# Inter-layer Information Similarity Assessment of Deep Neural Networks Via Topological Similarity and Persistence Analysis of Data Neighbour Dynamics

arXiv: https://arxiv.org/abs/2012.03793 · HTML: https://mlsanity.com/paper/2012.03793/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2020.

## Built on by (most cited first, 7 of 7)

- [Similarity of Neural Network Models: A Survey of Functional and Representational Measures](https://mlsanity.com/paper/2305.06329/) (2023)
- [Universal Neurons in GPT2 Language Models](https://mlsanity.com/paper/2401.12181/) (2024)
- [ReSi: A Comprehensive Benchmark for Representational Similarity Measures](https://mlsanity.com/paper/2408.00531/) (2024)
- [Understanding Multimodal Hallucination with Parameter-Free Representation Alignment](https://mlsanity.com/paper/2409.01151/) (2024)
- [Diagnosing Neural Convergence with Topological Alignment Spectra](https://mlsanity.com/paper/2411.08687/) (2024)
- [Systematic Architectural Design of Scale Transformed Attention Condenser DNNs via Multi-Scale Class Representational Response Similarity Analysis](https://mlsanity.com/paper/2306.10128/) (2023)
- [TopoAlign: Topology-Aware Visual Representation Alignment](https://mlsanity.com/paper/2605.25541/) (2026)

## Abstract (arXiv)

The quantitative analysis of information structure through a deep neural network (DNN) can unveil new insights into the theoretical performance of DNN architectures. Two very promising avenues of research towards quantitative information structure analysis are: 1) layer similarity (LS) strategies focused on the inter-layer feature similarity, and 2) intrinsic dimensionality (ID) strategies focused on layer-wise data dimensionality using pairwise information. Inspired by both LS and ID strategies for quantitative information structure analysis, we introduce two novel complimentary methods for inter-layer information similarity assessment premised on the interesting idea of studying a data sample's neighbourhood dynamics as it traverses through a DNN. More specifically, we introduce the concept of Nearest Neighbour Topological Similarity (NNTS) for quantifying the information topology similarity between layers of a DNN. Furthermore, we introduce the concept of Nearest Neighbour Topological Persistence (NNTP) for quantifying the inter-layer persistence of data neighbourhood relationships throughout a DNN. The proposed strategies facilitate the efficient inter-layer information similarity assessment by leveraging only local topological information, and we demonstrate their efficacy in this study by performing analysis on a deep convolutional neural network architecture on image data to study the insights that can be gained with respect to the theoretical performance of a DNN.