-spatial transformation while maintaining efficiency.

Formal Rationale: We define the CASE encoder not merely as a collection of components, but as a synergistic information bottleneck and a manifold pre-conditioner designed to address the fundamental problem of distorted input manifolds in existing frameworks. In this paper, structural manifold preconditioning refers to representation-level conditioning before the shared-specific disentanglement head, implemented through causal temporal masking and bottleneck-style channel recalibration. Existing multi-scale encoders often suffer from temporal blindness and channel homogeneity, which introduce future-information leakage and spatial noise. Such contaminated inputs force the downstream disentanglement loss (Ldiff ) to search within an excessively complex hypothesis space. By improving the input manifold through structural pre-conditioning before it enters the sensitive disentanglement backend, we significantly narrow the search space of the downstream loss function and promote high-resolution representations.

3.2 Generic Multi-Scale Projection

To capture the polymorphic feature mapping of MTS at different granularities, we construct a multi-scale input space consisting of S branches. Specifically, given the input X ∈ RN×L, we utilize a set of convolutional operators with heterogeneous receptive fields and strides to project it as a multiresolution view set V = {Vs}Ss=1 , where:

Non-uniform sampling here establishes multi-granularity representations, providing context for the CASE encoder. Importantly, this stage only initializes scale-specific views, while the subsequent weight-shared CASE encoder imposes a unified causal-spatial transformation across all resolutions.

3.3 Causal Adaptive Spatio-Temporal Encoder

The CASE encoder serves as the core architecture for spatio-temporal feature extraction and is designed to solve the representation fidelity bottleneck in multi-scale decoupling. Specifically, the encoder implements structural preconditioning by integrating two complementary modules: Causal Temporal Attention and Channel Adaptive Recalibration. This dual-constrained design encourages the resulting latent space to be both physically consistent and semantically sparse.

Causal Temporal Attention

The CTA module is designed to overcome the bottlenecks of traditional recurrent models in long-range dependency modeling while imposing a robust temporal causality constraint. By coupling local causal operators (Dilated Convolutions) with global masked self-attention, it promotes autoregressive consistency (ht = f({xτ}τ≤t)). This configuration mitigates future information leakage while capturing multi-scale, long-range dependencies across the sequence.

In contrast to bidirectional transformers or explicit discovery models [Xu et al., 2025], CASE-NET recognizes that in non-stationary regimes (e.g., NASDAQ), future observations often represent stochastic evolutionary noise relative to the current state. By enforcing causality, our CTA module functions as a Structural Noise Filter. This helps the encoder prioritize the capture of underlying action motifs rather than fitting transient signal fluctuations, effectively executing Temporal De-confounding through architectural constraints. By enforcing this Manifold Pre-conditioning, we narrow the downstream hypothesis space and help the representation manifold remain invariant to future-induced noise, preventing data leakage within the architecture.

To instantiate local causal modeling, we introduce dilated convolutional layers with asymmetric left padding. For an input sequence X, the temporal dimension is padded with Lpad = (k - 1) × d zeros on the left, where k denotes the kernel size and d is the dilation rate. The causal operator is defined as:

This operator forces the convolution kernel to slide only over current and historical trajectories, extracting local dynamics with high causal fidelity. Such a structured inductive bias is crucial for non-stationary sequences, since it keeps the transition probability P(xt|x<t) undisturbed by future observations.

To complement local causal filtering, we further integrate multi-head self-attention with an upper-triangular causal mask M ∈ RL×L. The mask is defined as:

Given linear projection matrices WQ, WK , and WV , the masked attention reconstructs the temporal manifold by:

Channel Adaptive Recalibration

To complement the temporal consistency established by CTA, this module uses the Information Bottleneck principle to address Channel Heterogeneity. Due to varying signal-to-noise ratios (SNRs) across sensors, the raw temporal representation H is frequently contaminated by non-discriminative channel noise.

The recalibration module complements CTA by constraining the channel dimension of the feature manifold. While Eq. (4) filters noise along the temporal axis through causality, channel recalibration suppresses redundant or low-saliency variables along the spatial axis, encouraging only discriminative and physically consistent spatio-temporal motifs to be propagated to the disentanglement head.

Given the temporal representation H ∈ RB×N×L, we first summarize the global response of each channel using a Global Average Pooling operator Fsq(·). For the n-th channel, the descriptor is computed as:

Although early states in a causal sequence have limited receptive fields, the later hidden states progressively accumulate historical context. Therefore, Eq. (5) can be viewed as a compact summary of the feature evolution trajectory rather than a naive temporal average, providing stable anchors for estimating channel saliency under non-stationary dynamics.

The channel descriptor z is then passed through a bottleneck excitation gate with dimensionality reduction and expansion N → N/r → N :

where σ(u) = 1/(1+exp(-u)) is the element-wise sigmoid function, a ∈ [0, 1]N denotes the channel saliency weights, and W1 and W2 are the reduction and expansion weights. The bottleneck ratio r encourages the model to learn essential inter-variable dependencies in a compact latent space.

Finally, the recalibrated representation is obtained by applying the learned channel saliency weights to the temporal representation:

where ⊙ denotes element-wise multiplication. This variablelevel filtering mechanism improves the separability and noise-resilience of the representation before shared-specific disentanglement. In this way, the downstream decomposition head receives a cleaner manifold rather than being forced to suppress temporal and channel noise simultaneously.

3.4 Multi-Scale Feature Decomposition and Prediction

We adopt a shared-specific disentanglement head inspired by multi-scale disentanglement learning [Liu et al., 2025] to evaluate the downstream utility and representational purity of the manifolds produced by the CASE encoder. This head explicitly separates each recalibrated scale representation into scale-shared and scale-private factors, enabling inter-scale redundancy reduction while preserving scale-dependent discriminative details.

While CASE-NET is designed to be compatible with various discriminative heads, we instantiate the decomposition module with an adaptive shared-specific gate. For each scale s, the disentanglement gate m(s) is generated from the recalibrated representation ˜H(s) :

Here, m(s) adaptively allocates each feature dimension to the scale-shared or scale-private subspace, Wg and bg are learnable gate parameters, and ⊙ denotes element-wise multiplication. The resulting shared and scale-private factors play complementary roles. The shared representation Hsh is encouraged to capture stationary rhythms and scale-invariant semantic cores, such as basal cardiac or neural oscillatory patterns. In contrast, Hsp preserves non-stationary residual dynamics, including high-frequency transients and localized paroxysmal events that may be suppressed during global aggregation. This complementary allocation prevents scale-invariant semantics and scale-private residuals from collapsing into a single entangled representation.

The efficacy of this decomposition is fundamentally predicated on the manifold pre-conditioning provided by the CASE encoder. By furnishing a noise-filtered and causallyconsistent input, we demonstrate that the backend can achieve a higher degree of Feature Orthogonality with minimal information leakage. The final prediction ˆ y is derived by fusing these descriptors:

where ⊕ denotes feature concatenation, G(·) denotes global aggregation over temporal and scale dimensions, and the MLP outputs class logits before the Softmax normalization. This design combines scale-invariant semantics with scaleprivate discriminative details for final classification.

3.5 Synergistic Manifold Optimization

We formulate a multi-objective functional Ltotal to supervise the latent manifold evolution:

where Lcls is the task-specific Negative Log-Likelihood applied to the fused representation [Hsh ⊕ Hsp], and λ1, λ2 are non-negative balancing coefficients controlling the contributions of cross-scale consistency and shared-private orthogonality, respectively. To capture invariant rhythmic motifs, Lsim minimizes the cosine distance between shared representations across resolutions [Chen et al., 2023; Chen et al., 2024]:

where ⟨·, ·⟩ denotes the inner product after flattening or pooling the corresponding representations. This inductive bias identifies the universal physiological core and filters stochastic noise inherent to specific resolutions. Conversely, Ldiff promotes Feature Orthogonality by penalizing the cross-covariance between Hsh and Hsp via the Frobenius Norm [Liu et al., 2025]:

By driving representational diversity, this constraint prunes the hypothesis space, suggesting that Hsp captures unique residual dynamics (e.g., pathological paroxysms) with less overlap with the global semantic anchor. Together, the three objectives couple task discrimination with representation geometry: Lcls preserves label separability, Lsim enforces cross-scale invariance, and Ldiff prevents shared-private feature leakage.

3.6 Computational Complexity Analysis

The computational overhead of CASE-NET is primarily dominated by the CASE encoder. The CTA module incurs a complexity of O(L2 · D) due to masked self-attention and O(L · k · D) for causal convolutions. The adaptive recalibration adds a negligible O(N 2 /r).

Although the CTA module has O(L2 ) attention complexity, it is fully parallelizable and remains practical for longrange sequences. Empirically, CASE-NET uses about 2.1M parameters and maintains competitive throughput, supporting its feasibility for real-time MTS applications.

The detailed step-by-step execution of the end-to-end training procedure is summarized in Algorithm S1 in the Supplementary Material.

4 Experiments

4.1 Experimental Setup

Datasets

We evaluate CASE-NET on six benchmark classification datasets following the protocol of DisMS-TS [Liu et al., 2025], including AWR (Articulary Word Recognition), FM (Finger Movements), and NASDAQ for market regime classification. The NASDAQ task is window-level classification rather than next-step price prediction, preventing look-ahead leakage (see Table S1 in Supplementary Material).

Evaluation Metrics

We employ Accuracy (Acc), Macro-averaged F1-score (F1), and Matthews Correlation Coefficient (MCC) to comprehensively assess performance.

Baseline Methods

We compare CASE-NET with eight representative baselines: LSTNet [Lai et al., 2018], DTP [Lee et al., 2021], TSTCC [Eldele et al., 2021], PatchTST [Nie et al., 2022], MAGNN [Chen et al., 2023], Pathformer [Chen et al., 2024], TimeMixer [Wang et al., 2024a], and DisMS-TS [Liu et al., 2025]. These baselines cover recurrent and pooling-based classifiers, contrastive representation learning, Transformerbased temporal modeling, graph-based multivariate modeling, and recent multi-scale architectures.

Implementation Details

We implement CASE-NET in PyTorch and report the average results over five independent runs. All models are optimized with Adam [Kingma and Ba, 2014], and key hyperparameters, including learning rate, batch size, hidden dimension, scale depth, and loss weights, are selected on a 20% holdout validation set. Dropout, layer normalization, and early stopping are applied for regularization. For each dataset, the validation split is used only for hyperparameter selection and early stopping, while the test split remains strictly held out for final reporting. The best checkpoint is selected according to validation accuracy, and all metrics are computed on the corresponding test set to reduce the influence of a single favorable initialization.

4.2 Comparative Analysis

Table 1 shows CASE-NET achieves SOTA performance on HAR, NASDAQ, AWR, and Epilepsy. On NASDAQ, CASENET leads by 7.05% via Causal Attention, which enforces temporal constraints to block future noise. For Epilepsy, SE

recalibration provides noise resistance against artifacts, consistent with [Sun et al., 2024], yielding a 2.18% gain. On HAR and AWR, CASE-NET achieves higher mean performance than bidirectional baselines. Unlike BERT-style models where future context clarifies semantics, high-frequency MTS future frames often introduce stochastic noise (e.g., sensor artifacts) inducing temporal confounding. By causal masking, our model acts as a directional filter, encouraging the encoder to capture discriminative action motifs rather than transient signal fluctuations through structural regularization.

Though ranking second on ISRUC-S3 and FM, CASENET remains competitive. DisMS-TS's seasonal decomposition better suits the extreme periodicity of ISRUC-S3 (L = 3000), while its simpler logic offers stronger regularization in the low-data FM regime (N = 284).

4.3 Ablation Study

We define the w/o Causal variant as the bidirectional version of our architecture, removing the temporal mask M to evaluate component efficacy. In Table 2, this variant on NASDAQ drops from 46.76% to 38.20% (-8.56%), suggesting that bidirectional context in non-stationary tasks may introduce future-induced stochastic noise rather than useful information.

Similarly, HAR performance decreases to 91.25% (-5.27%), confirming that unconstrained bidirectional context can blur discriminative temporal boundaries. The causal prior also improves Epilepsy and AWR, demonstrating its stabilizing effect under noisy and non-stationary dynamics. To isolate the contribution of the CASE encoder, we replace the disentanglement backend with a linear MLP. As shown in Table 2, this variant remains competitive, while the full model achieves the best results, indicating that causal and spatial priors jointly improve multi-scale representation learning.

4.4 Hyperparameter Analysis

Impact of Scale Levels S

As depicted in Fig. 3(a), different datasets require different optimal scale depths: S = 6 for AWR and S = 4 for HAR. The performance drop at lower S values, particularly for high-cardinality tasks like AWR where S ≥ 5 is required, does not indicate model instability. Instead, it reflects the necessity of resolution matching. A sufficient scale depth helps ensure an adequate temporal receptive field for domainspecific hierarchical motifs.

Sensitivity to Decoupling Intensity λ

As shown in Fig. 3(b), model performance remains stable across three orders of magnitude for the decoupling weight λ. This high consistency suggests that the performance gains originate from the inherent structural design of CASE-NET rather than from heuristic parameter fine-tuning.

4.5 Convergence and Stability Analysis

Fig. 2 shows stable optimization across domains: training and validation losses decrease consistently and converge within about 40 epochs, while accuracy curves remain smooth across four modalities. These results indicate that the causal-spatial encoder provides robust optimization behavior for heterogeneous MTS data. The close tracking between training and validation curves further suggests that the causal mask and channel bottleneck act as structural regularizers rather than merely increasing model capacity.

4.6 Representation Interpretability and Disentanglement

For visualization, we denote features derived from Hsh and Hsp as Fsha and Fspe, with Fi indexing scale branches; Fig. 4 and Fig. 5 show strong cross-scale correlations for Fsha and lower, more dispersed correlations for Fspe, indicating effective disentanglement. The t-SNE projections in Fig. 6 further visualize scale-specific representations on NASDAQ and Epilepsy, which respectively represent non-stationary financial dynamics and noisy biomedical signals. The different scale-specific factors form compact and distinguishable clusters, suggesting that CASE-NET learns structured scaleprivate manifolds rather than collapsing multi-scale information into an entangled latent space. In particular, the NASDAQ visualization supports the role of causal temporal filtering in non-stationary regime classification, while the Epilepsy visualization reflects the benefit of channel recalibration in suppressing noisy artifacts.

5 Conclusion

CASE-NET mitigates the representation bottleneck in multiscale MTS classification by combining causal temporal modeling with channel recalibration before shared-specific disentanglement. Experiments across six heterogeneous domains suggest that the proposed causal-spatial pre-conditioning improves robustness in non-stationary and noisy settings. The results further indicate that causal temporal filtering and channel recalibration play complementary roles: the former stabilizes temporal dynamics, while the latter suppresses channel-wise noise before disentanglement. Future work will explore large-scale spatio-temporal pre-training for broader sensing applications.

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grant Nos. U24A20219, 62272281, and U24A20328; the Yantai Natural Science Foundation under Grant No. 2024JCYJ034; and the Youth Innovation Technology Project of Higher School in Shandong Province under Grant No. 2023KJ212.