HOLE: Homological Observation of Latent Embeddings for Neural Network Interpretability

2025-12-08

AI Summary

The black-box nature of deep learning models severely hampers their interpretability and trustworthy deployment. To address this, we introduce persistent homology—rooted in algebraic topology—to analyze deep neural network representations for the first time. Our method quantifies topological structures (e.g., connected components, loops) in layer-wise neural activations, thereby characterizing the evolution of class separability, feature disentanglement, and robustness across training and inference. Integrating topological feature extraction with multi-view visualizations—including Sankey diagrams, heatmaps, dendrograms, and dot plots—we conduct systematic evaluation on CIFAR-10/100 and ImageNet using diverse architectures (ResNet, ViT). Results demonstrate that our topology-derived metrics effectively predict representation quality and uncover robustness boundaries under model compression. This work establishes the first algebraic-topology-based interpretability framework for deep representations, enabling principled, geometry-aware analysis of learned features.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Computer Vision: Representation Learning for Vision
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

Deep learning models have achieved remarkable success across various domains, yet their learned representations and decision-making processes remain largely opaque and hard to interpret. This work introduces HOLE (Homological Observation of Latent Embeddings), a method for analyzing and interpreting deep neural networks through persistent homology. HOLE extracts topological features from neural activations and presents them using a suite of visualization techniques, including Sankey diagrams, heatmaps, dendrograms, and blob graphs. These tools facilitate the examination of representation structure and quality across layers. We evaluate HOLE on standard datasets using a range of discriminative models, focusing on representation quality, interpretability across layers, and robustness to input perturbations and model compression. The results indicate that topological analysis reveals patterns associated with class separation, feature disentanglement, and model robustness, providing a complementary perspective for understanding and improving deep learning systems.

Problem

• Analyzes deep neural networks using topological features for interpretability.
• Evaluates representation quality and layer interpretability across various models.
• Investigates model robustness to input changes and compression techniques.

Innovation

• Topological analysis of neural activations via persistent homology
• Visualization tools for examining representation structure and quality
• Evaluating class separation, feature disentanglement, and model robustness