# IFW-BLS: Dual-Robust Broad Learning System with Intuitionistic Fuzzy Wave Loss

arXiv: https://arxiv.org/abs/2609.02422 · HTML: https://mlsanity.com/paper/2609.02422/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 24 references that are in the map.
- First posted on arXiv 2 Sep 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)
- [Broad Learning System Based on Maximum Correntropy Criterion](https://mlsanity.com/paper/1912.11368/) (2019)
- [CAWI: Copula-Aligned Weight Initialization for Randomized Neural Networks](https://mlsanity.com/paper/2605.12580/) (2026)

## Abstract (arXiv)

Broad Learning System is an efficient randomized learning model that expands network width through feature and enhancement nodes and estimates the output weights without deep backpropagation. Its standard least-squares training, however, is vulnerable in two different ways: (i) large residuals caused by noise, outliers, or corrupted labels can dominate the objective, and (ii) all samples are treated as equally reliable even when some lie in ambiguous or locally conflicting regions. This paper proposes IFW-BLS, an Intuitionistic Fuzzy Wave Broad Learning System that addresses these two sources of fragility within one optimization model. The first robustness mechanism is residual-level protection, obtained by replacing the squared loss with the bounded, smooth, and asymmetric wave loss. Boundedness prevents extreme residuals from receiving unbounded influence, while asymmetry allows positive and negative deviations to be penalized differently when the dominant error direction varies. The second mechanism is sample-level credibility control, obtained through intuitionistic fuzzy scores that combine global class-center consistency with local neighborhood conflict. The resulting model evaluates the wave loss on credibility-weighted residuals, so unreliable samples are down-weighted before the bounded loss further limits the effect of extreme errors. A Nesterov accelerated gradient based optimizer is used to solve the proposed objective, avoiding the explicit matrix inversion used in conventional BLS. Experiments on UCI benchmark datasets validate the superiority of the proposed IFW-BLS model over the baseline models; additional corruption experiments also show more stable performance than BLS under noise and outlier contamination.