Bayesian Topological Convolutional Neural Nets

2025-10-13

AI Summary

To address the low training efficiency, overconfident predictions, and lack of uncertainty quantification in CNNs under few-shot and noisy data regimes, this paper proposes a novel framework integrating topological-aware learning with Bayesian inference. Methodologically, it embeds persistent-homology-guided manifold structural priors into convolutional architectures and augments topological CNNs with dynamic prior adaptation, MCMC-based posterior sampling, and topological consistency regularization—yielding calibration-aware Bayesian learning. Experiments demonstrate that the proposed model significantly outperforms standard CNNs, Bayesian neural networks (BNNs), and existing topological CNNs in calibration error (ECE), out-of-distribution detection (AUROC), and few-shot robustness. Gains are particularly pronounced on CIFAR-10/100 and ImageNet subsets under data scarcity or label noise, establishing new state-of-the-art performance in uncertainty-aware visual recognition under challenging data conditions.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Adversarial Attacks & Robustness
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Convolutional neural networks (CNNs) have been established as the main workhorse in image data processing; nonetheless, they require large amounts of data to train, often produce overconfident predictions, and frequently lack the ability to quantify the uncertainty of their predictions. To address these concerns, we propose a new Bayesian topological CNN that promotes a novel interplay between topology-aware learning and Bayesian sampling. Specifically, it utilizes information from important manifolds to accelerate training while reducing calibration error by placing prior distributions on network parameters and properly learning appropriate posteriors. One important contribution of our work is the inclusion of a consistency condition in the learning cost, which can effectively modify the prior distributions to improve the performance of our novel network architecture. We evaluate the model on benchmark image classification datasets and demonstrate its superiority over conventional CNNs, Bayesian neural networks (BNNs), and topological CNNs. In particular, we supply evidence that our method provides an advantage in situations where training data is limited or corrupted. Furthermore, we show that the new model allows for better uncertainty quantification than standard BNNs since it can more readily identify examples of out-of-distribution data on which it has not been trained. Our results highlight the potential of our novel hybrid approach for more efficient and robust image classification.

Problem

• Addresses CNN limitations in training data efficiency and uncertainty quantification
• Proposes Bayesian topological CNN combining topology-aware learning with Bayesian sampling
• Improves performance with limited training data and out-of-distribution detection

Innovation

• Bayesian topological CNN combines topology and Bayesian sampling
• Uses manifold information to accelerate training and reduce error
• Includes consistency condition to modify priors and improve performance