# Isometry pursuit

arXiv: https://arxiv.org/abs/2411.18502 · HTML: https://mlsanity.com/paper/2411.18502/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 68 references that are in the map.
- First posted on arXiv 27 Nov 2024.

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

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Retrieval-Augmented Generation for Large Language Models: A Survey](https://mlsanity.com/paper/2312.10997/) (2023)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Towards Principled Evaluations of Sparse Autoencoders for Interpretability and Control](https://mlsanity.com/paper/2405.08366/) (2024)
- [A Greedy Approach for Budgeted Maximum Inner Product Search](https://mlsanity.com/paper/1610.03317/) (2016)
- [Managing Diversity in Airbnb Search](https://mlsanity.com/paper/2004.02621/) (2020)
- [Solving Large-Scale Sparse PCA to Certifiable (Near) Optimality](https://mlsanity.com/paper/2005.05195/) (2020)
- [LDLE: Low Distortion Local Eigenmaps](https://mlsanity.com/paper/2101.11055/) (2021)
- [Diversify-verify-adapt: Efficient and Robust Retrieval-Augmented Ambiguous Question Answering](https://mlsanity.com/paper/2409.02361/) (2024)
- [The Geometry of Uniqueness, Sparsity and Clustering in Penalized Estimation](https://mlsanity.com/paper/2004.09106/) (2020)
- [Selecting the independent coordinates of manifolds with large aspect ratios](https://mlsanity.com/paper/1907.01651/) (2019)
- [Better RAG using Relevant Information Gain](https://mlsanity.com/paper/2407.12101/) (2024)
- [Manifold Coordinates with Physical Meaning](https://mlsanity.com/paper/1811.11891/) (2018)
- [Diversity-Aware k-Maximum Inner Product Search Revisited](https://mlsanity.com/paper/2402.13858/) (2024)
- [Sparse PCA: a Geometric Approach](https://mlsanity.com/paper/2210.06590/) (2022)
- [Recent Advances in Diversified Recommendation](https://mlsanity.com/paper/1905.06589/) (2019)
- [Sparse principal component analysis and its l1-relaxation](https://mlsanity.com/paper/1712.00800/) (2017)
- [On the Distribution, Model Selection Properties and Uniqueness of the Lasso Estimator in Low and High Dimensions](https://mlsanity.com/paper/1708.09608/) (2017)
- [The Geometry of Sparse Analysis Regularization](https://mlsanity.com/paper/1907.01769/) (2019)
- [The Geometry and Well-Posedness of Sparse Regularized Linear Regression](https://mlsanity.com/paper/2409.03461/) (2024)
- [On the Uniqueness of Solutions for the Basis Pursuit in the Continuum](https://mlsanity.com/paper/2009.11855/) (2020)

## Abstract (arXiv)

Isometry pursuit is a convex algorithm for identifying orthonormal column-submatrices of wide matrices. It consists of a novel normalization method followed by multitask basis pursuit. Applied to Jacobians of putative coordinate functions, it helps identity isometric embeddings from within interpretable dictionaries. We provide theoretical and experimental results justifying this method. For problems involving coordinate selection and diversification, it offers a synergistic alternative to greedy and brute force search.