IBCapsNet: Information Bottleneck Capsule Network for Noise-Robust Representation Learning

Canqun Xiang; Chen Yang; Jiaoyan Zhao

cs.CVMar 21, 2026

IBCapsNet: Information Bottleneck Capsule Network for Noise-Robust Representation Learning

Authors: Canqun Xiang, Chen Yang, Jiaoyan Zhao

Organizations: an independent researcher · Institute of Applied Artificial Intelligence of the Guangdong-Hong Kong-Macao Greater Bay Area, Shenzhen Polytechnic University, Shenzhen, China

Abstract

Capsule networks (CapsNets) are superior at modeling hierarchical spatial relationships but suffer from two critical limitations: high computational cost due to iterative dynamic routing and poor robustness under input corruptions. To address these issues, we propose IBCapsNet, a novel capsule architecture grounded in the Information Bottleneck (IB) principle. Instead of iterative routing, IBCapsNet employs a one-pass variational aggregation mechanism, where primary capsules are first compressed into a global context representation and then processed by class-specific variational autoencoders (VAEs) to infer latent capsules regularized by the KL divergence. This design enables efficient inference while inherently filtering out noise. Experiments on MNIST, Fashion-MNIST, SVHN and CIFAR-10 show that IBCapsNet matches CapsNet in clean-data accuracy (achieving 99.41% on MNIST and 92.01% on SVHN), yet significantly outperforms it under four types of synthetic noise - demonstrating average improvements of +17.10% and +14.54% for clamped additive and multiplicative noise, respectively. Moreover, IBCapsNet achieves 2.54x faster training and 3.64x higher inference throughput compared to CapsNet, while reducing model parameters by 4.66%. Our work bridges information-theoretic representation learning with capsule networks, offering a principled path toward robust, efficient, and interpretable deep models. Code is available at https://github.com/cxiang26/IBCapsnet

Figures & tables

Fig. 1: This figure contrasts the iterative, computationally expensive dynamic routing machanism (A) with the proposed efficient, one-pass Information Bottleneck aggregation machanism (B).

Dataset	LeNet	CapsNet	IBCapsNet
MNIST	98.99	99.46	99.41
F-MNIST	90.17	90.83	90.78
SVHN	85.75	92.12	92.01

TABLE I: Test accuracy (%) on clean data

Metric	CapsNet	IBCapsNet	Improvement/Reduction
Training(s/epoch)	49.95	19.67	2.54 $\times$ Faster
Inference(FPS)	41.15	149.93	3.64 $\times$ Higher
Parameters	8,215,568	7,832,929	4.66% Reduction

TABLE II: Performance Comparison of CapsNet vs. IBCapsNet. All experiments are conducted on the MNIST dataset with identical hardware (A100) and batch size (128).

Fig. 2: Robustness comparison between IBCapsNet and vanilla CapsNet across multiple datasets and disturbance scenarios.

Noise Type	Clamped	Multiplicative	Gaussian Blur	Salt-Pepper
Avg. Gain	+17.10	+14.54	+6.50	+2.57

TABLE III: Average accuracy improvement (%) of IBCapsNet over CapsNet under noise

Fig. 3: This figure presents the qualitative recognition performance of CapsNet (left columns) and IBCapsNet (right columns) on handwritten digits, under various disturbances. GT: Ground Truth; Reco: Recognition results without any disturbance; Clmp: adding Clamped Additive Noise; Gaus: applying Gaussian Blur; S&P: adding Salt-Pepper Noise.

Model Variant	Acc. (%)	$\Delta$ vs. Baseline
Baseline	58.43	—
Multi-Classifier	59.62	+1.19
+ Squash & KL	61.55	+3.12
+ reconstruction	71.71	+13.28

TABLE IV: Ablation study on Fashion-MNIST. Impact of reconstruction and information bottleneck on model robustness under the clamped additive noise (

\sigma=0.3

Neural Network Robustness

Neural network robustness studies how models withstand adversarial inputs, data shifts, noise, and hardware faults while maintaining reliable predictions.

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What Should an Information Bottleneck Encoder Learn? Separating Representation Learning from Rate Control

Hassan Tavakoli, Bella Bose

School of EECS, Oregon State University, Corvallis, OR 97331, USA

Information Bottleneck Representation Learning Variational Information Bottleneck

Open paper AskPDF arXiv

The information bottleneck (IB) trades compression of an input

X

against prediction of a target

Y

through a multiplier

β=1/λ

, yet each operating point is usually served by training, or fully conditioning, a new encoder. For jointly Gaussian data, we show that the IB solution factorizes as

A(β)=D(β)W

: the information-bearing directions

W

do not depend on

β

, and

β

acts only through scalar gains. We ask whether this separation of representation from rate control survives beyond Gaussian models, treating the budget as a given operating parameter rather than a quantity to be optimized. For a budget-free representation

F(X)

, the separation gap is controlled by the sufficiency deficit

ε_F=I(X;Y\mid F(X))

: We show there is at least

ε_F

in the worst case for finite inputs, and it is bounded uniformly in

λ

by a function of

ε_F

for finite label alphabets. The same certificate extends to a new target distribution and to pooled multi-domain data, where a conditional-alignment term appears. On MNIST, SVHN, CIFAR-10 and STL-10 (10 seeds, eight prespecified budgets), a frozen CNN representation with one compressor--decoder pair per budget reduces estimated training multiply--accumulate operations (MACs) by

7.7\times

and wall-clock time by about

2\times

relative to end-to-end VIBs, and attains higher budget-averaged accuracy (

65.6\%

versus

57.3\%

per domain;

67.1\%

versus

57.1\%

pooled), with the advantage concentrated at strong compression, where the VIBs collapse. At weak compression (

λ\le0.036

), VIB has higher cross-entropy and ECE; its surrogate Lagrangian is higher per domain, indistinguishable from the pooled VIB in the macro average, and lower on the pooled test set.

Abstract

Neural Network Robustness

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