# Continual Optimization with Symmetry Teleportation for Multi-Task Learning

arXiv: https://arxiv.org/abs/2503.04046 · HTML: https://mlsanity.com/paper/2503.04046/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 46 references that are in the map.
- First posted on arXiv 6 Mar 2025.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentation](https://mlsanity.com/paper/1511.00561/) (2015)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [End-to-End Multi-Task Learning with Attention](https://mlsanity.com/paper/1803.10704/) (2018)
- [Conflict-Averse Gradient Descent for Multi-task Learning](https://mlsanity.com/paper/2110.14048/) (2021)
- [Multi-Task Learning as a Bargaining Game](https://mlsanity.com/paper/2202.01017/) (2022)
- [Controlling Text-to-Image Diffusion by Orthogonal Finetuning](https://mlsanity.com/paper/2306.07280/) (2023)
- [Just Pick a Sign: Optimizing Deep Multitask Models with Gradient Sign Dropout](https://mlsanity.com/paper/2010.06808/) (2020)
- [Attentive Single-Tasking of Multiple Tasks](https://mlsanity.com/paper/1904.08918/) (2019)
- [FedPara: Low-Rank Hadamard Product for Communication-Efficient Federated Learning](https://mlsanity.com/paper/2108.06098/) (2021)
- [Reasonable Effectiveness of Random Weighting: A Litmus Test for Multi-Task Learning](https://mlsanity.com/paper/2111.10603/) (2021)
- [Unified Optimal Analysis of the (Stochastic) Gradient Method](https://mlsanity.com/paper/1907.04232/) (2019)
- [FAMO: Fast Adaptive Multitask Optimization](https://mlsanity.com/paper/2306.03792/) (2023)
- [Do Current Multi-Task Optimization Methods in Deep Learning Even Help?](https://mlsanity.com/paper/2209.11379/) (2022)
- [Empirical Analysis of the Strengths and Weaknesses of PEFT Techniques for LLMs](https://mlsanity.com/paper/2304.14999/) (2023)
- [Fair Resource Allocation in Multi-Task Learning](https://mlsanity.com/paper/2402.15638/) (2024)
- [Meta-learning with an Adaptive Task Scheduler](https://mlsanity.com/paper/2110.14057/) (2021)
- [Symmetry Teleportation for Accelerated Optimization](https://mlsanity.com/paper/2205.10637/) (2022)
- [Improving Convergence and Generalization Using Parameter Symmetries](https://mlsanity.com/paper/2305.13404/) (2023)
- [LampMark: Proactive Deepfake Detection via Training-Free Landmark Perceptual Watermarks](https://mlsanity.com/paper/2411.17209/) (2024)
- [Neural Teleportation](https://mlsanity.com/paper/2012.01118/) (2020)
- [MultiTask-CenterNet (MCN): Efficient and Diverse Multitask Learning using an Anchor Free Approach](https://mlsanity.com/paper/2108.05060/) (2021)

## Built on by (most cited first, 3 of 3)

- [Symmetry in Neural Network Parameter Spaces](https://mlsanity.com/paper/2506.13018/) (2025)
- [Delve into the Applicability of Advanced Optimizers for Multi-Task Learning](https://mlsanity.com/paper/2604.08939/) (2026)
- [MOSAIC: Modality-Specific Adaptation for Incremental Continual Learning in Parkinson's Disease Gait Assessment](https://mlsanity.com/paper/2606.13258/) (2026)

## Abstract (arXiv)

Multi-task learning (MTL) is a widely explored paradigm that enables the simultaneous learning of multiple tasks using a single model. Despite numerous solutions, the key issues of optimization conflict and task imbalance remain under-addressed, limiting performance. Unlike existing optimization-based approaches that typically reweight task losses or gradients to mitigate conflicts or promote progress, we propose a novel approach based on Continual Optimization with Symmetry Teleportation (COST). During MTL optimization, when an optimization conflict arises, we seek an alternative loss-equivalent point on the loss landscape to reduce conflict. Specifically, we utilize a low-rank adapter (LoRA) to facilitate this practical teleportation by designing convergent, loss-invariant objectives. Additionally, we introduce a historical trajectory reuse strategy to continually leverage the benefits of advanced optimizers. Extensive experiments on multiple mainstream datasets demonstrate the effectiveness of our approach. COST is a plug-and-play solution that enhances a wide range of existing MTL methods. When integrated with state-of-the-art methods, COST achieves superior performance.