# Learn2Extend: Extending sequences by retaining their statistical properties with mixture models

arXiv: https://arxiv.org/abs/2312.01507 · HTML: https://mlsanity.com/paper/2312.01507/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 40 references that are in the map.
- First posted on arXiv 3 Dec 2023.

## Builds on (most cited first, 10 of 10)

- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [Intensity-Free Learning of Temporal Point Processes](https://mlsanity.com/paper/1909.12127/) (2019)
- [Fully Neural Network based Model for General Temporal Point Processes](https://mlsanity.com/paper/1905.09690/) (2019)
- [Fake News Detection on Social Media using Geometric Deep Learning](https://mlsanity.com/paper/1902.06673/) (2019)
- [Learning Temporal Point Processes via Reinforcement Learning](https://mlsanity.com/paper/1811.05016/) (2018)
- [Fixed-point algorithms for learning determinantal point processes](https://mlsanity.com/paper/1508.00792/) (2015)
- [Model Selection for Mixture Models - Perspectives and Strategies](https://mlsanity.com/paper/1812.09885/) (2018)
- [User Point Processes in Cellular Networks](https://mlsanity.com/paper/1611.08560/) (2016)

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

- [Language as Mathematical Structure: Examining Semantic Field Theory Against Language Games](https://mlsanity.com/paper/2601.00448/) (2026)

## Abstract (arXiv)

This paper addresses the challenge of extending general finite sequences of real numbers within a subinterval of the real line, maintaining their inherent statistical properties by employing machine learning. Our focus lies on preserving the gap distribution and pair correlation function of these point sets. Leveraging advancements in deep learning applied to point processes, this paper explores the use of an auto-regressive textitSequence Extension Mixture Model (SEMM) for extending finite sequences, by estimating directly the conditional density, instead of the intensity function. We perform comparative experiments on multiple types of point processes, including Poisson, locally attractive, and locally repelling sequences, and we perform a case study on the prediction of Riemann zeta function zeroes. The results indicate that the proposed mixture model outperforms traditional neural network architectures in sequence extension with the retention of statistical properties. Given this motivation, we showcase the capabilities of a mixture model to extend sequences, maintaining specific statistical properties, i.e. the gap distribution, and pair correlation indicators.