# Performance Scaling via Optimal Transport: Enabling Data Selection from Partially Revealed Sources arXiv: https://arxiv.org/abs/2307.02460 ยท HTML: https://mlsanity.com/paper/2307.02460/ ## Key facts - Cited by 16 papers in the map (data through 14 Oct 2026). - Builds on 35 of its 53 references that are in the map. - First posted on arXiv 5 Jul 2023. ## Builds on (most cited first, 30 of 35) - [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015) - [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014) - [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015) - [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014) - [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020) - [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013) - [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016) - [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017) - [BDD100K: A Diverse Driving Dataset for Heterogeneous Multitask Learning](https://mlsanity.com/paper/1805.04687/) (2018) - [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019) - [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020) - [Beyond neural scaling laws: beating power law scaling via data pruning](https://mlsanity.com/paper/2206.14486/) (2022) - [Explaining Neural Scaling Laws](https://mlsanity.com/paper/2102.06701/) (2021) - [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017) - [TRAK: Attributing Model Behavior at Scale](https://mlsanity.com/paper/2303.14186/) (2023) - [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017) - [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019) - [Sorting out Lipschitz function approximation](https://mlsanity.com/paper/1811.05381/) (2018) - [Coresets via Bilevel Optimization for Continual Learning and Streaming](https://mlsanity.com/paper/2006.03875/) (2020) - [Datamodels: Predicting Predictions from Training Data](https://mlsanity.com/paper/2202.00622/) (2022) - [Dataset Security for Machine Learning: Data Poisoning, Backdoor Attacks, and Defenses](https://mlsanity.com/paper/2012.10544/) (2020) - [Deep learning with noisy labels: exploring techniques and remedies in medical image analysis](https://mlsanity.com/paper/1912.02911/) (2019) - [Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2110.14049/) (2021) - [Geometric Dataset Distances via Optimal Transport](https://mlsanity.com/paper/2002.02923/) (2020) - [Efficient Task-Specific Data Valuation for Nearest Neighbor Algorithms](https://mlsanity.com/paper/1908.08619/) (2019) - [DeepCore: A Comprehensive Library for Coreset Selection in Deep Learning](https://mlsanity.com/paper/2204.08499/) (2022) - [Revisiting Neural Scaling Laws in Language and Vision](https://mlsanity.com/paper/2209.06640/) (2022) - [Improving GANs Using Optimal Transport](https://mlsanity.com/paper/1803.05573/) (2018) - [Agreement-on-the-Line: Predicting the Performance of Neural Networks under Distribution Shift](https://mlsanity.com/paper/2206.13089/) (2022) - [Practical Coreset Constructions for Machine Learning](https://mlsanity.com/paper/1703.06476/) (2017) ## Built on by (most cited first, 16 of 16) - [Get more for less: Principled Data Selection for Warming Up Fine-Tuning in LLMs](https://mlsanity.com/paper/2405.02774/) (2024) - [Unleashing the Power of Data Tsunami: A Comprehensive Survey on Data Assessment and Selection for Instruction Tuning of Language Models](https://mlsanity.com/paper/2408.02085/) (2024) - [Scaling laws for learning with real and surrogate data](https://mlsanity.com/paper/2402.04376/) (2024) - [Demystifying Synthetic Data in LLM Pre-training: A Systematic Study of Scaling Laws, Benefits, and Pitfalls](https://mlsanity.com/paper/2510.01631/) (2025) - [Data Valuation and Detections in Federated Learning](https://mlsanity.com/paper/2311.05304/) (2023) - [Data Acquisition: A New Frontier in Data-centric AI](https://mlsanity.com/paper/2311.13712/) (2023) - [TAROT: Targeted Data Selection via Optimal Transport](https://mlsanity.com/paper/2412.00420/) (2024) - [Can Generalist Agents Automate Data Curation?](https://mlsanity.com/paper/2606.04261/) (2026) - [AdaDeDup: Adaptive Hybrid Data Pruning for Efficient Large-Scale Object Detection Training](https://mlsanity.com/paper/2507.00049/) (2025) - [A Sustainable AI Economy Needs Data Deals That Work for Generators](https://mlsanity.com/paper/2601.09966/) (2026) - [Fair Classification with Partial Feedback: An Exploration-Based Data Collection Approach](https://mlsanity.com/paper/2402.11338/) (2024) - [MYCROFT: Towards Effective and Efficient External Data Augmentation](https://mlsanity.com/paper/2410.08432/) (2024) - [SEED: Targeted Data Selection by Weighted Independent Set](https://mlsanity.com/paper/2605.15691/) (2026) - [Sublinear Algorithms for Wasserstein and Total Variation Distances: Applications to Fairness and Privacy Auditing](https://mlsanity.com/paper/2503.07775/) (2025) - [Data Valuation and Selection in a Federated Model Marketplace](https://mlsanity.com/paper/2509.18104/) (2025) - [CRAFT: Clustered Regression for Adaptive Filtering of Training data](https://mlsanity.com/paper/2604.22693/) (2026) ## Abstract (arXiv) Traditionally, data selection has been studied in settings where all samples from prospective sources are fully revealed to a machine learning developer. However, in practical data exchange scenarios, data providers often reveal only a limited subset of samples before an acquisition decision is made. Recently, there have been efforts to fit scaling laws that predict model performance at any size and data source composition using the limited available samples. However, these scaling functions are black-box, computationally expensive to fit, highly susceptible to overfitting, or/and difficult to optimize for data selection. This paper proposes a framework called , which predicts model performance and supports data selection decisions based on partial samples of prospective data sources. Our approach distinguishes itself from existing work by introducing a novel *two-stage* performance inference process. In the first stage, we leverage the Optimal Transport distance to predict the model's performance for any data mixture ratio within the range of disclosed data sizes. In the second stage, we extrapolate the performance to larger undisclosed data sizes based on a novel parameter-free mapping technique inspired by neural scaling laws. We further derive an efficient gradient-based method to select data sources based on the projected model performance. Evaluation over a diverse range of applications demonstrates that significantly improves existing performance scaling approaches in terms of both the accuracy of performance inference and the computation costs associated with constructing the performance predictor. Also, outperforms by a wide margin in data selection effectiveness compared to a range of other off-the-shelf solutions.