# What Machine Learning Tells Us About the Mathematical Structure of Concepts

arXiv: https://arxiv.org/abs/2408.15507 · HTML: https://mlsanity.com/paper/2408.15507/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 51 references that are in the map.
- First posted on arXiv 28 Aug 2024.

## Builds on (most cited first, 14 of 14)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [The Mythos of Model Interpretability](https://mlsanity.com/paper/1606.03490/) (2016)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [Disentangled Representation Learning](https://mlsanity.com/paper/2211.11695/) (2022)
- [Probabilistic Embedding of Knowledge Graphs with Box Lattice Measures](https://mlsanity.com/paper/1805.06627/) (2018)
- [Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures](https://mlsanity.com/paper/2407.09468/) (2024)
- [Word2Box: Capturing Set-Theoretic Semantics of Words using Box Embeddings](https://mlsanity.com/paper/2106.14361/) (2021)
- [Subspace Representations for Soft Set Operations and Sentence Similarities](https://mlsanity.com/paper/2210.13034/) (2022)

## Abstract (arXiv)

This paper examines the connections among various approaches to understanding concepts in philosophy, cognitive science, and machine learning, with a particular focus on their mathematical nature. By categorizing these approaches into Abstractionism, the Similarity Approach, the Functional Approach, and the Invariance Approach, the study highlights how each framework provides a distinct mathematical perspective for modeling concepts. The synthesis of these approaches bridges philosophical theories and contemporary machine learning models, providing a comprehensive framework for future research. This work emphasizes the importance of interdisciplinary dialogue, aiming to enrich our understanding of the complex relationship between human cognition and artificial intelligence.