# PA-RNet: Perturbation-Aware Residual Network for Robust Multimodal Time Series Forecasting

arXiv: https://arxiv.org/abs/2508.04750 · HTML: https://mlsanity.com/paper/2508.04750/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 37 references that are in the map.
- First posted on arXiv 6 Aug 2025.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [FiLM: Frequency improved Legendre Memory Model for Long-term Time Series Forecasting](https://mlsanity.com/paper/2205.08897/) (2022)
- [LLM4TS: Aligning Pre-Trained LLMs as Data-Efficient Time-Series Forecasters](https://mlsanity.com/paper/2308.08469/) (2023)
- [TimeCMA: Towards LLM-Empowered Multivariate Time Series Forecasting via Cross-Modality Alignment](https://mlsanity.com/paper/2406.01638/) (2024)
- [From News to Forecast: Integrating Event Analysis in LLM-Based Time Series Forecasting with Reflection](https://mlsanity.com/paper/2409.17515/) (2024)
- [Deep Learning for Financial Applications : A Survey](https://mlsanity.com/paper/2002.05786/) (2020)
- [Context is Key: A Benchmark for Forecasting with Essential Textual Information](https://mlsanity.com/paper/2410.18959/) (2024)
- [Time-MMD: Multi-Domain Multimodal Dataset for Time Series Analysis](https://mlsanity.com/paper/2406.08627/) (2024)
- [Time-VLM: Exploring Multimodal Vision-Language Models for Augmented Time Series Forecasting](https://mlsanity.com/paper/2502.04395/) (2025)
- [Language in the Flow of Time: Time-Series-Paired Texts Weaved into a Unified Temporal Narrative](https://mlsanity.com/paper/2502.08942/) (2025)
- [TimeXL: Explainable Multi-modal Time Series Prediction with LLM-in-the-Loop](https://mlsanity.com/paper/2503.01013/) (2025)
- [Performance Metrics (Error Measures) in Machine Learning Regression, Forecasting and Prognostics: Properties and Typology](https://mlsanity.com/paper/1809.03006/) (2018)
- [Deep learning for temporal data representation in electronic health records: A systematic review of challenges and methodologies](https://mlsanity.com/paper/2107.09951/) (2021)
- [Text-CRS: A Generalized Certified Robustness Framework against Textual Adversarial Attacks](https://mlsanity.com/paper/2307.16630/) (2023)
- [Multi-Modal Forecaster: Jointly Predicting Time Series and Textual Data](https://mlsanity.com/paper/2411.06735/) (2024)
- [How Can Time Series Analysis Benefit From Multiple Modalities? A Survey and Outlook](https://mlsanity.com/paper/2503.11835/) (2025)
- [Robust Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2202.11910/) (2022)
- [There are no Champions in Supervised Long-Term Time Series Forecasting](https://mlsanity.com/paper/2502.14045/) (2025)

## Built on by (most cited first, 1 of 1)

- [Rethinking Multimodal Fusion for Time Series: Text Modalities Need Constrained Fusion](https://mlsanity.com/paper/2603.22372/) (2026)

## Abstract (arXiv)

In real-world applications, multimodal time-series forecasting faces a key challenge: textual information is often useful but unreliable. Auxiliary texts may contain irrelevant, ambiguous, incomplete, or structurally corrupted content, making direct text integration prone to introducing noisy semantic signals and degrading forecasting performance. Therefore, robust multimodal forecasting requires a model that can exploit useful textual context while suppressing misleading perturbations. To address this challenge, we propose PA-RNet, a carefully designed perturbation-aware residual network for robust multimodal time-series forecasting. Rather than directly fusing textual and numerical representations, PA-RNet first refines multimodal features in a perturbation-aware manner, preserving stable contextual information while reducing unstable or misleading signals. The refined textual representations are then aligned with temporal dynamics, enabling more reliable forecasting under noisy multimodal conditions. Theoretically, we prove that PA-RNet is Lipschitz continuous with respect to textual embeddings and show that the proposed spectral residual correction can reduce the expected prediction error under zero-mean textual perturbations. We further conduct supplementary experiments with injected textual perturbations to examine the robustness of PA-RNet. The results across diverse domains demonstrate that PA-RNet consistently outperforms state-of-the-art baselines and maintains stable forecasting performance under both original and noise-perturbed textual conditions.