# Dynamic Perturbed Adaptive Method for Infinite Task-Conflicting Time Series

arXiv: https://arxiv.org/abs/2505.11902 · HTML: https://mlsanity.com/paper/2505.11902/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 32 references that are in the map.
- First posted on arXiv 17 May 2025.

## Builds on (most cited first, 25 of 25)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [An Overview of Multi-Task Learning in Deep Neural Networks](https://mlsanity.com/paper/1706.05098/) (2017)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Fast and Flexible Multi-Task Classification Using Conditional Neural Adaptive Processes](https://mlsanity.com/paper/1906.07697/) (2019)
- [TimeFilter: Patch-Specific Spatial-Temporal Graph Filtration for Time Series Forecasting](https://mlsanity.com/paper/2501.13041/) (2025)
- [Learning Fast and Slow for Online Time Series Forecasting](https://mlsanity.com/paper/2202.11672/) (2022)
- [Stochastic Majorization-Minimization Algorithms for Large-Scale Optimization](https://mlsanity.com/paper/1306.4650/) (2013)
- [TimeRAF: Retrieval-Augmented Foundation model for Zero-shot Time Series Forecasting](https://mlsanity.com/paper/2412.20810/) (2024)
- [Channel-Aware Low-Rank Adaptation in Time Series Forecasting](https://mlsanity.com/paper/2407.17246/) (2024)
- [TRACE: Time SeRies PArameter EffiCient FinE-tuning](https://mlsanity.com/paper/2503.16991/) (2025)
- [Kernel-U-Net: Multivariate Time Series Forecasting using Custom Kernels](https://mlsanity.com/paper/2401.01479/) (2024)
- [An Efficient Continual Learning Framework for Multivariate Time Series Prediction Tasks with Application to Vehicle State Estimation](https://mlsanity.com/paper/2503.01669/) (2025)

## Abstract (arXiv)

We formulate time series tasks as input-output mappings under varying objectives, where the same input may yield different outputs. This challenges a model's generalization and adaptability. To study this, we construct a synthetic dataset with numerous conflicting subtasks to evaluate adaptation under frequent task shifts. Existing static models consistently fail in such settings. We propose a dynamic perturbed adaptive method based on a trunk-branch architecture, where the trunk evolves slowly to capture long-term structure, and branch modules are re-initialized and updated for each task. This enables continual test-time adaptation and cross-task transfer without relying on explicit task labels. Theoretically, we show that this architecture has strictly higher functional expressivity than static models and LoRA. We also establish exponential convergence of branch adaptation under the Polyak-Lojasiewicz condition. Experiments demonstrate that our method significantly outperforms competitive baselines in complex and conflicting task environments, exhibiting fast adaptation and progressive learning capabilities.