# Applying language models to algebraic topology: generating simplicial cycles using multi-labeling in Wu's formula

arXiv: https://arxiv.org/abs/2306.16951 · HTML: https://mlsanity.com/paper/2306.16951/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 69 references that are in the map.
- First posted on arXiv 1 Jun 2023.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing](https://mlsanity.com/paper/2107.13586/) (2021)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [CTRL: A Conditional Transformer Language Model for Controllable Generation](https://mlsanity.com/paper/1909.05858/) (2019)
- [SeqGAN: Sequence Generative Adversarial Nets with Policy Gradient](https://mlsanity.com/paper/1609.05473/) (2016)
- [Theoretical Limitations of Self-Attention in Neural Sequence Models](https://mlsanity.com/paper/1906.06755/) (2019)
- [Evaluation of Text Generation: A Survey](https://mlsanity.com/paper/2006.14799/) (2020)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [Thinking Like Transformers](https://mlsanity.com/paper/2106.06981/) (2021)
- [Formal Mathematics Statement Curriculum Learning](https://mlsanity.com/paper/2202.01344/) (2022)
- [Proof Artifact Co-training for Theorem Proving with Language Models](https://mlsanity.com/paper/2102.06203/) (2021)
- [A Survey on Generative Adversarial Networks: Variants, Applications, and Training](https://mlsanity.com/paper/2006.05132/) (2020)
- [Pretrained Language Models for Text Generation: A Survey](https://mlsanity.com/paper/2105.10311/) (2021)
- [Understanding Neural Networks via Feature Visualization: A survey](https://mlsanity.com/paper/1904.08939/) (2019)
- [How Can Self-Attention Networks Recognize Dyck-n Languages?](https://mlsanity.com/paper/2010.04303/) (2020)
- [Constructions in combinatorics via neural networks](https://mlsanity.com/paper/2104.14516/) (2021)
- [Generating and designing DNA with deep generative models](https://mlsanity.com/paper/1712.06148/) (2017)
- [Machine-Learning Mathematical Structures](https://mlsanity.com/paper/2101.06317/) (2021)
- [Learning selection strategies in Buchberger's algorithm](https://mlsanity.com/paper/2005.01917/) (2020)
- [Fast differentiable DNA and protein sequence optimization for molecular design](https://mlsanity.com/paper/2005.11275/) (2020)
- [Computing simplicial representatives of homotopy group elements](https://mlsanity.com/paper/1706.00380/) (2017)
- [IntersectGAN: Learning Domain Intersection for Generating Images with Multiple Attributes](https://mlsanity.com/paper/1909.09767/) (2019)

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

- [k-server-bench: Automating Potential Discovery for the k-Server Conjecture](https://mlsanity.com/paper/2604.07240/) (2026)

## Abstract (arXiv)

Computing homotopy groups of spheres has long been a fundamental objective in algebraic topology. Various theoretical and algorithmic approaches have been developed to tackle this problem. In this paper we take a step towards the goal of comprehending the group-theoretic structure of the generators of these homotopy groups by leveraging the power of machine learning. Specifically, in the simplicial group setting of Wu's formula, we reformulate the problem of generating simplicial cycles as a problem of sampling from the intersection of algorithmic datasets related to Dyck languages. We present and evaluate language modelling approaches that employ multi-label information for input sequences, along with the necessary group-theoretic toolkit and non-neural baselines.