# Designing a Robust, Bounded, and Smooth Loss Function for Improved Supervised Learning

arXiv: https://arxiv.org/abs/2602.06858 · HTML: https://mlsanity.com/paper/2602.06858/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 4 references that are in the map.
- First posted on arXiv 6 Feb 2026.

## Builds on (most cited first, 3 of 3)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Size-Independent Sample Complexity of Neural Networks](https://mlsanity.com/paper/1712.06541/) (2017)
- [RoBoSS: A Robust, Bounded, Sparse, and Smooth Loss Function for Supervised Learning](https://mlsanity.com/paper/2309.02250/) (2023)

## Abstract (arXiv)

The loss function is crucial to machine learning, especially in supervised learning frameworks. It is a fundamental component that controls the behavior and general efficacy of learning algorithms. However, despite their widespread use, traditional loss functions have significant drawbacks when dealing with high-dimensional and outlier-sensitive datasets, which frequently results in reduced performance and slower convergence during training. In this work, we develop a robust, bounded, and smooth (RoBoS-NN) loss function to resolve the aforementioned hindrances. The generalization ability of the loss function has also been theoretically analyzed to rigorously justify its robustness. Moreover, we implement RoboS-NN loss in the framework of a neural network (NN) to forecast time series and present a new robust algorithm named LRoBoS-NN. To assess the potential of LRoBoS-NN, we conduct experiments on multiple real-world datasets. In addition, we infuse outliers into data sets to evaluate the performance of LRoBoS-NN in more challenging scenarios. Numerical results show that LRoBoS-NN outperforms the other benchmark models in terms of accuracy measures.