# Robust Broad Learning System with Wave Loss for Classification under Data Uncertainty

arXiv: https://arxiv.org/abs/2608.29983 · HTML: https://mlsanity.com/paper/2608.29983/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 23 references that are in the map.
- First posted on arXiv 30 Aug 2026.

## Builds on (most cited first, 9 of 9)

- [Random vector functional link network: recent developments, applications, and future directions](https://mlsanity.com/paper/2203.11316/) (2022)
- [RoBoSS: A Robust, Bounded, Sparse, and Smooth Loss Function for Supervised Learning](https://mlsanity.com/paper/2309.02250/) (2023)
- [Intuitionistic Fuzzy Broad Learning System: Enhancing Robustness Against Noise and Outliers](https://mlsanity.com/paper/2307.08713/) (2023)
- [Enhancing Multiview Synergy: Robust Learning by Exploiting the Wave Loss Function with Consensus and Complementarity Principles](https://mlsanity.com/paper/2408.06819/) (2024)
- [Advancing Supervised Learning with the Wave Loss Function: A Robust and Smooth Approach](https://mlsanity.com/paper/2404.18101/) (2024)
- [Wave-RVFL: A Randomized Neural Network Based on Wave Loss Function](https://mlsanity.com/paper/2408.02824/) (2024)
- [Advancing RVFL networks: Robust classification with the HawkEye loss function](https://mlsanity.com/paper/2410.00510/) (2024)
- [CAWI: Copula-Aligned Weight Initialization for Randomized Neural Networks](https://mlsanity.com/paper/2605.12580/) (2026)
- [Multi-party Secure Broad Learning System for Privacy Preserving](https://mlsanity.com/paper/2206.11133/) (2022)

## Abstract (arXiv)

Broad Learning System (BLS) offers an efficient alternative to deep architectures by enabling fast learning through randomized feature mapping and closed-form solutions. However, its reliance on squared error loss makes it highly sensitive to noise, outliers, and corrupted labels, limiting its reliability in real-world scenarios. To address this limitation, we propose Wave-BLS, a robust broad learning framework that integrates the wave loss function, which is asymmetric, bounded, and smooth, enabling controlled penalization of large errors. The proposed formulation replaces the standard least-squares objective with a wave-loss-based optimization problem, solved efficiently using a Nesterov accelerated gradient (NAG)-based scheme without requiring matrix inversion, thereby improving scalability. Extensive experiments on 30 UCI benchmark datasets demonstrate that Wave-BLS consistently outperforms classical BLS and several robust variants. Statistical validation using Friedman and Nemenyi post-hoc tests confirms the significance of the observed improvements. Furthermore, robustness evaluations under controlled noise and outlier injection reveal that Wave-BLS exhibits substantially slower performance degradation compared to BLS, even in challenging contamination settings. These results establish Wave-BLS as a stable and robust alternative to existing broad learning models for learning under data uncertainty.