# SIMS: Scale-Invariant Merit-Function-Based Scalarization for Multi-Task Learning

arXiv: https://arxiv.org/abs/2609.12599 · HTML: https://mlsanity.com/paper/2609.12599/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 56 references that are in the map.
- First posted on arXiv 11 Sep 2026.

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

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- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [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)
- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [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)
- [An Overview of Multi-Task Learning in Deep Neural Networks](https://mlsanity.com/paper/1706.05098/) (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)
- [On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems](https://mlsanity.com/paper/1906.00331/) (2019)
- [Multi-Task Learning as a Bargaining Game](https://mlsanity.com/paper/2202.01017/) (2022)
- [Entire Space Multi-Task Model: An Effective Approach for Estimating Post-Click Conversion Rate](https://mlsanity.com/paper/1804.07931/) (2018)
- [Attentive Single-Tasking of Multiple Tasks](https://mlsanity.com/paper/1904.08918/) (2019)
- [NDDR-CNN: Layerwise Feature Fusing in Multi-Task CNNs by Neural Discriminative Dimensionality Reduction](https://mlsanity.com/paper/1801.08297/) (2018)
- [A Unified Single-loop Alternating Gradient Projection Algorithm for Nonconvex-Concave and Convex-Nonconcave Minimax Problems](https://mlsanity.com/paper/2006.02032/) (2020)
- [Polyhistor: Parameter-Efficient Multi-Task Adaptation for Dense Vision Tasks](https://mlsanity.com/paper/2210.03265/) (2022)
- [MultiNet++: Multi-Stream Feature Aggregation and Geometric Loss Strategy for Multi-Task Learning](https://mlsanity.com/paper/1904.08492/) (2019)
- [Vision Transformer Adapters for Generalizable Multitask Learning](https://mlsanity.com/paper/2308.12372/) (2023)
- [Using Well-Understood Single-Objective Functions in Multiobjective Black-Box Optimization Test Suites](https://mlsanity.com/paper/1604.00359/) (2016)
- [Mitigating Negative Transfer in Multi-Task Learning with Exponential Moving Average Loss Weighting Strategies](https://mlsanity.com/paper/2211.12999/) (2022)
- [Generalization Bounds of Nonconvex-(Strongly)-Concave Stochastic Minimax Optimization](https://mlsanity.com/paper/2205.14278/) (2022)
- [Efficient First-Order Optimization on the Pareto Set for Multi-Objective Learning under Preference Guidance](https://mlsanity.com/paper/2504.02854/) (2025)

## Abstract (arXiv)

Multi-task learning (MTL) requires navigating unavoidable trade-offs among competing objectives. This paradigm is frequently formulated as multi-objective optimization (MOO), where the scalarization is favored to reduce an MOO problem to a single objective. We empirically find that existing merit-function-based scalarization approaches are sensitive to the relative scales of different objectives in practical MTL, where task losses commonly differ by orders of magnitude. The optimization process often favors objectives with larger scales even though the underlying Pareto optimal solutions remains invariant to rescaling (i.e., multiplying an objective by a positive constant). To address this issue, we propose Scale-Invariant Merit-function-based Scalarization (SIMS) for MTL. Specifically, SIMS adopts a transformation-induced merit function to convert the MOO problem of MTL to a single objective that renders optimization invariant to the magnitudes of losses. Theoretically, we prove that the requirement for scale invariance uniquely determines this transformation to be logarithmic. We further show that this general transformation-induced merit function preserves weak Pareto optimality and admits a smooth surrogate with controllable approximation error. Extensive experiments on representative multi-task benchmarks demonstrate that SIMS consistently outperforms existing scalarization methods and achieves state-of-the-art performance.