AnoMamba: Aligning Reconstruction with Time Series Anomaly Detection via Selective Global Dependency Modeling

1 Introduction

Time Series Anomaly Detection (TSAD) has attracted increasing attention due to its critical role in a wide range of real-world applications, including medical diagnosis, fault detection, and instruction detection [Zamanzadeh Darban et al., 2024]. Among various approaches, reconstructionbased frameworks are widely-adopted in TSAD, as they can detect anomalies by measuring reconstruction errors under the core assumption that only normal patterns can be accurately reconstructed [Schmidl et al., 2022]. Despite the in-

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(a) Misalignment between reconstruction and anomaly detection. Top: the detector overfits to local patterns and fails to learn normal behavior, leading to misalignment. Bottom: expected alignment, where reconstruction fits normal behavior but not anomalies. MSE denotes mean square error.

Figure 1: Challenges in reconstruction-based TSAD.

tegration of powerful sequence models over the past decade, reconstruction-based methods remain fundamentally susceptible to overfitting [Boniol et al., 2024]. In particular, an overfitted detector may reconstruct anomalies with high accuracy, thereby violating the foundational assumption of reconstruction-based TSAD.

This overfitting issue stems from a fundamental misalignment between the reconstruction objective and the anomaly detection objective. In TSAD, the goal of reconstruction is not merely to minimize reconstruction error, but to learn a reliable normal behavior. However, in the absence of labeled anomalies, optimizing reconstruction loss alone encourages models to overfit local dependencies, which are easier to reconstruct [Xu et al., 2021]. As a result, the learned model fails to fully characterize normal behavior, leading to the unexpected reconstruction of anomalies. As shown in Fig. 1 (a), this local overfitting issue directly undermines the anomaly detection objective and raises a core challenge for reconstruction-based TSAD: Challenge1: The misalignment between reconstruction and anomaly detection hinders the normal behavior learning.

A natural solution to alleviate this misalignment is to enforce the learning of global dependencies. By modeling global dependencies, the model is encouraged to learn more complete normal behavior beyond trivial local patterns. Existing methods lie in two perspectives. Featurelevel methods construct multi-scale inputs, such as multiresolution views [Wang et al., 2024b; Zhong et al., 2025] and decomposition-based components [Wu et al., 2021; Chen et al., 2024], to encourage detectors learn global dependencies residing in coarse resolutions or low-frequency components. However, the feature construction is not trained end-to-end (E2E) with the detector, making performance highly sensitive to hyperparameters. In contrast, objective-level methods integrate regularization to E2E guide the detector to capture global dependency. Typical methods use attention priors [Xu et al., 2021] or global windows [Chen et al., 2025; Peng et al., 2025] to constrain the detector's attentions to predefined global regions. Despite being E2E, these designs still fix in advance where the model should attend, imposing overly strong assumptions on the global regions. In practice, the required global dependencies vary across time and context, as illustrated in Fig. 1 (b). This leads to the second challenge: Challenge2: It is difficult to define global dependencies for normal behavior in advance.

To tackle the above challenges, we explore alternative solutions from the recently proposed Mamba model [Gu and Dao, 2024]. A key characteristic of it is its input-dependent step-size, which controls the contribution of historical information and enables the selectively modeling of global dependencies. However, existing applications of Mamba to time series are predominantly in supervised settings [Xu et al., 2024; Karadag et al., 2025], where the step-size is guided by labels. In unsupervised TSAD, this selective mechanism cannot be effectively exploited, leaving the challenges unsolved.

To fill this gap, we propose Global Step-size Reweighting Mamba (GSRMamba), a Mamba variant tailored for unsupervised TSAD. The design centers on controlling step-sizes via global context and multi-scale priors. First, we introduce a global step-size reweighting model, which modulates the step-size with global contextual information. Second, we develop a multi-scale prior regularization strategy to guide the learning of this reweighting process. Unlike previous attention priors that directly impose importance on predefined positions, our step-size priors only balance the importance of global and local dependencies without making positional assumptions. We further associate the reweighted step-sizes with a hidden attention map [Ali et al., 2025] to enhance the interpretability of normal behavior learning. Finally, we incorporate patch embedding into GSRMamba to reduce local dependency redundancy. These components are integrated into a unified reconstruction-based TSAD framework, termed AnoMamba, which enables capturing variable global dependencies and realigns reconstruction with anomaly detection.

The contributions of this paper are summarized as follows:

• We propose AnoMamba, a novel reconstruction-based anomaly detector that enhances global dependencies modeling to align reconstruction with TSAD.
• To address the challenges of variable global dependencies modeling, we introduce GSRMamba, which leverages step-size control and multi-scale prior guidance to fully exploit Mamba's selective capability for precise global information selection.
• We connect the learned step-size with a hidden attention map to enhance the interpretability of normal behavior learning.
• Extensive experiments on both univariate and multivariate datasets demonstrate the superior detection performance and efficiency of AnoMamba compared to stateof-the-art (SOTA) methods.

2 RelatedWorks

In this section, we review reconstruction-based TSAD methods and recent Mamba-based approaches for TSAD.

2.1 Reconstruction-based TSAD

Reconstruction-based TSAD aims to learn normal behavior by training a model to reconstruct the input series. Early reconstruction ideas can be traced back to PCA [Hoffmann, 2007] and autoencoder-based methods [An and Cho, 2015], where normal patterns are captured by principal components or low-dimensional representations. However, these methods ignore temporal structure and thus struggle with time series contained strong contextual dependencies. To model temporal dependencies, reconstruction is typically performed on windowed sequences, and various deep sequential architectures have been explored, including Multi-Layer Perceptron (MLP)-based [Zeng et al., 2023], Convolutional Neural Network (CNN)-based [Wu et al., 2023], Recurrent Neural Network (RNN)-based [Su et al., 2019], and Transformerbased [Xu et al., 2021] models. MLPs and CNNs are computationally efficient, whereas RNNs and Transformers are more suitable for long-range dependencies. More recently, State Space Models (SSM), such as Mamba [Gu and Dao, 2024], have been proposed to strike a balance between efficiency and modeling power.

Despite these advances, reconstruction-based TSAD remains vulnerable to overfitting to local patterns, due to the misalignment between reconstruction and anomaly detection in unsupervised settings. Existing methods attempt to alleviate this by emphasizing global dependencies, but they often rely on strong assumptions such as fixed positional priors [Xu et al., 2021] or windowing schemes [Chen et al., 2025]. In this work, we instead develop a Mamba variant that captures meaningful global dependencies required for normal behavior learning. Our design enables the model to adaptively focus on different global ranges, thereby mitigating overfitting and improving anomaly detection performance.

2.2 Mamba for TSAD

Mamba [Gu and Dao, 2024] is a recently proposed variant of SSMs that overcomes the time-invariance limitation present in earlier SSMs. Its core innovation lies in the introduction of the selective SSM (S6), which incorporates time-dependent parameters into the SSM process. Building on this, recent works such as SST [Xu et al., 2024] and DMamba [Chen et al., 2024] have replaced Transformers with Mamba to better capture global dependencies in time series. Among the timedependent parameters in Mamba, the step-size plays a critical role in controlling the contribution of history information, enabling global information selection. MS-Mamba [Karadag et al., 2025] further scales the step-size with a learned scalar to modulate this effect. However, these methods still rely on supervised training and lack fine-grained control at the individual time-step level. When trained in an unsupervised setting, Mamba-based models still tend to overfit local patterns and cannot fully exploit their inherent selective capability.

In this paper, we introduce a global step-size reweighting model that adaptively adjusts step-sizes across time, enabling finer control of Mamba's selective behavior for global dependency modeling. We further propose a multi-scale prior regularization strategy to guide this reweighting process in the unsupervised setting, effectively alleviating local overfitting. In addition, by linking the learned step-sizes to hidden attention maps, our method offers interpretable insights into the learned normal behaviors, improving the transparency of the anomaly detection process.

3 Preliminaries

In this section, we define the TSAD problem and present the Mamba formulation together with its hidden attention map.

3.1 The Task Definition of TSAD

Given a multivariate time series xt ∈ RD with D channels, the task of TSAD is to predict the anomaly label using an anomaly detector F(·). During inference, the anomaly detector computes an anomaly score at for each time step t based on a sliding window of inputs, formulated as: at = F(xt-T:t), where T denotes the window size. The predicted anomaly label ˆ yt is then obtained by thresholding the anomaly score: ˆ yt = 1 if at > ath, and ˆ yt = 0 otherwise, where ath is a predefined threshold.

3.2 The MambaModel

The core model in Mamba is the S6, which extends conventional SSM by incorporating time-dependent parameters. It can be formulated as follows:

where the SSM process SSM(·) is defined by:

with ⊙ denoting the Hadamard product, xt ∈ R representing the input at t-th time step, ht ∈ RN the hidden state, and yt ∈ R the output. The key distinction from conventional SSMs lies in the time-dependent and input-adaptive parameters: At ∈ RN , Bt ∈ RN , and Ct ∈ RN which are dynamically computed at each time step based on the current input xt and a learnable step-size ∆t ∈ R:

where A ∈ RN , WB ∈ RN , WC ∈ RN , and WD ∈ R are trainable parameters. Softplus(·) denotes the Softplus activation function.

The time-dependent nature of these parameters, particularly the step-size ∆t, enables S6 to dynamically regulate the influence of current versus historical information. Specifically, when ∆t → 0, the model downweights the current input, emphasizing historical context. Conversely, a larger ∆t increases the influence of the current input, allowing the model to focus on new information. It is worth noting that the above formulation describes the univariate case. For multivariate time series, this mechanism can be naturally extended by generating ∆t, At, and Bt in a channel-independent manner, while sharing Ct across all channels.

3.3 Hidden AttentionMap inMamba

As noted in [Ali et al., 2025], Mamba can provide a hidden attention map analogous to the SA mechanism, thereby enhancing the interpretability of its internal representations. Assuming the initial hidden state h0 = 0, Eq. (2)-(3) can be unrolled as follows:

yt =CTt · ht

This unrolled formulation can be expressed in matrix form as:

where

Clearly, ˜αt plays a role similar to the attention weights in Transformer models, providing interpretable attribution over the input sequence. Specifically, the contribution of input xi to the output yt (t ≥ i) can be written as:

This perspective endows Mamba with self-attention-like interpretability and reveals how the influence of step-size ∆t.

where W1,W2 ∈ RDm×2Dm , W3 are trainable projection matrices, SiLU(·) denotes the SiLU activation function. The process in Eq. (15) denotes a reweighted step-size guided S6, which is shown in Fig. 2 (c). The reweighted step-size computed by: ∆GSR n = ∆n ⊙ ωn ∈ R2Dm , where ωn is the reweighting coefficient. The step-size reweighting process is a central design in GSRMamba for global dependencies capturing, which will be detailed next.

4.3 Global Step-size ReweightingModel

As discussed above, the input-dependent step-size in Mamba has the potential to select reliable global dependencies. However, the step-size in original S6 depends only on the current time step, making it vulnerable to local overfitting. To exploit global information, we introduce a Global Step-size Reweighting (GSR) model that generates coefficients ω1:N from the global context and uses them to reweight the step-size. The architecture of GSR is illustrated in Fig. 3 and defined as:

where FFN1(·) and FFN2(·) are two Feed-Forward Networks (FFN) to capture intra- and inter-patch information. The resulting coefficients ωn thus encode global context and provide a more reliable estimate of the importance for each time step. By reweighting the original step-sizes to ∆GSR n , the model focuses more on globally consistent dependencies and alleviates local overfitting.

4 Methodology

To align the reconstruction with anomaly detection, a novel detector named AnoMamba is proposed. The overall framework is illustrated in Fig. 2, and its core design principles can be summarized in two key aspects: First, AnoMamba utilizing channel independent patch embedding to disentangle the channel dependencies and reduce the local dependency redundancy. Second, the GSRMamba blocks fully unleash the selective property of Mamba to capture appropriate global dependencies, facilitating normal behavior learning. Moreover, it offers an interpretability interface via the hidden attention map, which reveals what normal behavior has been learned by the model. In the following sections, we provide a detailed description of the AnoMamba architecture and its training objective.

4.1 Patch Embedding Layer

Given a D-channel input time series xt ∈ RD , a channelindependent patch embedding layer is first applied to capture local dependencies. Specifically, the input xt is segmented into N patches, where the n-the patch sn ∈ RP is defined as:

with P and S denoting the patch size and patch stride, respectively. Each patch is then processed by a 1D convolutional layer Conv(·) to obtain the corresponding patch embedding {en}Nn=1 ∈ RDm , where en = Conv(sn).

4.2 GSRMamba

The patch embedding has reduced the local dependencies redundancy by intra-patch modeling. However, when trained solely with a reconstruction loss, the model remains prone to overfitting, and global dependency tends to be gradually discarded. To address this issue, GSRMamba is proposed to continuously track global dependencies. The architecture of GSRMamba is depicted in Fig. 2 (b), and its processing steps can be expressed as follows:

4.4 Multi-scale Priors Regularization

To further prevent trivial reconstructions under unsupervised settings, we propose multi-scale priors to guide GSR. Intuitively, we expect larger step-sizes for global dependencies and smaller but non-zero step-sizes for local ones, so that global information is emphasized without discarding local context. To fulfill this, we design a family of Gamma-like long-tail distributions:

where n indexes the time step and α ≥ 1 controls the tradeoff between global and local importance. A smaller α places more emphasis on global dependencies. The derivation of these distributions is provided in the appendix.

Motivated by multi-scale modeling, we adopt multi-scale priors by using multiple values of α instead of a single scale. To avoid hyperparameter tuning and reduce computational overhead, we randomly sample α ∈ [1, T] at each training iteration to guide the coefficients generated by GSR. As formulated in Eq. (11), the prior on step-sizes only biases how strongly global information is propagated, while the hidden attention scores are still determined jointly by the learnable parameters A, Bt, and Ct. Thus, unlike attention priors, it does not impose any positional assumptions.

4.5 Reconstruction Output

After being processed by multiple GSRMamba blocks, the channel dependencies are finally mixed using an FFN model:

After flattening and projection, the final reconstructed output ˆxt is obtained as:

where WO ∈ RT×N·Dm is a trainable parameter matrix.

4.6 Training Objective and Anomaly Score

During training, the objective is defined as:

where Lrec = MSE(xt, ˆxt) is the Mean Squared Error (MSE) between the original input and the reconstructed output, and LKL is the averaged Kullback-Leibler (KL) divergence between the reweighting coefficients and the prior. In each block and for the i-th dimension, the KL term is computed as ∑Tn=1 ωi,n (log ωi,n - log P (n)). The hyperparameter λ balances the two loss terms.

During inference, the reconstruction error is used as the anomaly scores: at = Lrec(xt, ˆxt).

5 Experiments

In this section, we provide the experimental setups, results, and the corresponding conclusions.

5.1 Datasets

Experiments were conducted on eight real-world benchmark datasets, including four univariate datasets from UCR Anomaly [Wu and Keogh, 2021] (ECG, EPG, Gait, NASA) and four multivariate datasets from TSB-AD [Liu and Paparrizos, 2024] (LTDB, MITDB, SVDB, SMD).

5.2 Baselines

Our method was compared against representative and SOTA TSAD methods, including: (i) MLP-based methods: Dlinear [Zeng et al., 2023], TimeMixer [Wang et al., 2024b], and LTFAD [Chen et al., 2025]. (ii) CNN-based methods: TimesNet [Wu et al., 2023], MICN [Wang et al., 2023], ModernTCN [Luo and Wang, 2024]. (iii) RNN-based methods: Omnianomaly [Su et al., 2019]. (iv) Transformer-based methods: Autoformer [Wu et al., 2021], AnomalyTrans [Xu et al., 2021], PatchTST [Nie et al., 2023], D3R [Wang et al., 2024a], and RTdetector [Liu et al., 2025] (v) Mamba-based methods: SST [Xu et al., 2024], MS-Mamba [Karadag et al., 2025] and DMamba [Chen et al., 2024].

5.3 Implemented Details

For fair comparison, the window size of all baselines was set to 100, following recommendations from most prior works. As noted by [Kim et al., 2022], point-adjustment metrics can lead to misleading rankings, we adopt two alternative evaluation metrics: affiliation-based F1 score (F1-AF) [Huet et al., 2022] and the volume under the ROC surface (VUSROC) [Paparrizos et al., 2022]. Higher values in both metrics indicate better anomaly detection performance. All thresholds were selected by SPOT [Siffer et al., 2017]. For AnoMamba, we set the model size to 16, the state size to 8, and the number of blocks to 3. All experiments were conducted in PyTorch on an NVIDIA P40 24GB GPU, with results averaged over five seeds.

5.4 Main Results

Tab. 1 and Tab. 2 report the results on univariate and multivariate datasets. The best results are bolded and the secondbest are underlined. AnoMamba achieves the best F1-AF on 7/8 datasets, the best VUS-ROC on 6/8 datasets, and the best overall averaged performance. Notably, TimeMixer performs well on Gait and NASA due to its multi-resolution views, but degrades on other datasets. Similarly, MS-Mamba works better on multivariate datasets but struggles on univariate ones, suggesting high sensitivity to hyperparameters and limited generalizability. Transformer-based methods perform relatively poorly, especially AnomalyTrans, whose attention priors impose overly strong positional assumptions. Other Mamba-based methods, such as SST, are also unstable, especially on Gait with many contextual anomalies. These results show that existing Mamba-based methods still suffer from overfitting in unsupervised TSAD, while AnoMamba successfully resolves this issue and consistently achieves robust performance across diverse datasets and settings.

5.5 Ablation Studies

Tab. 3 evaluates each component of AnoMamba and several conclusions can be drawn. First, removing the GSR model leads to a significant performance drop, especially on univariate datasets dominated by contextual anomalies, underscoring the importance of reweighting in AnoMamba. Second, with fixed priors, the performance is insensitive to the choice of α, showing that the designed prior guides step-sizes to capture appropriate dependencies without introducing strong assumptions. Finally, multi-scale priors further enhances generalizability.

5.6 Sensitivity Analysis

Fig. 4 shows the sensitivity of AnoMamba to key hyperparameters. For λ, overly large values cause a sharp drop in F1-AF, while performance is stable when λ < 0.1. Based on this observation, we set λ = 0.1 in our experiments. As for the patch size, performance remains within a reasonable range, and we choose a smaller size of 8 to prioritize F1-AF and better exploit GSRMamba's global information selection.

5.7 Efficiency Analysis

To evaluate the efficiency of AnoMamba, we analyze training time and memory usage on the MITDB dataset, comparing it with representative baselines, as presented in Fig. 5. AnoMamba demonstrates higher efficiency than multi-scale based methods, such as TimeMixer and MS-Mamba, and Transformer-based methods, such as Autoformer. Its efficiency is comparable to most CNN-based approaches, while achieving superior detection performance. Although AnoMamba is less efficient than DLinear, it significantly outperforms DLinear in detection performance.

5.8 Interpretability Analysis

To better understand the role of GSR in AnoMamba, Fig. 6 visualizes the hidden attention scores on the "GP711MarkerLFM5z1" dataset, with and without GSR guidance. It shows that vanilla Mamba overfits to local patterns, while applying GSR effectively captures global dependencies and alleviates local overfitting. Fig. 7 further visualizes the corresponding anomaly scores. The input sequence in the first row exhibits a global pattern characterized by a "large peak-small peak" structure, where the anomaly is caused by

• (b) Results with different patch sizes.

Figure 5: Visualization of the computational complexity.

the absence of the "small peak". In the second and third rows, we observe that under GSR guidance, the reconstruction of the anomalous region attends to the "large peak," indicating that the model has successfully learned the global dependencies of the normal behavior. This allows AnoMamba to precisely detect the anomaly via reconstruction error. In contrast, the fourth and fifth rows show that without GSR, Mamba tends to overfit local dependencies, resulting in false negatives. These visualizations demonstrate that AnoMamba can effectively learn global normal behavior to realign reconstruction with anomaly detection.

6 Conclusions

In this paper, we identify a critical issue in reconstructionbased TSAD, namely the objective misalignment caused by local overfitting in unsupervised settings. To address this issue, we propose AnoMamba, a novel detector that aligns the reconstruction and anomaly detection objectives. The key design centers on GSRMamba with a step-size reweighting process, which enhances global dependency modeling. To further alleviate local overfitting in the unsupervised settings, a multi-scale prior strategy is designed to guide the reweighting coefficients. Extensive experiments demonstrate both the effectiveness and efficiency of AnoMamba across diverse datasets. In addition, AnoMamba provides interpretability by revealing learned normal behavior through its hidden attention map.

Acknowledgments

The work was supported by Shenzhen Science and Technology Program under Grants KCXFZ20240903094406009 and JCYJ20230807145600001, and NSFC Grant No. 62192713.