# CUPID: Curating Data your Robot Loves with Influence Functions

arXiv: https://arxiv.org/abs/2506.19121 · HTML: https://mlsanity.com/paper/2506.19121/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Placed in Robot manipulation imitation learning, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 55 of its 63 references that are in the map.
- First posted on arXiv 23 Jun 2025.

## Placed in

- Offline RL and imitation learning from data / [Robot manipulation imitation learning](https://mlsanity.com/offlinerl/robot-manipulation-imitation-learning/)

## Builds on (most cited first, 30 of 55)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [OpenVLA: An Open-Source Vision-Language-Action Model](https://mlsanity.com/paper/2406.09246/) (2024)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Octo: An Open-Source Generalist Robot Policy](https://mlsanity.com/paper/2405.12213/) (2024)
- [DROID: A Large-Scale In-The-Wild Robot Manipulation Dataset](https://mlsanity.com/paper/2403.12945/) (2024)
- [What Matters in Learning from Offline Human Demonstrations for Robot Manipulation](https://mlsanity.com/paper/2108.03298/) (2021)
- [Deduplicating Training Data Makes Language Models Better](https://mlsanity.com/paper/2107.06499/) (2021)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [Robotic Control via Embodied Chain-of-Thought Reasoning](https://mlsanity.com/paper/2407.08693/) (2024)
- [MimicGen: A Data Generation System for Scalable Robot Learning using Human Demonstrations](https://mlsanity.com/paper/2310.17596/) (2023)
- [Studying Large Language Model Generalization with Influence Functions](https://mlsanity.com/paper/2308.03296/) (2023)
- [Causal Confusion in Imitation Learning](https://mlsanity.com/paper/1905.11979/) (2019)
- [TRAK: Attributing Model Behavior at Scale](https://mlsanity.com/paper/2303.14186/) (2023)
- [Influence Functions in Deep Learning Are Fragile](https://mlsanity.com/paper/2006.14651/) (2020)
- [A Survey on Data Selection for Language Models](https://mlsanity.com/paper/2402.16827/) (2024)
- [Scaling Robot Learning with Semantically Imagined Experience](https://mlsanity.com/paper/2302.11550/) (2023)
- [D4: Improving LLM Pretraining via Document De-Duplication and Diversification](https://mlsanity.com/paper/2308.12284/) (2023)
- [On the Accuracy of Influence Functions for Measuring Group Effects](https://mlsanity.com/paper/1905.13289/) (2019)
- [If Influence Functions are the Answer, Then What is the Question?](https://mlsanity.com/paper/2209.05364/) (2022)
- [Training Data Influence Analysis and Estimation: A Survey](https://mlsanity.com/paper/2212.04612/) (2022)
- [DsDm: Model-Aware Dataset Selection with Datamodels](https://mlsanity.com/paper/2401.12926/) (2024)

## Built on by (most cited first, 23 of 23)

- [Robometer: Scaling General-Purpose Robotic Reward Models via Trajectory Comparisons](https://mlsanity.com/paper/2603.02115/) (2026)
- [World Action Verifier: Self-Improving World Models via Forward-Inverse Asymmetry](https://mlsanity.com/paper/2604.01985/) (2026)
- [Interpretability Can Be Actionable](https://mlsanity.com/paper/2605.11161/) (2026)
- [X-Diffusion: Training Diffusion Policies on Cross-Embodiment Human Demonstrations](https://mlsanity.com/paper/2511.04671/) (2025)
- [Using Non-Expert Data to Robustify Imitation Learning via Offline Reinforcement Learning](https://mlsanity.com/paper/2510.19495/) (2025)
- [Ambient Diffusion Policy: Imitation Learning from Suboptimal Data in Robotics](https://mlsanity.com/paper/2606.12365/) (2026)
- [Uncertainty Quantification for Flow-Based Vision-Language-Action Models](https://mlsanity.com/paper/2606.18043/) (2026)
- [RDD: Retrieval-Based Demonstration Decomposer for Planner Alignment in Long-Horizon Tasks](https://mlsanity.com/paper/2510.14968/) (2025)
- [Learning from the Best: Smoothness-Driven Metrics for Data Quality in Imitation Learning](https://mlsanity.com/paper/2604.23000/) (2026)
- [SiMDex: Mining Similar Egocentric Videos for Cross-Embodiment Dexterous Manipulation](https://mlsanity.com/paper/2608.04196/) (2026)
- [An Efficient Metric for Data Quality Measurement in Imitation Learning](https://mlsanity.com/paper/2605.01544/) (2026)
- [FACTR 2: Learning External Force Sensing for Commodity Robot Arms Improves Policy Learning](https://mlsanity.com/paper/2606.12406/) (2026)
- [Revisiting Data Attribution for Influence Functions](https://mlsanity.com/paper/2508.07297/) (2025)
- [Quality over Quantity: Demonstration Curation via Influence Functions for Data-Centric Robot Learning](https://mlsanity.com/paper/2603.09056/) (2026)
- [ATHENA: Accelerated Multi-Task Heterogeneous Influence Functions for Robot Data Curation](https://mlsanity.com/paper/2606.16208/) (2026)
- [Active Real-World Factor-Based Evaluation for Generalist Robot Policies](https://mlsanity.com/paper/2607.14439/) (2026)
- [Rethinking Demonstration Unlearning in Imitation Learning for Robotics](https://mlsanity.com/paper/2608.20784/) (2026)
- [Geometric Entropy: When Trajectory Diversity Helps and Hurts in Imitation Learning](https://mlsanity.com/paper/2606.20871/) (2026)
- [Auditing Instruction-Trajectory Mismatches in Multimodal Robot Demonstrations](https://mlsanity.com/paper/2608.07895/) (2026)
- [Imperfection for Precision: Upcycling Imperfect Data for High-Precision Robotic Manipulation](https://mlsanity.com/paper/2609.26672/) (2026)
- [Beyond State-as-Action: Exploiting Command-State Discrepancy for Robot Imitation Learning](https://mlsanity.com/paper/2609.33145/) (2026)
- [NEEDLEWORK: Offline Rewriting of Robot Data with Verified Local Stitches](https://mlsanity.com/paper/2610.02339/) (2026)
- [Where Small Mistakes Matter: Quantifying State Criticality for Imitation Learning](https://mlsanity.com/paper/2610.17709/) (2026)

## Abstract (arXiv)

In robot imitation learning, policy performance is tightly coupled with the quality and composition of the demonstration data. Yet, developing a precise understanding of how individual demonstrations contribute to downstream outcomes - such as closed-loop task success or failure - remains a persistent challenge. We propose CUPID, a robot data curation method based on a novel influence function-theoretic formulation for imitation learning policies. Given a set of evaluation rollouts, CUPID estimates the influence of each training demonstration on the policy's expected return. This enables ranking and selection of demonstrations according to their impact on the policy's closed-loop performance. We use CUPID to curate data by 1) filtering out training demonstrations that harm policy performance and 2) subselecting newly collected trajectories that will most improve the policy. Extensive simulated and hardware experiments show that our approach consistently identifies which data drives test-time performance. For example, training with less than 33% of curated data can yield state-of-the-art diffusion policies on the simulated RoboMimic benchmark, with similar gains observed in hardware. Furthermore, hardware experiments show that our method can identify robust strategies under distribution shift, isolate spurious correlations, and even enhance the post-training of generalist robot policies. Videos and code are made available at: https://cupid-curation.github.io.