# Mathematics of Data Science

arXiv: https://arxiv.org/abs/2607.11938 · HTML: https://mlsanity.com/paper/2607.11938/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 478 references that are in the map.
- First posted on arXiv 11 Jul 2026.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [End-to-end Optimized Image Compression](https://mlsanity.com/paper/1611.01704/) (2016)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Are Transformers universal approximators of sequence-to-sequence functions?](https://mlsanity.com/paper/1912.10077/) (2019)
- [Randomized Block Krylov Methods for Stronger and Faster Approximate Singular Value Decomposition](https://mlsanity.com/paper/1504.05477/) (2015)
- [Optimality of the Johnson-Lindenstrauss Lemma](https://mlsanity.com/paper/1609.02094/) (2016)
- [A Proof Of The Block Model Threshold Conjecture](https://mlsanity.com/paper/1311.4115/) (2013)
- [Achieving Exact Cluster Recovery Threshold via Semidefinite Programming](https://mlsanity.com/paper/1412.6156/) (2014)
- [Mathematical theory of deep learning](https://mlsanity.com/paper/2407.18384/) (2024)
- [Strong Consistency, Graph Laplacians, and the Stochastic Block Model](https://mlsanity.com/paper/2004.09780/) (2020)
- [Random Laplacian matrices and convex relaxations](https://mlsanity.com/paper/1504.03987/) (2015)
- [Permutation methods for factor analysis and PCA](https://mlsanity.com/paper/1710.00479/) (2017)
- [Detectability thresholds and optimal algorithms for community structure in dynamic networks](https://mlsanity.com/paper/1506.06179/) (2015)
- [Optimality and Sub-optimality of PCA for Spiked Random Matrices and Synchronization](https://mlsanity.com/paper/1609.05573/) (2016)
- [Acceleration by Random Stepsizes: Hedging, Equalization, and the Arcsine Stepsize Schedule](https://mlsanity.com/paper/2412.05790/) (2024)
- [The Unique Games Conjecture, Integrality Gap for Cut Problems and Embeddability of Negative Type Metrics into ℓ1](https://mlsanity.com/paper/1305.4581/) (2013)
- [Detection in the stochastic block model with multiple clusters: proof of the achievability conjectures, acyclic BP, and the information-computation gap](https://mlsanity.com/paper/1512.09080/) (2015)
- [Randomstrasse101: Open Problems of 2024](https://mlsanity.com/paper/2504.20539/) (2025)
- [Auto-Calibration and Biconvex Compressive Sensing with Applications to Parallel MRI](https://mlsanity.com/paper/2401.10400/) (2024)
- [An Introduction to Transformers](https://mlsanity.com/paper/2304.10557/) (2023)

## Abstract (arXiv)

This book is about the mathematical foundations of data science. 1. Introduction 2. Curses, Blessings, and Surprises in High Dimensions 3. Singular Value Decomposition and Principal Component Analysis 4. Linear Regression and Regularization 5. Graphs, Networks, and Clustering 6. Nonlinear Dimension Reduction and Diffusion Maps 7. Linear Dimension Reduction via Random Projections 8. Optimization for Data Science 9. Classification 10. A Mathematical Introduction to Deep Learning 11. Large Sample Limit of Graph Laplacians 12. Community 13. Concentration of Measure and Gaussian Analysis 14. Matrix Concentration Inequalities 15. Compressive Sensing and Sparsity 16. Low-Rank Matrix Recovery