# Interpretable deep convolutional model for nonlinear multivariate time series in complex systems

arXiv: https://arxiv.org/abs/2501.04339 · HTML: https://mlsanity.com/paper/2501.04339/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 33 references that are in the map.
- First posted on arXiv 8 Jan 2025.

## Builds on (most cited first, 20 of 20)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Attention is not Explanation](https://mlsanity.com/paper/1902.10186/) (2019)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Attention is not not Explanation](https://mlsanity.com/paper/1908.04626/) (2019)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction](https://mlsanity.com/paper/1704.02971/) (2017)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [TSMixer: An All-MLP Architecture for Time Series Forecasting](https://mlsanity.com/paper/2303.06053/) (2023)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [Deep Learning for Time Series Forecasting: Tutorial and Literature Survey](https://mlsanity.com/paper/2004.10240/) (2020)
- [Multilevel Wavelet Decomposition Network for Interpretable Time Series Analysis](https://mlsanity.com/paper/1806.08946/) (2018)
- [Exploring Interpretable LSTM Neural Networks over Multi-Variable Data](https://mlsanity.com/paper/1905.12034/) (2019)
- [Multi-scale Attention Flow for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2205.07493/) (2022)
- [Spatiotemporal Attention for Multivariate Time Series Prediction and Interpretation](https://mlsanity.com/paper/2008.04882/) (2020)
- [Counterfactual Explanations for Time Series Forecasting](https://mlsanity.com/paper/2310.08137/) (2023)
- [An Empirical Study of Explainable AI Techniques on Deep Learning Models For Time Series Tasks](https://mlsanity.com/paper/2012.04344/) (2020)
- [A Performance-Explainability Framework to Benchmark Machine Learning Methods: Application to Multivariate Time Series Classifiers](https://mlsanity.com/paper/2005.14501/) (2020)
- [TSEM: Temporally Weighted Spatiotemporal Explainable Neural Network for Multivariate Time Series](https://mlsanity.com/paper/2205.13012/) (2022)
- [Interpretability for Time Series Transformers using A Concept Bottleneck Framework](https://mlsanity.com/paper/2410.06070/) (2024)
- [XForecast: Evaluating Natural Language Explanations for Time Series Forecasting](https://mlsanity.com/paper/2410.14180/) (2024)

## Abstract (arXiv)

We introduce the Deep Convolutional Interpreter for Time Series (DCIts), a deep-learning architecture for nonlinear multivariate time series that provides sample-specific, locally interpretable descriptions of the underlying interaction structure. Unlike standard black-box forecasters, DCIts learns a time- and lag-dependent transition tensor explicitly factorized into two components: a Focuser, which selects relevant source series and time lags via a sparse masking mechanism, and a Modeler, which assigns signed coefficients to these selected interactions. This decomposition yields a local lag-adjacency structure and signed source-lag contributions for every forecast instance, enabling direct inspection of effective connectivity; when higher-order branches are activated, the same framework yields order-resolved elementwise polynomial contributions. Architecturally, DCIts uses a diverse bank of convolutional filters to capture temporal and cross-variable dependencies, which are mapped through a bottleneck network to the transition tensor. On controlled benchmark datasets with a known interaction structure, we demonstrate that DCIts achieves competitive forecasting error relative to a strong interpretable baseline while recovering stable, signed, lag-resolved interaction patterns. The framework thus prioritizes intrinsic interpretability, using forecasting accuracy as a faithfulness constraint rather than the sole objective.