# FAST: Topology-Aware Frequency-Domain Distribution Matching for Coreset Selection

arXiv: https://arxiv.org/abs/2511.19476 · HTML: https://mlsanity.com/paper/2511.19476/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 51 references that are in the map.
- First posted on arXiv 22 Nov 2025.

## Builds on (most cited first, 30 of 31)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [DeepFool: a simple and accurate method to fool deep neural networks](https://mlsanity.com/paper/1511.04599/) (2015)
- [CodeGen: An Open Large Language Model for Code with Multi-Turn Program Synthesis](https://mlsanity.com/paper/2203.13474/) (2022)
- [Deep Learning on a Data Diet: Finding Important Examples Early in Training](https://mlsanity.com/paper/2107.07075/) (2021)
- [Dataset Condensation with Gradient Matching](https://mlsanity.com/paper/2006.05929/) (2020)
- [Dataset Distillation by Matching Training Trajectories](https://mlsanity.com/paper/2203.11932/) (2022)
- [Dataset Condensation with Distribution Matching](https://mlsanity.com/paper/2110.04181/) (2021)
- [GRAD-MATCH: Gradient Matching based Data Subset Selection for Efficient Deep Model Training](https://mlsanity.com/paper/2103.00123/) (2021)
- [GLISTER: Generalization based Data Subset Selection for Efficient and Robust Learning](https://mlsanity.com/paper/2012.10630/) (2020)
- [Dataset Distillation using Neural Feature Regression](https://mlsanity.com/paper/2206.00719/) (2022)
- [Online Coreset Selection for Rehearsal-based Continual Learning](https://mlsanity.com/paper/2106.01085/) (2021)
- [Submodular Combinatorial Information Measures with Applications in Machine Learning](https://mlsanity.com/paper/2006.15412/) (2020)
- [Zeus: Understanding and Optimizing GPU Energy Consumption of DNN Training](https://mlsanity.com/paper/2208.06102/) (2022)
- [Fast Two-Sample Testing with Analytic Representations of Probability Measures](https://mlsanity.com/paper/1506.04725/) (2015)
- [Dataset Distillation with Neural Characteristic Function: A Minmax Perspective](https://mlsanity.com/paper/2502.20653/) (2025)
- [A Characteristic Function Approach to Deep Implicit Generative Modeling](https://mlsanity.com/paper/1909.07425/) (2019)
- [InstructEval: Systematic Evaluation of Instruction Selection Methods](https://mlsanity.com/paper/2307.00259/) (2023)
- [Self-Supervised Dataset Distillation for Transfer Learning](https://mlsanity.com/paper/2310.06511/) (2023)
- [Generative neural networks for characteristic functions](https://mlsanity.com/paper/2401.04778/) (2024)

## Built on by (most cited first, 2 of 2)

- [TopoPrune: Robust Data Pruning via Unified Latent Space Topology](https://mlsanity.com/paper/2602.02739/) (2026)
- [CAST: Collapse-Aware multi-Scale Topology Fusion for Multimodal Coreset Selection](https://mlsanity.com/paper/2605.11705/) (2026)

## Abstract (arXiv)

Coreset selection compresses large datasets into compact, representative subsets, reducing the energy and computational burden of training deep neural networks. Existing methods are either: (i) DNN-based, which are tied to model-specific parameters and introduce architectural bias; or (ii) DNN-free, which rely on heuristics lacking theoretical guarantees. Neither approach explicitly constrains distributional equivalence, largely because continuous distribution matching is considered inapplicable to discrete sampling. Moreover, prevalent metrics (e.g., MSE, KL, CE, MMD) cannot accurately capture higher-order moment discrepancies, leading to suboptimal coresets. In this work, we propose FAST, the first DNN-free distribution-matching coreset selection framework that formulates the coreset selection task as a graph-constrained optimization problem grounded in spectral graph theory and employs the Characteristic Function Distance (CFD) to capture full distributional information in the frequency domain. We further discover that naive CFD suffers from a "vanishing phase gradient" issue in medium and high-frequency regions; to address this, we introduce an Attenuated Phase-Decoupled CFD. Furthermore, for better convergence, we design a Progressive Discrepancy-Aware Sampling strategy that progressively schedules frequency selection from low to high, preserving global structure before refining local details and enabling accurate matching with fewer frequencies while avoiding overfitting. Extensive experiments demonstrate that FAST significantly outperforms state-of-the-art coreset selection methods across all evaluated benchmarks, achieving an average accuracy gain of 9.12%. Compared to other baseline coreset methods, it reduces power consumption by 96.57% and achieves a 2.2x average speedup, underscoring its high performance and energy efficiency.