# Curvature-based Comparison of Two Neural Networks

arXiv: https://arxiv.org/abs/1801.06801 · HTML: https://mlsanity.com/paper/1801.06801/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2018.

## Built on by (most cited first, 6 of 6)

- [Topology and geometry of data manifold in deep learning](https://mlsanity.com/paper/2204.08624/) (2022)
- [Data Representations' Study of Latent Image Manifolds](https://mlsanity.com/paper/2305.19730/) (2023)
- [Deep Double Descent via Smooth Interpolation](https://mlsanity.com/paper/2209.10080/) (2022)
- [Deep neural networks architectures from the perspective of manifold learning](https://mlsanity.com/paper/2306.03406/) (2023)
- [Analyzing Deep Transformer Models for Time Series Forecasting via Manifold Learning](https://mlsanity.com/paper/2410.13792/) (2024)
- [Privacy-Utility Trade-off in Data Publication: A Bilevel Optimization Framework with Curvature-Guided Perturbation](https://mlsanity.com/paper/2509.02048/) (2025)

## Abstract (arXiv)

In this paper we show the similarities and differences of two deep neural networks by comparing the manifolds composed of activation vectors in each fully connected layer of them. The main contribution of this paper includes 1) a new data generating algorithm which is crucial for determining the dimension of manifolds; 2) a systematic strategy to compare manifolds. Especially, we take Riemann curvature and sectional curvature as part of criterion, which can reflect the intrinsic geometric properties of manifolds. Some interesting results and phenomenon are given, which help in specifying the similarities and differences between the features extracted by two networks and demystifying the intrinsic mechanism of deep neural networks.