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Isometry pursuit

arXiv 2411.18502 ↗First posted 27 Nov 2024stat.ML cs.AI cs.IRcited by 0

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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.

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.

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22 of 68 references.

References · 22

  1. 2021Convex optimizationcited by 2,515
  2. 2023Retrieval-Augmented Generation for Large Language Models: A Surveycited by 2,212
  3. 2016CVXPY: A Python-Embedded Modeling Language for Convex Optimizationcited by 641
  4. 2017A Rewriting System for Convex Optimization Problemscited by 179
  5. 2024Towards Principled Evaluations of Sparse Autoencoders for Interpretability and Controlcited by 86
  6. 2016A Greedy Approach for Budgeted Maximum Inner Product Searchcited by 11
  7. 2020Managing Diversity in Airbnb Searchcited by 11
  8. 2020Solving Large-Scale Sparse PCA to Certifiable (Near) Optimalitycited by 11
  9. 2021LDLE: Low Distortion Local Eigenmapscited by 11
  10. 2024Diversify-verify-adapt: Efficient and Robust Retrieval-Augmented Ambiguous Question Answeringcited by 10
  11. 2020The Geometry of Uniqueness, Sparsity and Clustering in Penalized Estimationcited by 9
  12. 2019Selecting the independent coordinates of manifolds with large aspect ratioscited by 8
10 more
  1. 2024Better RAG using Relevant Information Gaincited by 8
  2. 2018Manifold Coordinates with Physical Meaningcited by 7
  3. 2024Diversity-Aware k-Maximum Inner Product Search Revisitedcited by 7
  4. 2022Sparse PCA: a Geometric Approachcited by 6
  5. 2019Recent Advances in Diversified Recommendationcited by 5
  6. 2017Sparse principal component analysis and its l1-relaxationcited by 4
  7. 2017On the Distribution, Model Selection Properties and Uniqueness of the Lasso Estimator in Low and High Dimensionscited by 2
  8. 2019The Geometry of Sparse Analysis Regularizationcited by 2
  9. 2024The Geometry and Well-Posedness of Sparse Regularized Linear Regressioncited by 2
  10. 2020On the Uniqueness of Solutions for the Basis Pursuit in the Continuumcited by 1

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