# GRAIN: Group Aggregation via Min-Norm Objective

arXiv: https://arxiv.org/abs/2606.22917 · HTML: https://mlsanity.com/paper/2606.22917/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 46 of its 56 references that are in the map.
- First posted on arXiv 22 Jun 2026.

## Builds on (most cited first, 30 of 46)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
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- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [PubMedQA: A Dataset for Biomedical Research Question Answering](https://mlsanity.com/paper/1909.06146/) (2019)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
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- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
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- [Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss](https://mlsanity.com/paper/1906.07413/) (2019)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Training Region-based Object Detectors with Online Hard Example Mining](https://mlsanity.com/paper/1604.03540/) (2016)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [A systematic study of the class imbalance problem in convolutional neural networks](https://mlsanity.com/paper/1710.05381/) (2017)
- [Conflict-Averse Gradient Descent for Multi-task Learning](https://mlsanity.com/paper/2110.14048/) (2021)
- [Fine-Tuning Pretrained Language Models: Weight Initializations, Data Orders, and Early Stopping](https://mlsanity.com/paper/2002.06305/) (2020)
- [ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks](https://mlsanity.com/paper/2102.11600/) (2021)
- [On the Stability of Fine-tuning BERT: Misconceptions, Explanations, and Strong Baselines](https://mlsanity.com/paper/2006.04884/) (2020)
- [Revisiting Few-sample BERT Fine-tuning](https://mlsanity.com/paper/2006.05987/) (2020)
- [R-Drop: Regularized Dropout for Neural Networks](https://mlsanity.com/paper/2106.14448/) (2021)
- [Just Pick a Sign: Optimizing Deep Multitask Models with Gradient Sign Dropout](https://mlsanity.com/paper/2010.06808/) (2020)
- [Mixout: Effective Regularization to Finetune Large-scale Pretrained Language Models](https://mlsanity.com/paper/1909.11299/) (2019)

## Abstract (arXiv)

Learning instability is a long-standing problem across machine learning, but it is especially acute in the overparameterized regime that defines modern deep learning: large models fine-tuned or trained on limited data traverse flat loss landscapes with many nearly-equivalent minima, and stochastic factors (initialization, data order, dropout, hardware non-determinism) can route optimization to very different solutions. The rise of large pretrained models (LPMs) makes the problem more urgent: training cost is high, downstream data is often small, and repeated runs for variance reduction are prohibitive. We introduce GRAIN (Group Aggregation via mIN-norm objective), a lightweight training algorithm that replaces the mean aggregation used in mini-batch optimization (both across mini-batches and within a mini-batch) with a min-norm convex combination of group-wise gradients. mName guarantees a non-negative inner product between the aggregated update and every group gradient, resolving intra- and inner-batch gradient conflict, and retains an O(1/T) convergence rate comparable to SGD. Under mild smoothness and absolute-continuity assumptions, the min-norm solution differs almost surely from the arithmetic mean, which yields a uniform-stability bound for mName strictly tighter than the standard bound for SGD. Empirically across generation, classification, and regression at LPM scale, mName delivers consistent improvements in mean performance and reductions in run-to-run variance over a broad suite of tasks, with no extra training-time or storage cost beyond a single backward pass.