HiER-BLS: A Hierarchy-Guided and Error-Correcting Robust Incremental Broad Learning System
Authors: Gongli Zhang, C. L. Philip Chen, Zhulin Liu
Organizations: Guangdong Provincial Key Laboratory of Computational AI Models and Cognitive Intelligence, the School of Computer Science and Engineering, South China University of Technology, Guangzhou 510006, China, also with the Pazhou Lab, Guangzhou 510335, China, and also with the Engineering Research Center of the Ministry of Education on Health Intelligent Perception and Paralleled Digital-Human, Guangzhou 510641, China
Broad Learning System (BLS) supports analytical training and incremental expansion, but its growth needs guidance on which inputs new blocks should learn from. Weight errors pose a further challenge by displacing learned outputs across class boundaries. We propose HiER-BLS to couple hierarchy-guided representation growth with error-correcting learning. Successive blocks focus on inputs selected by feature importance and correlation while preserving earlier representations. The evolving branch guides encoded learners through subspace size and sample confidence, so its learning experience informs both their feature views and supervision. For finite broad readouts, we show how codeword correlations transform fitted class scores. Prediction preservation depends on the distance from the actual output to the nearest decoding boundary relative to the model's sensitivity to weight errors. Experiments on five image and five tabular datasets demonstrate improved classification performance over representative BLS variants. Component studies show that hierarchy guidance benefits the encoded branch even when the guiding branch has lower standalone accuracy, with further gains from combining their scores. Longer codes continue to improve accuracy under stronger Gaussian weight errors after clean accuracy has largely saturated.
Figures & tables
Fig. 1 : Architecture of HiER-BLS. HGEE constructs incremental features using importance-guided subspaces. ECEO trains encoded bases and prunes output columns. BADF combines the branches’ scores through an additional BLS.
Importance profile
Schedule
Raw size st
Dense
Exponential
Mγt−1
Uniform
Linear
M[1−α(t−1)]
Mixed
Cosine
2M[1+cos(π(t−1)/T)]
TABLE I : Raw subspace schedules selected by the importance profile.
Operation
Leading cost
Spearman correlations and cached FSR
O(MNlogN+NM2+M2)
ECB b , qb=fb+hb
Cmap(M,fb,hb)+Cfit(qb,Lb,0)
PCP over all added columns
O(NvCL03) directly; O(NvCL02) with cached scores
BADF, qBA=fBA+hBA
Cmap(2C,fBA,hBA)+Cfit(qBA,C)
TABLE II : Costs outside the HGEE updates. Here fb,hb and fBA,hBA are the feature and enhancement widths of an ECB and BADF, respectively.
Dataset
Type
Input
Class
Train
Test
HGEE
ECEO
BADF
λ
Feature
Enh.
Feature
Enh.
L
Feature
Enh.
MNIST
Image
(28,28,1)
10
60000
10000
(30,40)
(1,11000)
(10,10)
(1,11000)
20
(20,10)
(1,30)
10−6
Fashion-MNIST
Image
(28,28,1)
10
60000
10000
(100,10)
(1,9000)
(100,10)
(1,11000)
20
(30,40)
(1,770)
10−6
NORB
Image
(32,32,2)
5
24300
24300
(10,100)
(1,8000)
(30,50)
(1,8000)
10
(50,35)
(1,10)
10−3
CIFAR10
Image
(32,32,3)
10
50000
10000
(128,20)
(1,5000)
(128,20)
(1,10000)
20
(20,25)
(1,22)
10−7
CIFAR100
Image
(32,32,3)
100
50000
10000
(128,20)
(1,5000)
(128,20)
(1,10000)
200
(10,10)
(1,10)
10−6
TABLE III : Dataset sizes and model settings. Feature and Enh. specify the feature- and enhancement-window configurations, respectively, as (number of windows, nodes per window).
TABLE IV : Image-classification accuracy (%). Avg and Std denote the reported mean and standard deviation. Bold marks the largest mean or smallest standard deviation in each column.
TABLE V : Testing accuracy and training time on tabular datasets.
Fig. 2 : Feature-importance distributions (left) and HGEE accuracy versus evolution step for selected schedule parameters (right).
Fig. 3 : Classification accuracy versus ECOC code length under zero-mean Gaussian weight errors. Each panel includes three fixed values of σ ; dashed horizontal lines denote the corresponding one-hot baselines.
TABLE VI : Testing accuracies (%) of HiER-BLS and its ablated variants. HTI, SA, ASR, SS, and CS denote hierarchy type identification, subspace alignment, AdaBoost sample reweighting, subspace sampling, and confidence scaling. Removing HTI means randomly selecting one of the other two schedules.
Fig. 4 : Two-dimensional t-SNE projections of HGEE features on CIFAR100 without and with subspace alignment. Colors identify the full feature space and subspaces 1–4.
Fig. 5 : CIFAR10 accuracy (%) and LTSC (%) across ensemble stages, with and without PCP. LTSC is displayed as 100× the value in Eq. ( 72 ).