# Efficient Pareto Manifold Learning with Low-Rank Structure

arXiv: https://arxiv.org/abs/2407.20734 · HTML: https://mlsanity.com/paper/2407.20734/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 55 references that are in the map.
- First posted on arXiv 30 Jul 2024.

## Builds on (most cited first, 30 of 32)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (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)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentation](https://mlsanity.com/paper/1511.00561/) (2015)
- [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)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [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)
- [Age Progression/Regression by Conditional Adversarial Autoencoder](https://mlsanity.com/paper/1702.08423/) (2017)
- [Orthogonal Subspace Learning for Language Model Continual Learning](https://mlsanity.com/paper/2310.14152/) (2023)
- [Pareto Multi-Task Learning](https://mlsanity.com/paper/1912.12854/) (2019)
- [Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models](https://mlsanity.com/paper/2305.12827/) (2023)
- [Multi-Task Learning as a Bargaining Game](https://mlsanity.com/paper/2202.01017/) (2022)
- [Just Pick a Sign: Optimizing Deep Multitask Models with Gradient Sign Dropout](https://mlsanity.com/paper/2010.06808/) (2020)
- [Routing Networks: Adaptive Selection of Non-linear Functions for Multi-Task Learning](https://mlsanity.com/paper/1711.01239/) (2017)
- [Learning the Pareto Front with Hypernetworks](https://mlsanity.com/paper/2010.04104/) (2020)
- [Orthogonal Convolutional Neural Networks](https://mlsanity.com/paper/1911.12207/) (2019)
- [Auto-Lambda: Disentangling Dynamic Task Relationships](https://mlsanity.com/paper/2202.03091/) (2022)
- [All You Need is Beyond a Good Init: Exploring Better Solution for Training Extremely Deep Convolutional Neural Networks with Orthonormality and Modulation](https://mlsanity.com/paper/1703.01827/) (2017)
- [Efficient Continuous Pareto Exploration in Multi-Task Learning](https://mlsanity.com/paper/2006.16434/) (2020)
- [Scalable Pareto Front Approximation for Deep Multi-Objective Learning](https://mlsanity.com/paper/2103.13392/) (2021)
- [Pareto Manifold Learning: Tackling multiple tasks via ensembles of single-task models](https://mlsanity.com/paper/2210.09759/) (2022)

## Built on by (most cited first, 9 of 9)

- [PARM: Multi-Objective Test-Time Alignment via Preference-Aware Autoregressive Reward Model](https://mlsanity.com/paper/2505.06274/) (2025)
- [Gradient-Based Multi-Objective Deep Learning: Algorithms, Theories, Applications, and Beyond](https://mlsanity.com/paper/2501.10945/) (2025)
- [Safe Delta: Consistently Preserving Safety when Fine-Tuning LLMs on Diverse Datasets](https://mlsanity.com/paper/2505.12038/) (2025)
- [LibMOON: A Gradient-based MultiObjective OptimizatioN Library in PyTorch](https://mlsanity.com/paper/2409.02969/) (2024)
- [Efficient Knowledge Transfer in Multi-Task Learning through Task-Adaptive Low-Rank Representation](https://mlsanity.com/paper/2505.00009/) (2025)
- [UniARM: Towards a Unified Autoregressive Reward Model for Multi-Objective Test-Time Alignment](https://mlsanity.com/paper/2602.09538/) (2026)
- [Learning Pareto manifolds in high dimensions: How can regularization help?](https://mlsanity.com/paper/2503.08849/) (2025)
- [Towards Relaxed Multimodal Inputs for Gait-based Parkinson's Disease Assessment](https://mlsanity.com/paper/2510.15748/) (2025)
- [Multi-Objective Exploration and Preference Optimization via Mutual Information](https://mlsanity.com/paper/2607.01392/) (2026)

## Abstract (arXiv)

Multi-task learning, which optimizes performance across multiple tasks, is inherently a multi-objective optimization problem. Various algorithms are developed to provide discrete trade-off solutions on the Pareto front. Recently, continuous Pareto front approximations using a linear combination of base networks have emerged as a compelling strategy. However, it suffers from scalability issues when the number of tasks is large. To address this issue, we propose a novel approach that integrates a main network with several low-rank matrices to efficiently learn the Pareto manifold. It significantly reduces the number of parameters and facilitates the extraction of shared features. We also introduce orthogonal regularization to further bolster performance. Extensive experimental results demonstrate that the proposed approach outperforms state-of-the-art baselines, especially on datasets with a large number of tasks.