# On original and latent space connectivity in deep neural networks

arXiv: https://arxiv.org/abs/2311.06816 · HTML: https://mlsanity.com/paper/2311.06816/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 26 references that are in the map.
- First posted on arXiv 12 Nov 2023.

## Builds on (most cited first, 21 of 21)

- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Understanding Deep Image Representations by Inverting Them](https://mlsanity.com/paper/1412.0035/) (2014)
- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [Essentially No Barriers in Neural Network Energy Landscape](https://mlsanity.com/paper/1803.00885/) (2018)
- [Insights on representational similarity in neural networks with canonical correlation](https://mlsanity.com/paper/1806.05759/) (2018)
- [Exponential expressivity in deep neural networks through transient chaos](https://mlsanity.com/paper/1606.05340/) (2016)
- [Bounding and Counting Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1711.02114/) (2017)
- [Generalization in Deep Learning](https://mlsanity.com/paper/1710.05468/) (2017)
- [Reconstructing Training Data from Trained Neural Networks](https://mlsanity.com/paper/2206.07758/) (2022)
- [Topology and Geometry of Half-Rectified Network Optimization](https://mlsanity.com/paper/1611.01540/) (2016)
- [Distilling Model Failures as Directions in Latent Space](https://mlsanity.com/paper/2206.14754/) (2022)
- [Classification and Geometry of General Perceptual Manifolds](https://mlsanity.com/paper/1710.06487/) (2017)
- [Dimensionality compression and expansion in Deep Neural Networks](https://mlsanity.com/paper/1906.00443/) (2019)
- [Everything is There in Latent Space: Attribute Editing and Attribute Style Manipulation by StyleGAN Latent Space Exploration](https://mlsanity.com/paper/2207.09855/) (2022)
- [NormLime: A New Feature Importance Metric for Explaining Deep Neural Networks](https://mlsanity.com/paper/1909.04200/) (2019)
- [Effects of Data Geometry in Early Deep Learning](https://mlsanity.com/paper/2301.00008/) (2022)
- [Deep neural networks architectures from the perspective of manifold learning](https://mlsanity.com/paper/2306.03406/) (2023)
- [Classify and Generate: Using Classification Latent Space Representations for Image Generations](https://mlsanity.com/paper/2004.07543/) (2020)

## Built on by (most cited first, 1 of 1)

- [Disentangling Dynamical Systems: Causal Representation Learning Meets Local Sparse Attention](https://mlsanity.com/paper/2603.14483/) (2026)

## Abstract (arXiv)

We study whether inputs from the same class can be connected by a continuous path, in original or latent representation space, such that all points on the path are mapped by the neural network model to the same class. Understanding how the neural network views its own input space and how the latent spaces are structured has value for explainability and robustness. We show that paths, linear or nonlinear, connecting same-class inputs exist in all cases studied.