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NVExplain: Explaining Time Series Forecasting with Latent Trajectory Analysis and Structure-Preserving Surrogates
Muyan Anna Li, Manikandan Ravikiran, Aditi Gautam
TL;DR
NVExplain addresses the opacity of time-series forecasting explanations, especially methods that overlook temporal dependence and horizon-specific lag influence. It analyzes latent temporal evolution with semantic flow, builds horizon-resolved lag attributions, and adds structure-preserving sparse surrogates; semantic flow achieves competitive faithfulness with lower computational cost, while stability diagnostics identify when interpretation requires caution.
Problem
Existing post-hoc forecasting explanations often overlook temporal dependence, horizon-specific lag influence, and the evolution of information through latent representations, limiting interpretability in high-stakes settings.
Method
NVExplain is a model-agnostic framework that uses semantic flow over rolling latent trajectories to construct lag–horizon attributions and structure-preserving sparse local surrogates.
Results
Semantic flow achieves competitive or stronger faithfulness across multiple datasets, with lower computational cost than standard post-hoc baselines.
Takeaways & Limitations
Horizon-specific latent-flow attributions, supplemented by stability diagnostics and optional surrogates, provide temporally coherent explanations of forecasting behavior.
Takeaways & Limitations
In highly nonlinear temporal regimes, sparse local surrogates may sacrifice fidelity, so the semantic-flow matrix and stability diagnostics should be used when surrogate fits are unreliable.
Abstract
from arXiv · showhide
Time series forecasting models are widely used in high-stakes settings, yet their predictions remain difficult to interpret because existing post-hoc methods often ignore temporal dependence and fail to provide horizon-specific explanations. We propose a model-agnostic explainability framework that explains forecasting predictions by attributing each forecast horizon to temporally relevant historical lags. The framework models forecasting as a latent trajectory and introduces semantic flow to quantify how information evolves across time in the model's internal representations. By aggregating semantic flow, it constructs a lag-horizon attribution matrix that captures horizon-resolved temporal influence. To improve explainability, we further generate structure-preserving perturbations and fit sparse local surrogate models, producing human-readable and temporally coherent explanations. We evaluate the method using faithfulness and stability diagnostics across multiple benchmark datasets. Results show that the semantic-flow variant achieves competitive or superior faithfulness compared to standard post-hoc baselines, while being substantially more computationally efficient. Stability analysis further demonstrates that the explanations are robust and identifies regimes where interpretation should be applied with caution.
1 Introduction
NVExplain addresses temporal and horizon-specific gaps in forecasting explainability by analyzing latent evolution and producing structure-preserving, human-readable explanations. Evaluations use forecasting-specific faithfulness and stability diagnostics, with semantic flow showing competitive or stronger faithfulness across datasets.
- High-stakes forecasting decisions remain difficult to trust because modern forecasters’ internal reasoning is opaque.
- Existing sequential explainers can violate temporal continuity, miss horizon-specific lag effects, and overlook information evolution in latent representations.
- NVExplain constructs latent trajectories, measures semantic flow, and aggregates it into a lag-by-horizon matrix of horizon-resolved historical-lag influence.
- Structure-preserving perturbations and sparse local surrogate models produce temporally coherent, human-readable explanations.
- Semantic flow achieves competitive or stronger faithfulness across multiple datasets while offering more temporally coherent explanations than standard post-hoc approaches.
- The framework evaluates explanation quality with forecasting-specific faithfulness and stability diagnostics.
2 Methodology
NVExplain explains multi-step forecasts by tracing latent representations across rolling context windows, converting semantic changes into horizon-specific lag attributions. Structure-preserving perturbations and sparse local surrogates add temporally coherent, human-readable approximations.
- 2.1 Latent Trajectory Construction: The model-agnostic pipeline constructs latent trajectories from rolling context windows and analyzes how internal representations evolve without modifying or retraining the forecaster.Its stages are latent trajectory construction, semantic flow computation, lag–horizon attribution, and structure-preserving local surrogates.
- 2.2 Semantic Flow Magnitudes: Semantic flow measures changes between consecutive latent states, quantifying how strongly new information influences the representation at each temporal step.An optional exponential moving average smooths the trajectory to reduce sensitivity to noise.
- 2.3 Lag–Horizon Attribution Matrix: The lag–horizon score matrix aggregates semantic-flow signals over temporal history to quantify each historical lag’s contribution to each forecast horizon.A horizon-dependent kernel weights transition ages, with longer horizons incorporating broader history as temporal relevance decays.
- 2.3 Lag–Horizon Attribution Matrix: A horizon-wise softmax converts lag scores into attribution distributions, so each matrix column represents the lag distribution for one forecast horizon.The softmax temperature controls attribution sharpness and is distinct from trajectory length and the rolling-window index.
- 2.4 Structure-Preserving Local Surrogates: Structure-preserving local surrogates use block-bootstrap resampling and Fourier-domain amplitude perturbations to preserve temporal continuity and seasonal structure.Sparse linear surrogates are fitted with locality-weighted ℓ1 regularization and latent-space weights.
- 2.5 Outputs: The framework produces lag–horizon attribution matrices, semantic-flow statistics, and optional surrogate coefficients for quantitative and qualitative analysis of forecasting behavior.Together, these outputs provide temporal influence summaries, latent-dynamics measurements, and locally faithful approximations.
3 Experimental Setup
The evaluation uses four long-horizon datasets and compares faithfulness and stability through perturbation-based metrics and latent-representation diagnostics.
- Datasets and protocol: Experiments use ETTh1, Exchange, ILI, and Weather, with explanations computed over the most recent 128 lags for a 72-step horizon.The MOMENT model uses context length 512 and is evaluated across industrial monitoring, finance, epidemiology, and meteorology.
- Evaluation metrics: Faithfulness measures whether explanations identify consequential temporal inputs through forecast changes after ranked lag removal.The evaluation includes faithfulness pass rate and AOPC-based comparisons between top- and bottom-ranked lag removals.
- Evaluation metrics: Higher AOPC and larger Gap indicate more faithful identification of consequential lags, with values averaged across forecast horizons.AOPC measures cumulative forecast degradation as top-ranked lags are progressively removed.
- Stability diagnostics: Stability evaluates latent representations under small input perturbations and the smoothness of their temporal evolution.Embedding stability uses perturbation summary statistics, while trajectory stability uses zero-crossing rate, direction flip, and relative jitter.
- Stability diagnostics: Lower stability-diagnostic values indicate more stable and trustworthy explanations.The diagnostics are motivated by the need for temporally consistent representations in forecasting.
4 Preliminary Results
Preliminary results show that direct semantic-flow attribution is generally faithful, efficient, and temporally coherent, while surrogate explanations can lose fidelity in nonlinear settings.
- Faithfulness: Semantic flow matches the best FPR on ETTh1 at 99.1% and outperforms all baselines on Exchange at 88.9% and Weather at 96.3%.On ILI, Integrated Gradients leads at 76.1%, while semantic flow remains competitive at 67.1% at far lower cost.
- Faithfulness: Semantic flow produces the largest AOPC and strongest separation from control perturbations on ETTh1, Exchange, and Weather while running faster than Integrated Gradients and TimeSHAP.These results indicate that the identified lags carry substantial predictive signal.
- Surrogate behavior: The full surrogate variant remains strong on ETTh1 but degrades on Exchange, ILI, and Weather.The paper suggests that surrogate approximation error emerges under highly nonlinear temporal dynamics.
- Attribution structure: On Weather, semantic-flow attribution concentrates on recent lags and decays smoothly across horizons, unlike fragmented and noisy TimeSHAP attribution.The reported total variation is 0.010 for semantic flow versus 0.474 for TimeSHAP.
- Stability: Exchange, ILI, and Weather have embedding sensitivity below 0.02, whereas ETTh1 is substantially more sensitive but still achieves the highest faithfulness.The results suggest strong temporal dependence can persist under unstable latent dynamics.
- Interpretation: Smoother horizon-wise attribution patterns are easier to interpret, but readability is treated as a qualitative diagnostic rather than a human-subject measure.The paper leaves formal human-subject evaluation for future work.
- Interpretation: Faithfulness and stability provide complementary evidence about temporal influence and representation robustness.Datasets combining high faithfulness with stable latents, such as Weather, form the most reliable interpretive regime, while unstable regimes warrant caution.
5 Conclusion
NVExplain attributes each forecast horizon to relevant historical lags through semantic flow in latent space, with stability diagnostics assessing explanation reliability. The framework reports competitive faithfulness at lower computational cost, while sparse surrogates may lose fidelity in highly nonlinear regimes.
- NVExplain attributes each forecast horizon to relevant historical lags through semantic flow in latent space.
- The method achieves competitive faithfulness with lower computational cost than standard post-hoc baselines.
- The framework includes stability diagnostics to assess explanation reliability.
- In highly nonlinear temporal regimes, sparse local surrogates may sacrifice fidelity even when semantic-flow attribution remains faithful.