# Farzi Data: Autoregressive Data Distillation

arXiv: https://arxiv.org/abs/2310.09983 · HTML: https://mlsanity.com/paper/2310.09983/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 77 references that are in the map.
- First posted on arXiv 15 Oct 2023.

## Builds on (most cited first, 30 of 59)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Robust Speech Recognition via Large-Scale Weak Supervision](https://mlsanity.com/paper/2212.04356/) (2022)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Scalability in Perception for Autonomous Driving: Waymo Open Dataset](https://mlsanity.com/paper/1912.04838/) (2019)
- [Improving language models by retrieving from trillions of tokens](https://mlsanity.com/paper/2112.04426/) (2021)
- [Self-Attentive Sequential Recommendation](https://mlsanity.com/paper/1808.09781/) (2018)
- [LIMA: Less Is More for Alignment](https://mlsanity.com/paper/2305.11206/) (2023)
- [Scaling Vision Transformers](https://mlsanity.com/paper/2106.04560/) (2021)
- [BERT4Rec: Sequential Recommendation with Bidirectional Encoder Representations from Transformer](https://mlsanity.com/paper/1904.06690/) (2019)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [Session-based Recommendations with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06939/) (2015)
- [An Empirical Study of Example Forgetting during Deep Neural Network Learning](https://mlsanity.com/paper/1812.05159/) (2018)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Deep Learning on a Data Diet: Finding Important Examples Early in Training](https://mlsanity.com/paper/2107.07075/) (2021)
- [Beyond neural scaling laws: beating power law scaling via data pruning](https://mlsanity.com/paper/2206.14486/) (2022)
- [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)
- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Dataset Condensation with Distribution Matching](https://mlsanity.com/paper/2110.04181/) (2021)
- [Gradient-based Hyperparameter Optimization through Reversible Learning](https://mlsanity.com/paper/1502.03492/) (2015)
- [Selection via Proxy: Efficient Data Selection for Deep Learning](https://mlsanity.com/paper/1906.11829/) (2019)
- [Variational Autoencoders for Collaborative Filtering](https://mlsanity.com/paper/1802.05814/) (2018)

## Built on by (most cited first, 3 of 3)

- [How to Train Data-Efficient LLMs](https://mlsanity.com/paper/2402.09668/) (2024)
- [TD3: Tucker Decomposition Based Dataset Distillation Method for Sequential Recommendation](https://mlsanity.com/paper/2502.02854/) (2025)
- [Distilling Dataset into Neural Field](https://mlsanity.com/paper/2503.04835/) (2025)

## Abstract (arXiv)

We study data distillation for auto-regressive machine learning tasks, where the input and output have a strict left-to-right causal structure. More specifically, we propose Farzi, which summarizes an event sequence dataset into a small number of synthetic sequences -- Farzi Data -- which are optimized to maintain (if not improve) model performance compared to training on the full dataset. Under the hood, Farzi conducts memory-efficient data distillation by (i) deriving efficient reverse-mode differentiation of the Adam optimizer by leveraging Hessian-Vector Products; and (ii) factorizing the high-dimensional discrete event-space into a latent-space which provably promotes implicit regularization. Empirically, for sequential recommendation and language modeling tasks, we are able to achieve 98-120% of downstream full-data performance when training state-of-the-art models on Farzi Data of size as little as 0.1% of the original dataset. Notably, being able to train better models with significantly less data sheds light on the design of future large auto-regressive models, and opens up new opportunities to further scale up model and data sizes.