# Dataset Distillation by Influence Matching

arXiv: https://arxiv.org/abs/2607.16859 · HTML: https://mlsanity.com/paper/2607.16859/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 46 of its 67 references that are in the map.
- First posted on arXiv 18 Jul 2026.

## Builds on (most cited first, 30 of 46)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Flickr30k Entities: Collecting Region-to-Phrase Correspondences for Richer Image-to-Sentence Models](https://mlsanity.com/paper/1505.04870/) (2015)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [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)
- [High-Performance Large-Scale Image Recognition Without Normalization](https://mlsanity.com/paper/2102.06171/) (2021)
- [Studying Large Language Model Generalization with Influence Functions](https://mlsanity.com/paper/2308.03296/) (2023)
- [Dataset Condensation with Differentiable Siamese Augmentation](https://mlsanity.com/paper/2102.08259/) (2021)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [Dataset Meta-Learning from Kernel Ridge-Regression](https://mlsanity.com/paper/2011.00050/) (2020)
- [Scaling Up Dataset Distillation to ImageNet-1K with Constant Memory](https://mlsanity.com/paper/2211.10586/) (2022)
- [Dataset Distillation using Neural Feature Regression](https://mlsanity.com/paper/2206.00719/) (2022)
- [On the Accuracy of Influence Functions for Measuring Group Effects](https://mlsanity.com/paper/1905.13289/) (2019)
- [Minimizing the Accumulated Trajectory Error to Improve Dataset Distillation](https://mlsanity.com/paper/2211.11004/) (2022)
- [Squeeze, Recover and Relabel: Dataset Condensation at ImageNet Scale From A New Perspective](https://mlsanity.com/paper/2306.13092/) (2023)
- [Training Data Influence Analysis and Estimation: A Survey](https://mlsanity.com/paper/2212.04612/) (2022)
- [Dataset Pruning: Reducing Training Data by Examining Generalization Influence](https://mlsanity.com/paper/2205.09329/) (2022)
- [Scaling Up Influence Functions](https://mlsanity.com/paper/2112.03052/) (2021)
- [Generalizing Dataset Distillation via Deep Generative Prior](https://mlsanity.com/paper/2305.01649/) (2023)
- [Improved Distribution Matching for Dataset Condensation](https://mlsanity.com/paper/2307.09742/) (2023)
- [Privacy for Free: How does Dataset Condensation Help Privacy?](https://mlsanity.com/paper/2206.00240/) (2022)
- [Towards Lossless Dataset Distillation via Difficulty-Aligned Trajectory Matching](https://mlsanity.com/paper/2310.05773/) (2023)
- [Efficient Dataset Distillation Using Random Feature Approximation](https://mlsanity.com/paper/2210.12067/) (2022)
- [On the Diversity and Realism of Distilled Dataset: An Efficient Dataset Distillation Paradigm](https://mlsanity.com/paper/2312.03526/) (2023)
- [Soft-Label Dataset Distillation and Text Dataset Distillation](https://mlsanity.com/paper/1910.02551/) (2019)
- [Neural Networks as Kernel Learners: The Silent Alignment Effect](https://mlsanity.com/paper/2111.00034/) (2021)

## Abstract (arXiv)

We revisit dataset distillation from an outcome-centric perspective. Rather than aligning process surrogates (per-step gradients or training trajectories), Influence Matching (Inf-Match) aligns the final outcome of training: it learns a compact synthetic set whose effect on the converged parameters matches that of the full dataset. Concretely, we introduce a fully differentiable, sample-level influence estimator that quantifies parameter shifts from adding or removing data, without time-consuming inverse-Hessian products or convexity assumptions. The estimator runs in linear time by unrolling the optimization dynamics and applying a first-order Taylor approximation. We then learn the synthetic set by minimizing the mismatch between its influence and that of the real dataset, yielding outcome alignment rather than heuristic process imitation. Inf-Match delivers the best accuracy across standard classification benchmarks. For instance, on Tiny-ImageNet (IPC=10), Inf-Match attains 31.5%, a +4.7% improvement over NCFM. Beyond classification, Inf-Match scales to vision-language distillation on Flickr30K, outperforming strong process-matching baselines. For instance, with 200 to 1000 synthetic samples, our method achieved a leading impressive average on image/text retrieval tasks, higher than NCFM by 2.5%. The code will be released via https://github.com/hrtan/infmatch.