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Learning Continuous and Discrete Dynamics for Time Series Anomaly Detection via Probabilistic Modeling

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Time Series Anomaly DetectionContinuous and Discrete Dynamics
Abstract:

Anomaly detection for multivariate time series plays an important role in many applications, enabling, e.g., risk monitoring in cyber-physical systems. While existing methods achieve good results on continuous variates, they struggle when having to learn both continuous and discrete dynamics across continuous time. Further, existing methods simply sum up reconstruction or contrastive errors from each variate to obtain final anomaly scores without recognizing differences in importance of variates with different measurement units. To overcome these limitations, we propose TAD-UP that learns both continuous and discrete dynamics for Time series Anomaly Detection via Unified Probabilistic modeling. First, we propose two co-dependent branches of efficient neural ordinary differential equations with the compound Poisson process to learn both continuous and discrete dynamics for different variates. We also propose a gate mechanism to learn correlations among different dynamics. Second, we propose to model a joint probability distribution for anomaly detection. The resulting model is optimized using Maximum Likelihood Estimation on joint variates, instead of using reconstruction or contrastive losses on each variate. We detect anomalies using joint probabilities, which take the marginal probabilities of different variates into account. Experiments on nine real-world datasets from different domains offer evidence that TAD-UP is capable of state-of-the-art accuracy and better efficiency tradeoff.

Disclaimer
This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper proposes TAD-UP, which learns both continuous and discrete dynamics for multivariate time series anomaly detection through unified probabilistic modeling. It resides in the 'Probabilistic Joint Modeling Approaches' leaf, which contains only two papers including this one. This leaf sits under 'Unified Continuous-Discrete Dynamics Modeling', a branch explicitly focused on methods that model both temporal regimes within a single framework. The sparse population of this specific leaf suggests that probabilistic joint modeling for mixed dynamics remains relatively underexplored compared to reconstruction-based or purely continuous-time approaches elsewhere in the taxonomy.

The taxonomy reveals several neighboring directions: 'Hybrid System and State-Space Modeling' (two papers) formulates systems as hybrid models with discrete event transitions, while 'Latent Continuity Recovery from Discrete States' (two papers) converts discrete states to continuous representations. Nearby branches include 'Neural Differential Equation-Based Methods' (three papers) and 'Autoencoder-Based Reconstruction Methods' (three papers), which handle temporal dynamics but typically focus on continuous data or use reconstruction error rather than joint probabilistic modeling. The scope notes clarify that deterministic or reconstruction-based methods without probabilistic frameworks belong outside this leaf, positioning TAD-UP's probabilistic approach as distinct from these alternative paradigms.

Among 25 candidates examined across three contributions, the analysis found one refutable pair. The first contribution (co-dependent neural ODEs with compound Poisson process) examined five candidates with zero refutations, suggesting limited prior work on this specific architectural combination. The second contribution (unified probabilistic modeling with joint distribution) examined ten candidates and found one refutable match, indicating some overlap in probabilistic formulations. The third contribution (first method for both dynamics) examined ten candidates with zero refutations, though this claim's strength depends on how narrowly 'both dynamics' is defined. The limited search scope (25 candidates, not exhaustive) means these statistics reflect top semantic matches rather than comprehensive field coverage.

Based on the top-25 semantic matches examined, the work appears to occupy a relatively sparse research direction within probabilistic joint modeling for mixed dynamics. The single refutable pair suggests some prior probabilistic formulations exist, but the architectural choices (neural ODEs with compound Poisson process) and the joint distribution approach show limited direct overlap in the examined literature. However, the analysis does not cover broader differential equation methods or reconstruction-based approaches that might address similar problems through different paradigms, leaving open questions about novelty relative to the wider field.

Taxonomy

Core-task Taxonomy Papers
31
3
Claimed Contributions
25
Contribution Candidate Papers Compared
1
Refutable Paper

Research Landscape Overview

Core task: anomaly detection for multivariate time series with continuous and discrete dynamics. The field addresses systems where smooth, continuous evolution coexists with abrupt, discrete transitions—common in cyber-physical systems, industrial processes, and healthcare monitoring. The taxonomy reveals several major branches: some focus on unified modeling that explicitly captures both continuous flows and discrete jumps (e.g., Continuous Discrete Dynamics[0], CPS Time Series Discretization[3]), while others leverage neural differential equations to learn continuous-time representations (e.g., NCDE Normalizing Flow[16]). Autoencoder-based reconstruction methods remain popular for learning normal behavior patterns (Dual Transformer Autoencoder[4], Autoencoder Mechatronic Systems[13]), and contrastive or semi-supervised approaches (SSDCL[5]) exploit limited labels. Additional branches tackle sparse representation (Sparse Dictionary Learning[18]), discrete event mining (Discrete Event Sequences[25]), mixed data types (Mixed Data Factor[14]), and domain-specific applications in industrial settings or prognostics (Temporal Relational Learning[22]). A particularly active line of work explores probabilistic joint modeling that treats continuous and discrete components in a unified framework, aiming to capture mode switches and hybrid dynamics without separating them into independent pipelines. Continuous Discrete Dynamics[0] sits squarely in this branch, emphasizing probabilistic integration of both regimes. Nearby, Dual Transformer Autoencoder[4] also addresses mixed dynamics but leans more heavily on reconstruction-based detection with transformer architectures. Meanwhile, approaches like CPS Time Series Discretization[3] and Hybrid Sequences Effect[27] focus on discretization strategies or sequence-level modeling, offering complementary perspectives on how to represent transitions. The central tension across these methods involves balancing expressiveness—capturing complex mode changes—with computational tractability and interpretability, especially when labeled anomalies are scarce. Continuous Discrete Dynamics[0] contributes to this landscape by proposing a joint probabilistic framework that aims to model both dynamics cohesively, distinguishing it from purely reconstruction-driven or purely discrete-event approaches.

Claimed Contributions

Co-dependent neural ODEs with compound Poisson process for learning continuous and discrete dynamics

The authors introduce a novel architecture with two co-dependent branches of neural ordinary differential equations (NODEs). One branch learns continuous dynamics for continuous variates, while the other uses a compound Poisson process to learn discrete dynamics that can jump for discrete variates. Gate temporal convolution networks model correlations between these different dynamics.

5 retrieved papers
Unified probabilistic modeling with joint probability distribution for anomaly detection

The authors propose modeling a joint probability distribution across continuous and discrete variates using multivariate Gaussian and softmax distributions respectively. The model is optimized via Maximum Likelihood Estimation in a unified probabilistic space, and anomalies are detected using joint probabilities that account for the marginal probabilities and importance of different variates.

10 retrieved papers
Can Refute
First method for learning both continuous and discrete dynamics in multivariate time series anomaly detection

The authors claim to be the first to discriminate between and simultaneously learn continuous dynamics (for real-valued variates) and discrete dynamics (for natural-number-valued variates) in the context of multivariate time series anomaly detection, addressing a gap in existing methods that treat all variates uniformly.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Co-dependent neural ODEs with compound Poisson process for learning continuous and discrete dynamics

The authors introduce a novel architecture with two co-dependent branches of neural ordinary differential equations (NODEs). One branch learns continuous dynamics for continuous variates, while the other uses a compound Poisson process to learn discrete dynamics that can jump for discrete variates. Gate temporal convolution networks model correlations between these different dynamics.

Contribution

Unified probabilistic modeling with joint probability distribution for anomaly detection

The authors propose modeling a joint probability distribution across continuous and discrete variates using multivariate Gaussian and softmax distributions respectively. The model is optimized via Maximum Likelihood Estimation in a unified probabilistic space, and anomalies are detected using joint probabilities that account for the marginal probabilities and importance of different variates.

Contribution

First method for learning both continuous and discrete dynamics in multivariate time series anomaly detection

The authors claim to be the first to discriminate between and simultaneously learn continuous dynamics (for real-valued variates) and discrete dynamics (for natural-number-valued variates) in the context of multivariate time series anomaly detection, addressing a gap in existing methods that treat all variates uniformly.

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