# TRAM: Bridging Trust Regions and Sharpness Aware Minimization

arXiv: https://arxiv.org/abs/2310.03646 · HTML: https://mlsanity.com/paper/2310.03646/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 50 references that are in the map.
- First posted on arXiv 5 Oct 2023.

## Builds on (most cited first, 30 of 37)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Unsupervised Cross-lingual Representation Learning at Scale](https://mlsanity.com/paper/1911.02116/) (2019)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [XNLI: Evaluating Cross-lingual Sentence Representations](https://mlsanity.com/paper/1809.05053/) (2018)
- [Symbolic Discovery of Optimization Algorithms](https://mlsanity.com/paper/2302.06675/) (2023)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks](https://mlsanity.com/paper/2102.11600/) (2021)
- [FreeLB: Enhanced Adversarial Training for Natural Language Understanding](https://mlsanity.com/paper/1909.11764/) (2019)
- [SMART: Robust and Efficient Fine-Tuning for Pre-trained Natural Language Models through Principled Regularized Optimization](https://mlsanity.com/paper/1911.03437/) (2019)
- [Accuracy on the Line: On the Strong Correlation Between Out-of-Distribution and In-Distribution Generalization](https://mlsanity.com/paper/2107.04649/) (2021)
- [XGLUE: A New Benchmark Dataset for Cross-lingual Pre-training, Understanding and Generation](https://mlsanity.com/paper/2004.01401/) (2020)
- [Emerging Cross-lingual Structure in Pretrained Language Models](https://mlsanity.com/paper/1911.01464/) (2019)
- [Surrogate Gap Minimization Improves Sharpness-Aware Training](https://mlsanity.com/paper/2203.08065/) (2022)
- [Better Fine-Tuning by Reducing Representational Collapse](https://mlsanity.com/paper/2008.03156/) (2020)
- [Sharpness-Aware Minimization Improves Language Model Generalization](https://mlsanity.com/paper/2110.08529/) (2021)
- [Sharpness-Aware Training for Free](https://mlsanity.com/paper/2205.14083/) (2022)
- [A Modern Look at the Relationship between Sharpness and Generalization](https://mlsanity.com/paper/2302.07011/) (2023)
- [Fisher SAM: Information Geometry and Sharpness Aware Minimisation](https://mlsanity.com/paper/2206.04920/) (2022)
- [AdapterSoup: Weight Averaging to Improve Generalization of Pretrained Language Models](https://mlsanity.com/paper/2302.07027/) (2023)
- [When Do Flat Minima Optimizers Work?](https://mlsanity.com/paper/2202.00661/) (2022)

## Built on by (most cited first, 6 of 6)

- [Implicit Regularization of Sharpness-Aware Minimization for Scale-Invariant Problems](https://mlsanity.com/paper/2410.14802/) (2024)
- [From Robustness to Improved Generalization and Calibration in Pre-trained Language Models](https://mlsanity.com/paper/2404.00758/) (2024)
- [Convergence of Sharpness-Aware Minimization Algorithms using Increasing Batch Size and Decaying Learning Rate](https://mlsanity.com/paper/2409.09984/) (2024)
- [Flatness Preserves Instruction Following in Vision-Language-Action Models](https://mlsanity.com/paper/2606.23641/) (2026)
- [Fast Forwarding Low-Rank Training](https://mlsanity.com/paper/2409.04206/) (2024)
- [Zeroth-Order Sharpness-Aware Learning with Exponential Tilting](https://mlsanity.com/paper/2510.16157/) (2025)

## Abstract (arXiv)

Sharpness-aware minimization (SAM) reports improving domain generalization by reducing the loss surface curvature in the parameter space. However, generalization during fine-tuning is often more dependent on the transferability of representations in the function space. Trust-region methods (TR) target this goal by regularizing representation curvature to reduce catastrophic forgetting of pre-trained task-agnostic information while adopting task-specific skills. We consider unifying these strategies for low curvature in both parameter space and function space to improve out-of-domain (OOD) generalization. We propose Trust Region Aware Minimization (TRAM), a SAM algorithm fine-tuning for low parameter sharpness and smooth, informative representations preserving pre-trained structure. TRAM uses a trust region bound to inform the SAM adversarial neighborhood, introducing an awareness of function curvature within optimization for flatter minima. We empirically validate TRAM in vision (cross-dataset adaptation) and text (OOD language modeling, zero-shot cross-lingual transfer) tasks where robust domain transfer and representation generality are critical. TRAM outperforms SAM- and TR-based optimization across all tasks, notably surpassing competing methods for hard transfer between anticorrelated domains. TRAM establishes a novel standard in fine-tuning for domain-generalizable models with minimal additional computation over previous sharpness-aware methods.