# EMAN: Optimization-Driven Capacity Growth through Path Emergence in Multi-Task Learning

arXiv: https://arxiv.org/abs/2608.16930 · HTML: https://mlsanity.com/paper/2608.16930/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 41 references that are in the map.
- First posted on arXiv 5 Aug 2026.

## Builds on (most cited first, 21 of 21)

- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [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)
- [Lifelong Learning with Dynamically Expandable Networks](https://mlsanity.com/paper/1708.01547/) (2017)
- [End-to-End Multi-Task Learning with Attention](https://mlsanity.com/paper/1803.10704/) (2018)
- [Cross-stitch Networks for Multi-task Learning](https://mlsanity.com/paper/1604.03539/) (2016)
- [Conflict-Averse Gradient Descent for Multi-task Learning](https://mlsanity.com/paper/2110.14048/) (2021)
- [PathNet: Evolution Channels Gradient Descent in Super Neural Networks](https://mlsanity.com/paper/1701.08734/) (2017)
- [Net2Net: Accelerating Learning via Knowledge Transfer](https://mlsanity.com/paper/1511.05641/) (2015)
- [PAD-Net: Multi-Tasks Guided Prediction-and-Distillation Network for Simultaneous Depth Estimation and Scene Parsing](https://mlsanity.com/paper/1805.04409/) (2018)
- [Multi-Task Learning as a Bargaining Game](https://mlsanity.com/paper/2202.01017/) (2022)
- [AdaShare: Learning What To Share For Efficient Deep Multi-Task Learning](https://mlsanity.com/paper/1911.12423/) (2019)
- [MTI-Net: Multi-Scale Task Interaction Networks for Multi-Task Learning](https://mlsanity.com/paper/2001.06902/) (2020)
- [Are Neural Nets Modular? Inspecting Functional Modularity Through Differentiable Weight Masks](https://mlsanity.com/paper/2010.02066/) (2020)
- [Discovering modular solutions that generalize compositionally](https://mlsanity.com/paper/2312.15001/) (2023)
- [On The Specialization of Neural Modules](https://mlsanity.com/paper/2409.14981/) (2024)
- [DiTASK: Multi-Task Fine-Tuning with Diffeomorphic Transformations](https://mlsanity.com/paper/2502.06029/) (2025)
- [How Many Experts Are Enough? Towards Optimal Semantic Specialization for Mixture-of-Experts](https://mlsanity.com/paper/2512.19765/) (2025)

## Abstract (arXiv)

Existing multi-task learning methods rely on hard sharing, multiple paths or experts, adaptive sharing, and dynamic expansion. However, their capacity changes are usually constrained by predefined structures or triggered by task boundaries and conflict signals. This raises a fundamental question: can a network start from exact single-path computation and grow a new independent path only when persistent optimization evidence appears? We propose the Emergent Modular Atomic Network (EMAN), an optimization-driven framework for exposing an antisymmetric growth direction through latent relative phases without instantiating a second path, and for monitoring multiple decision signals during training to transform local optimization evidence into a structural decision. EMAN materializes two equal-capacity independent paths only after certification. EMAN adaptively allocates shared and task-specific representation capacity to accommodate varying task requirements. Extensive experiments on controlled rank settings, PASCAL-Context, and NYUv2 validate its effectiveness, achieving improved performance at a competitive computational cost.