ReGEN-TAD: Interpretable Anomaly Detection

• The paper introduces ReGEN-TAD, a framework that jointly reconstructs historical windows and forecasts future blocks to detect structural anomalies in high-dimensional financial time series.
• It integrates convolutional, transformer, and bidirectional LSTM modules to capture both local interactions and long-range dependencies, ensuring robust anomaly detection without labeled data.
• The method fuses six distinct diagnostic signals and employs gradient-based factor attribution, providing economically coherent explanations for detected anomalies.

Searching arXiv for the specified paper to ground the article in the primary source. ReGEN-TAD is an interpretable generative framework for anomaly detection in high-dimensional financial time series, introduced for the problem of detecting structural instability and anomalies under complex temporal dependence and evolving cross-sectional structure. It jointly reconstructs historical windows and forecasts future blocks, combines modern machine learning with econometric diagnostics, and aggregates complementary anomaly signals capturing predictive inconsistency, reconstruction degradation, latent distortion, and volatility shifts. The framework is designed to operate without labeled data through robust calibration of a unified anomaly score, while also supporting economically coherent factor-level attribution in high-dimensional financial panels (Martinez, 9 Mar 2026).

1. Problem setting and conceptual scope

ReGEN-TAD is formulated for a multivariate time series $x_t \in \mathbb{R}^p$, observed for $t=1,\dots,T$. From this series, a rolling window of length $L$ and a forecast block of length $H$ are constructed as

$$X_t = [x_{t-L+1}, \dots, x_t] \in \mathbb{R}^{L\times p}, \qquad F_t = [x_{t+1}, \dots, x_{t+H}] \in \mathbb{R}^{H\times p}.$$

The core operational objective is joint reconstruction of $X_t$ and forecasting of $F_t$ (Martinez, 9 Mar 2026).

The framework targets anomaly detection in settings where purely residual-based monitoring is insufficient because deviations may manifest as changes in forecastability, latent geometry, or residual dispersion. In the formulation given for ReGEN-TAD, anomaly detection is therefore not reduced to a single reconstruction or prediction error; instead, it is based on an ensemble of six diagnostics extracted from the observed window, the forecast block, and the learned latent state. This suggests a deliberate attempt to capture both pointwise deviations and structural departures in latent and cross-sectional dynamics.

The paper positions the method specifically in high-dimensional financial time series, where cross-sectional co-movement, volatility clustering, regime shifts, contagion, and structural breaks can coexist. A plausible implication is that the architecture is intended to remain sensitive to departures that are economically meaningful even when they are not easily separable in the raw observation space.

2. Backbone architecture

The backbone begins with a temporal convolutional block. It applies $d$ one-dimensional causal filters of width $k$ along time, shared over the $p$ channels. The hidden states are defined by

$t=1,\dots,T$0

and are stacked into

$t=1,\dots,T$1

In the description of the model, this stage encodes local cross-sectional interactions (Martinez, 9 Mar 2026).

Fixed sinusoidal positional encodings $t=1,\dots,T$2 are then added:

$t=1,\dots,T$3

These encodings inject absolute and relative time information into the latent representation (Martinez, 9 Mar 2026).

A transformer encoder operates on $t=1,\dots,T$4 through multi-head self-attention. For one attention head,

$t=1,\dots,T$5

$t=1,\dots,T$6

This component is used to capture long-range dependencies in the sequence (Martinez, 9 Mar 2026).

In parallel with attention-based sequence modeling, a bidirectional LSTM processes $t=1,\dots,T$7 in both forward and backward time. Its final pooled outputs are

$t=1,\dots,T$8

which are concatenated and projected to a $t=1,\dots,T$9-dimensional latent variable,

$L$0

According to the technical summary, the bidirectional LSTM models sequential propagation, complementing the transformer's long-range dependence modeling (Martinez, 9 Mar 2026).

Two output heads are then defined from $L$1. The first yields an initial forecast

$L$2

and the second yields a reconstruction

$L$3

A two-stage refinement is applied to the forecast: the residual $L$4 is computed, vectorized, concatenated with $L$5, and passed through a small MLP to produce a corrected forecast $L$6. The stated role of this two-stage forecast head is to increase sensitivity to evolving drift and structural shifts (Martinez, 9 Mar 2026).

3. Anomaly signals and fused scoring

For each window $L$7, ReGEN-TAD extracts $L$8 raw diagnostics, denoted $L$9. The six diagnostics are designed to reflect different modes of abnormality rather than a single error channel (Martinez, 9 Mar 2026).

The first signal is predictive inconsistency, defined as the refined-forecast residual magnitude:

$H$0

The second is reconstruction degradation:

$H$1

These two terms anchor the detector in observable discrepancies in future and past windows, respectively (Martinez, 9 Mar 2026).

The third signal is latent density distortion, computed with $H$2-nearest neighbors in latent space:

$H$3

The fourth is latent dynamics deviation:

$H$4

where $H$5 is the one-step-ahead latent predicted from $H$6 and $H$7 is small, for example $H$8. The fifth is Mahalanobis regime distance in latent space:

$H$9

with $$X_t = [x_{t-L+1}, \dots, x_t] \in \mathbb{R}^{L\times p}, \qquad F_t = [x_{t+1}, \dots, x_{t+H}] \in \mathbb{R}^{H\times p}.$$0 estimated on purified data and shrinkage-regularized (Martinez, 9 Mar 2026).

The sixth signal is a volatility-shift diagnostic defined as the dispersion of forecast residuals:

$$X_t = [x_{t-L+1}, \dots, x_t] \in \mathbb{R}^{L\times p}, \qquad F_t = [x_{t+1}, \dots, x_{t+H}] \in \mathbb{R}^{H\times p}.$$1

Taken together, these six signals combine predictive error, reconstruction error, latent neighborhood structure, latent temporal consistency, latent regime deviation, and residual volatility behavior. This suggests that ReGEN-TAD treats anomalies as potentially heterogeneous objects: some are primarily predictive failures, some are latent-distribution shifts, and others are volatility or regime events.

Each component is robustly standardized across calibration windows:

$$X_t = [x_{t-L+1}, \dots, x_t] \in \mathbb{R}^{L\times p}, \qquad F_t = [x_{t+1}, \dots, x_{t+H}] \in \mathbb{R}^{H\times p}.$$2

The fused anomaly score is then formed as

$$X_t = [x_{t-L+1}, \dots, x_t] \in \mathbb{R}^{L\times p}, \qquad F_t = [x_{t+1}, \dots, x_{t+H}] \in \mathbb{R}^{H\times p}.$$3

This robust standardization and weighted fusion mechanism is central to the framework’s unlabeled calibration strategy (Martinez, 9 Mar 2026).

4. Calibration and decision rules

ReGEN-TAD supports two decision rules for converting the fused score into anomaly labels. The first is quantile thresholding:

$$X_t = [x_{t-L+1}, \dots, x_t] \in \mathbb{R}^{L\times p}, \qquad F_t = [x_{t+1}, \dots, x_{t+H}] \in \mathbb{R}^{H\times p}.$$4

The second is rank-based picking:

$$X_t = [x_{t-L+1}, \dots, x_t] \in \mathbb{R}^{L\times p}, \qquad F_t = [x_{t+1}, \dots, x_{t+H}] \in \mathbb{R}^{H\times p}.$$5

An optional EWMA smoothing of $$X_t = [x_{t-L+1}, \dots, x_t] \in \mathbb{R}^{L\times p}, \qquad F_t = [x_{t+1}, \dots, x_{t+H}] \in \mathbb{R}^{H\times p}.$$6 can be applied to promote temporal coherence (Martinez, 9 Mar 2026).

The use of median- and IQR-based standardization before score fusion indicates that calibration is explicitly designed to reduce sensitivity to extreme values in any one diagnostic. A plausible implication is that the framework aims to stabilize decisions under contaminated or weakly nonstationary calibration sets, especially when anomaly labels are unavailable. The support for both quantile thresholding and rank-based selection also makes the detector adaptable to fixed-rate alarm regimes and retrospective top-fraction screening.

The paper describes this calibration process as yielding a unified anomaly score without labeled data. In that sense, ReGEN-TAD belongs to a class of unsupervised or label-free anomaly detectors, but its formulation emphasizes calibrated aggregation over a heterogeneous diagnostic ensemble rather than reliance on a single implicit reconstruction objective (Martinez, 9 Mar 2026).

5. Factor-level attribution and interpretability

When $$X_t = [x_{t-L+1}, \dots, x_t] \in \mathbb{R}^{L\times p}, \qquad F_t = [x_{t+1}, \dots, x_{t+H}] \in \mathbb{R}^{H\times p}.$$7, the anomaly is decomposed into factor-specific contributions. For each cross-sectional index $$X_t = [x_{t-L+1}, \dots, x_t] \in \mathbb{R}^{L\times p}, \qquad F_t = [x_{t+1}, \dots, x_{t+H}] \in \mathbb{R}^{H\times p}.$$8, the first component is a standardized deviation from the baseline mean:

$$X_t = [x_{t-L+1}, \dots, x_t] \in \mathbb{R}^{L\times p}, \qquad F_t = [x_{t+1}, \dots, x_{t+H}] \in \mathbb{R}^{H\times p}.$$9

where $X_t$0 are the calibration mean and standard deviation of factor $X_t$1 (Martinez, 9 Mar 2026).

The second component is latent sensitivity, defined via the gradient of a latent-space anomaly functional

$X_t$2

with

$X_t$3

The multiplicative factor contribution is then

$X_t$4

optionally normalized so that $X_t$5 (Martinez, 9 Mar 2026).

The factors with largest $X_t$6 are described as forming a sparse, economically interpretable explanation of the detected anomaly. The attribution mechanism therefore combines an observable baseline deviation term with a latent sensitivity term. This suggests that the method does not treat large raw deviations as sufficient evidence of explanatory importance; rather, explanatory salience arises when a factor is both unusually displaced and influential with respect to the latent anomaly functional.

Within the paper’s framing, interpretability is not merely post hoc visualization. It is operationalized as factor-level attribution linked to the same latent structure used for detection. This is especially consequential in financial panels, where the ability to localize sectoral or factor disturbances can matter as much as the detection event itself (Martinez, 9 Mar 2026).

6. Training objective, purification, and empirical protocol

The training objective is

$X_t$7

The defaults are $X_t$8 and $X_t$9. Before fitting the full backbone, a two-stage reconstruction-only “purification” is run first to remove high-reconstruction-error windows by quantile trim, for example at $F_t$0 (Martinez, 9 Mar 2026).

Evaluation uses Precision, Recall, F$F_t$1-score, False-Positive Rate (FPR), AUROC, and Average Precision. Runtime is measured wall-clock on matched hardware. The experimental setup includes synthetic structural anomalies such as mean and trend shifts, volatility spikes, and collective and contextual anomalies in $F_t$2 dimensions with $F_t$3 and Monte Carlo replications. It also includes financially structured simulations featuring market-wide bull and bear regimes, volatility spikes, correlation breakdown, contagion, momentum crashes, flash events, and microstructure noise (Martinez, 9 Mar 2026).

Additional tests include clean-regime false-alarm experiments on IID processes, GARCH, factor models, and VAR with smooth volatility drift to check FPR under $F_t$4. Sector-shock experiments are conducted on NASDAQ-100 returns with controlled injections including vol spike, mean shift, trend, and jump bursts, and historical case studies examine the 2008 crisis and the 2020 COVID crash on Dow30 returns (Martinez, 9 Mar 2026).

This empirical protocol indicates that the framework is evaluated across both controlled synthetic deviations and historically salient financial stress episodes. A plausible implication is that the authors intend the method to be judged simultaneously on statistical detection performance, false-alarm control, and explanatory localization.

7. Reported performance and significance

On synthetic structural experiments, ReGEN-TAD achieves top overall F$F_t$5 of approximately $F_t$6 versus a next-best value of $F_t$7, with extremely low FPR of approximately $F_t$8. On financial simulations, it ranks first in F$F_t$9 at approximately $d$0 and AUROC, while maintaining precision of approximately $d$1 and FPR of approximately $d$2 (Martinez, 9 Mar 2026).

Under clean regimes, false-alarm rates average $d$3, described as comparable to other deep methods and well below naïve residual monitors. In sector attribution, the method recovers $d$4–$d$5 of truly perturbed assets for sustained disturbances and clearly localizes sectors in real-world crises (Martinez, 9 Mar 2026).

The paper summarizes these results by stating that ReGEN-TAD unifies joint forecasting, reconstruction, ensemble scoring, robust calibration, and gradient-based attribution in a single interpretable framework, delivering state-of-the-art anomaly detection and economically coherent explanations in high-dimensional financial panels (Martinez, 9 Mar 2026). More specifically, the framework’s significance lies in the coupling of detection and attribution within one model pipeline: anomalies are identified through fused diagnostics derived from the learned representation, and explanations are produced through factor-level contributions tied to both standardized deviations and latent sensitivity.

A common misconception in anomaly detection is that interpretability necessarily requires sacrificing detection power, or that performance gains arise solely from more expressive forecasting backbones. ReGEN-TAD’s design, as described, instead attributes performance to the interaction among joint forecasting and reconstruction, multi-signal scoring, robust calibration, and gradient-based attribution. This suggests that its contribution is as much about the composition of diagnostics and decision logic as about the refined convolutional-transformer architecture itself.