# Revisiting Latent-Space Interpolation via a Quantitative Evaluation Framework

arXiv: https://arxiv.org/abs/2110.06421 · HTML: https://mlsanity.com/paper/2110.06421/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 44 references that are in the map.
- First posted on arXiv 13 Oct 2021.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Common Objects in 3D: Large-Scale Learning and Evaluation of Real-life 3D Category Reconstruction](https://mlsanity.com/paper/2109.00512/) (2021)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [Adversarial Feature Learning](https://mlsanity.com/paper/1605.09782/) (2016)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [DeepView: View Synthesis with Learned Gradient Descent](https://mlsanity.com/paper/1906.07316/) (2019)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)
- [Free View Synthesis](https://mlsanity.com/paper/2008.05511/) (2020)
- [Learning to Predict 3D Objects with an Interpolation-based Differentiable Renderer](https://mlsanity.com/paper/1908.01210/) (2019)
- [DynGEM: Deep Embedding Method for Dynamic Graphs](https://mlsanity.com/paper/1805.11273/) (2018)
- [Variational Graph Recurrent Neural Networks](https://mlsanity.com/paper/1908.09710/) (2019)
- [Dynamic Graph Convolutional Networks](https://mlsanity.com/paper/1704.06199/) (2017)
- [Predicting Path Failure In Time-Evolving Graphs](https://mlsanity.com/paper/1905.03994/) (2019)
- [GCN-GAN: A Non-linear Temporal Link Prediction Model for Weighted Dynamic Networks](https://mlsanity.com/paper/1901.09165/) (2019)
- [Optimal transport maps for distribution preserving operations on latent spaces of Generative Models](https://mlsanity.com/paper/1711.01970/) (2017)

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

- [Geometry-Aware Generative Autoencoders for Warped Riemannian Metric Learning and Generative Modeling on Data Manifolds](https://mlsanity.com/paper/2410.12779/) (2024)
- [Self Supervised Networks for Learning Latent Space Representations of Human Body Scans and Motions](https://mlsanity.com/paper/2411.03475/) (2024)
- [High-throughput 3D shape completion of potato tubers on a harvester](https://mlsanity.com/paper/2407.21341/) (2024)
- [Reconstructing Spatiotemporal Data with C-VAEs](https://mlsanity.com/paper/2307.06243/) (2023)
- [Intelligent Generation of Graphical Game Assets: A Conceptual Framework and Systematic Review of the State of the Art](https://mlsanity.com/paper/2311.10129/) (2023)
- [Underwater Organism Color Enhancement via Color Code Decomposition, Adaptation and Interpolation](https://mlsanity.com/paper/2409.19685/) (2024)
- [Ensemble Visualization With Variational Autoencoder](https://mlsanity.com/paper/2509.13000/) (2025)

## Abstract (arXiv)

Latent-space interpolation is commonly used to demonstrate the generalization ability of deep latent variable models. Various algorithms have been proposed to calculate the best trajectory between two encodings in the latent space. In this work, we show how data labeled with semantically continuous attributes can be utilized to conduct a quantitative evaluation of latent-space interpolation algorithms, for variational autoencoders. Our framework can be used to complement the standard qualitative comparison, and also enables evaluation for domains (such as graph) in which the visualization is difficult. Interestingly, our experiments reveal that the superiority of interpolation algorithms could be domain-dependent. While normalised interpolation works best for the image domain, spherical linear interpolation achieves the best performance in the graph domain. Next, we propose a simple-yet-effective method to restrict the latent space via a bottleneck structure in the encoder. We find that all interpolation algorithms evaluated in this work can benefit from this restriction. Finally, we conduct interpolation-aware training with the labeled attributes, and show that this explicit supervision can improve the interpolation performance.