# A Smoother Way to Train Structured Prediction Models

arXiv: https://arxiv.org/abs/1902.03228 · HTML: https://mlsanity.com/paper/1902.03228/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2019.

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

- [FedBalancer: Data and Pace Control for Efficient Federated Learning on Heterogeneous Clients](https://mlsanity.com/paper/2201.01601/) (2022)
- [Sparsity-Constrained Optimal Transport](https://mlsanity.com/paper/2209.15466/) (2022)
- [Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenters](https://mlsanity.com/paper/2202.03813/) (2022)
- [Online Structured Prediction with Fenchel--Young Losses and Improved Surrogate Regret for Online Multiclass Classification with Logistic Loss](https://mlsanity.com/paper/2402.08180/) (2024)
- [Joint Learning of Energy-based Models and their Partition Function](https://mlsanity.com/paper/2501.18528/) (2025)
- [Scaling Structured Inference with Randomization](https://mlsanity.com/paper/2112.03638/) (2021)
- [Modified Gauss-Newton Algorithms under Noise](https://mlsanity.com/paper/2305.10634/) (2023)
- [Federated Learning with Superquantile Aggregation for Heterogeneous Data](https://mlsanity.com/paper/2112.09429/) (2021)
- [Dual Gauss-Newton Directions for Deep Learning](https://mlsanity.com/paper/2308.08886/) (2023)

## Abstract (arXiv)

We present a framework to train a structured prediction model by performing smoothing on the inference algorithm it builds upon. Smoothing overcomes the non-smoothness inherent to the maximum margin structured prediction objective, and paves the way for the use of fast primal gradient-based optimization algorithms. We illustrate the proposed framework by developing a novel primal incremental optimization algorithm for the structural support vector machine. The proposed algorithm blends an extrapolation scheme for acceleration and an adaptive smoothing scheme and builds upon the stochastic variance-reduced gradient algorithm. We establish its worst-case global complexity bound and study several practical variants, including extensions to deep structured prediction. We present experimental results on two real-world problems, namely named entity recognition and visual object localization. The experimental results show that the proposed framework allows us to build upon efficient inference algorithms to develop large-scale optimization algorithms for structured prediction which can achieve competitive performance on the two real-world problems.