# Neural Distance Embeddings for Biological Sequences

arXiv: https://arxiv.org/abs/2109.09740 · HTML: https://mlsanity.com/paper/2109.09740/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 80 references that are in the map.
- First posted on arXiv 20 Sep 2021.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Deep metric learning using Triplet network](https://mlsanity.com/paper/1412.6622/) (2014)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [A Survey on Learning to Hash](https://mlsanity.com/paper/1606.00185/) (2016)
- [Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoders](https://mlsanity.com/paper/1901.06033/) (2019)
- [Mixed-curvature Variational Autoencoders](https://mlsanity.com/paper/1911.08411/) (2019)
- [From Trees to Continuous Embeddings and Back: Hyperbolic Hierarchical Clustering](https://mlsanity.com/paper/2010.00402/) (2020)
- [A cost function for similarity-based hierarchical clustering](https://mlsanity.com/paper/1510.05043/) (2015)
- [A Survey on Metric Learning for Feature Vectors and Structured Data](https://mlsanity.com/paper/1306.6709/) (2013)
- [Neural Embeddings of Graphs in Hyperbolic Space](https://mlsanity.com/paper/1705.10359/) (2017)
- [Edit Distance Cannot Be Computed in Strongly Subquadratic Time (unless SETH is false)](https://mlsanity.com/paper/1412.0348/) (2014)

## Built on by (most cited first, 17 of 17)

- [Learning Weakly Supervised Audio-Visual Violence Detection in Hyperbolic Space](https://mlsanity.com/paper/2305.18797/) (2023)
- [Bringing motion taxonomies to continuous domains via GPLVM on hyperbolic manifolds](https://mlsanity.com/paper/2210.01672/) (2022)
- [Neural Embedding: Learning the Embedding of the Manifold of Physics Data](https://mlsanity.com/paper/2208.05484/) (2022)
- [Fast hyperboloid decision tree algorithms](https://mlsanity.com/paper/2310.13841/) (2023)
- [ProteinZero: Self-Improving Protein Generation via Online Reinforcement Learning](https://mlsanity.com/paper/2506.07459/) (2025)
- [A group-theoretic framework for machine learning in hyperbolic spaces](https://mlsanity.com/paper/2501.06934/) (2025)
- [Variational Combinatorial Sequential Monte Carlo for Bayesian Phylogenetics in Hyperbolic Space](https://mlsanity.com/paper/2501.17965/) (2025)
- [Hyperbolic Genome Embeddings](https://mlsanity.com/paper/2507.21648/) (2025)
- [Deep Squared Euclidean Approximation to the Levenshtein Distance for DNA Storage](https://mlsanity.com/paper/2207.04684/) (2022)
- [Manify: A Python Library for Learning Non-Euclidean Representations](https://mlsanity.com/paper/2503.09576/) (2025)
- [BarcodeBERT: Transformers for Biodiversity Analysis](https://mlsanity.com/paper/2311.02401/) (2023)
- [Levenshtein Distance Embedding with Poisson Regression for DNA Storage](https://mlsanity.com/paper/2312.07931/) (2023)
- [DoDo-Code: an Efficient Levenshtein Distance Embedding-based Code for 4-ary IDS Channel](https://mlsanity.com/paper/2312.12717/) (2023)
- [Neural Embeddings for Protein Graphs](https://mlsanity.com/paper/2306.04667/) (2023)
- [Blind Biological Sequence Denoising with Self-Supervised Set Learning](https://mlsanity.com/paper/2309.01670/) (2023)
- [Breaking the Euclidean Barrier: Hyperboloid-Based Biological Sequence Analysis](https://mlsanity.com/paper/2510.01118/) (2025)
- [When do cheap embeddings beat protein language models? A theoretically-grounded hashing sketch for biological sequence classification](https://mlsanity.com/paper/2512.10147/) (2025)

## Abstract (arXiv)

The development of data-dependent heuristics and representations for biological sequences that reflect their evolutionary distance is critical for large-scale biological research. However, popular machine learning approaches, based on continuous Euclidean spaces, have struggled with the discrete combinatorial formulation of the edit distance that models evolution and the hierarchical relationship that characterises real-world datasets. We present Neural Distance Embeddings (NeuroSEED), a general framework to embed sequences in geometric vector spaces, and illustrate the effectiveness of the hyperbolic space that captures the hierarchical structure and provides an average 22% reduction in embedding RMSE against the best competing geometry. The capacity of the framework and the significance of these improvements are then demonstrated devising supervised and unsupervised NeuroSEED approaches to multiple core tasks in bioinformatics. Benchmarked with common baselines, the proposed approaches display significant accuracy and/or runtime improvements on real-world datasets. As an example for hierarchical clustering, the proposed pretrained and from-scratch methods match the quality of competing baselines with 30x and 15x runtime reduction, respectively.