# Probabilistic Bilevel Coreset Selection

arXiv: https://arxiv.org/abs/2301.09880 · HTML: https://mlsanity.com/paper/2301.09880/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 64 references that are in the map.
- First posted on arXiv 24 Jan 2023.

## Builds on (most cited first, 30 of 42)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (2019)
- [Efficient Neural Architecture Search via Parameter Sharing](https://mlsanity.com/paper/1802.03268/) (2018)
- [An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks](https://mlsanity.com/paper/1312.6211/) (2013)
- [Learning to Reweight Examples for Robust Deep Learning](https://mlsanity.com/paper/1803.09050/) (2018)
- [Gradient based sample selection for online continual learning](https://mlsanity.com/paper/1903.08671/) (2019)
- [Gradient-based Hyperparameter Optimization through Reversible Learning](https://mlsanity.com/paper/1502.03492/) (2015)
- [Optimizing Millions of Hyperparameters by Implicit Differentiation](https://mlsanity.com/paper/1911.02590/) (2019)
- [Forward and Reverse Gradient-Based Hyperparameter Optimization](https://mlsanity.com/paper/1703.01785/) (2017)
- [Hyperparameter optimization with approximate gradient](https://mlsanity.com/paper/1602.02355/) (2016)
- [Dataset Meta-Learning from Kernel Ridge-Regression](https://mlsanity.com/paper/2011.00050/) (2020)
- [Task-Free Continual Learning](https://mlsanity.com/paper/1812.03596/) (2018)
- [Coresets via Bilevel Optimization for Continual Learning and Streaming](https://mlsanity.com/paper/2006.03875/) (2020)
- [On the Iteration Complexity of Hypergradient Computation](https://mlsanity.com/paper/2006.16218/) (2020)
- [Mini-batch Stochastic Approximation Methods for Nonconvex Stochastic Composite Optimization](https://mlsanity.com/paper/1308.6594/) (2013)
- [A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications](https://mlsanity.com/paper/1705.06270/) (2017)
- [Memory Efficient Experience Replay for Streaming Learning](https://mlsanity.com/paper/1809.05922/) (2018)
- [A Sufficient Condition for Convergences of Adam and RMSProp](https://mlsanity.com/paper/1811.09358/) (2018)
- [Self-Tuning Networks: Bilevel Optimization of Hyperparameters using Structured Best-Response Functions](https://mlsanity.com/paper/1903.03088/) (2019)
- [Memory Replay with Data Compression for Continual Learning](https://mlsanity.com/paper/2202.06592/) (2022)
- [Coresets for Scalable Bayesian Logistic Regression](https://mlsanity.com/paper/1605.06423/) (2016)

## Built on by (most cited first, 27 of 27)

- [On Penalty-based Bilevel Gradient Descent Method](https://mlsanity.com/paper/2302.05185/) (2023)
- [Image Textualization: An Automatic Framework for Creating Accurate and Detailed Image Descriptions](https://mlsanity.com/paper/2406.07502/) (2024)
- [ScaleBiO: Scalable Bilevel Optimization for LLM Data Reweighting](https://mlsanity.com/paper/2406.19976/) (2024)
- [TAGCOS: Task-agnostic Gradient Clustered Coreset Selection for Instruction Tuning Data](https://mlsanity.com/paper/2407.15235/) (2024)
- [A Coreset Selection of Coreset Selection Literature: Introduction and Recent Advances](https://mlsanity.com/paper/2505.17799/) (2025)
- [How Benchmark Prediction from Fewer Data Misses the Mark](https://mlsanity.com/paper/2506.07673/) (2025)
- [Lightweight Dataset Pruning without Full Training via Example Difficulty and Prediction Uncertainty](https://mlsanity.com/paper/2502.06905/) (2025)
- [On the Intrinsic Self-Correction Capability of LLMs: Uncertainty and Latent Concept](https://mlsanity.com/paper/2406.02378/) (2024)
- [Refined Coreset Selection: Towards Minimal Coreset Size under Model Performance Constraints](https://mlsanity.com/paper/2311.08675/) (2023)
- [Direct Prediction Set Minimization via Bilevel Conformal Classifier Training](https://mlsanity.com/paper/2506.06599/) (2025)
- [Advancing Deep Active Learning & Data Subset Selection: Unifying Principles with Information-Theory Intuitions](https://mlsanity.com/paper/2401.04305/) (2024)
- [Distributional Dataset Distillation with Subtask Decomposition](https://mlsanity.com/paper/2403.00999/) (2024)
- [Data Optimization in Deep Learning: A Survey](https://mlsanity.com/paper/2310.16499/) (2023)
- [Tuning-Free Bilevel Optimization: New Algorithms and Convergence Analysis](https://mlsanity.com/paper/2410.05140/) (2024)
- [Optimal Sample Selection Through Uncertainty Estimation and Its Application in Deep Learning](https://mlsanity.com/paper/2309.02476/) (2023)
- [BLISS: A Lightweight Bilevel Influence Scoring Method for Data Selection in Language Model Pretraining](https://mlsanity.com/paper/2510.06048/) (2025)
- [Fine-grained Analysis of Stability and Generalization for Stochastic Bilevel Optimization](https://mlsanity.com/paper/2604.04090/) (2026)
- [Efficient and Robust Quantization-aware Training via Adaptive Coreset Selection](https://mlsanity.com/paper/2306.07215/) (2023)
- [Computational Budget Should Be Considered in Data Selection](https://mlsanity.com/paper/2510.16806/) (2025)
- [BLADE: Scalable Bi-level Adaptive Data Selection for LLM Training](https://mlsanity.com/paper/2606.18650/) (2026)
- [MYCROFT: Towards Effective and Efficient External Data Augmentation](https://mlsanity.com/paper/2410.08432/) (2024)
- [Distill on a Diet: Efficient Knowledge Distillation via Learnable Data Pruning](https://mlsanity.com/paper/2606.25488/) (2026)
- [What is the role of memorization in Continual Learning?](https://mlsanity.com/paper/2505.17664/) (2025)
- [Memory-efficient Continual Learning with Prototypical Exemplar Condensation](https://mlsanity.com/paper/2603.13804/) (2026)
- [Meta Additive Model: Interpretable Sparse Learning With Auto Weighting](https://mlsanity.com/paper/2604.20111/) (2026)
- [First-order Constrained Trilevel Optimization Over Distributed Networks for Robust Coreset Selection](https://mlsanity.com/paper/2607.27632/) (2026)
- [Probabilistic Multi-Source Data Selection via Learnable Categorical Priors: Variance Reduction and Guaranteed Derandomization](https://mlsanity.com/paper/2610.14942/) (2026)

## Abstract (arXiv)

The goal of coreset selection in supervised learning is to produce a weighted subset of data, so that training only on the subset achieves similar performance as training on the entire dataset. Existing methods achieved promising results in resource-constrained scenarios such as continual learning and streaming. However, most of the existing algorithms are limited to traditional machine learning models. A few algorithms that can handle large models adopt greedy search approaches due to the difficulty in solving the discrete subset selection problem, which is computationally costly when coreset becomes larger and often produces suboptimal results. In this work, for the first time we propose a continuous probabilistic bilevel formulation of coreset selection by learning a probablistic weight for each training sample. The overall objective is posed as a bilevel optimization problem, where 1) the inner loop samples coresets and train the model to convergence and 2) the outer loop updates the sample probability progressively according to the model's performance. Importantly, we develop an efficient solver to the bilevel optimization problem via unbiased policy gradient without trouble of implicit differentiation. We provide the convergence property of our training procedure and demonstrate the superiority of our algorithm against various coreset selection methods in various tasks, especially in more challenging label-noise and class-imbalance scenarios.