# Tensor-Train Point Cloud Compression and Efficient Approximate Nearest-Neighbor Search

arXiv: https://arxiv.org/abs/2410.04462 · HTML: https://mlsanity.com/paper/2410.04462/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 28 references that are in the map.
- First posted on arXiv 6 Oct 2024.

## Builds on (most cited first, 13 of 13)

- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Towards Total Recall in Industrial Anomaly Detection](https://mlsanity.com/paper/2106.08265/) (2021)
- [PaDiM: a Patch Distribution Modeling Framework for Anomaly Detection and Localization](https://mlsanity.com/paper/2011.08785/) (2020)
- [Sub-Image Anomaly Detection with Deep Pyramid Correspondences](https://mlsanity.com/paper/2005.02357/) (2020)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Generative Modeling using the Sliced Wasserstein Distance](https://mlsanity.com/paper/1803.11188/) (2018)
- [Stable Low-rank Tensor Decomposition for Compression of Convolutional Neural Network](https://mlsanity.com/paper/2008.05441/) (2020)
- [A Survey on Locality Sensitive Hashing Algorithms and their Applications](https://mlsanity.com/paper/2102.08942/) (2021)
- [Tensor-Train Density Estimation](https://mlsanity.com/paper/2108.00089/) (2021)
- [A Prior of a Googol Gaussians: a Tensor Ring Induced Prior for Generative Models](https://mlsanity.com/paper/1910.13148/) (2019)
- [Efficient GPT Model Pre-training using Tensor Train Matrix Representation](https://mlsanity.com/paper/2306.02697/) (2023)
- [Automatic differentiation for Riemannian optimization on low-rank matrix and tensor-train manifolds](https://mlsanity.com/paper/2103.14974/) (2021)

## Abstract (arXiv)

Nearest-neighbor search in large vector databases is crucial for various machine learning applications. This paper introduces a novel method using tensor-train (TT) low-rank tensor decomposition to efficiently represent point clouds and enable fast approximate nearest-neighbor searches. We propose a probabilistic interpretation and utilize density estimation losses like Sliced Wasserstein to train TT decompositions, resulting in robust point cloud compression. We reveal an inherent hierarchical structure within TT point clouds, facilitating efficient approximate nearest-neighbor searches. In our paper, we provide detailed insights into the methodology and conduct comprehensive comparisons with existing methods. We demonstrate its effectiveness in various scenarios, including out-of-distribution (OOD) detection problems and approximate nearest-neighbor (ANN) search tasks.